1,1,279,0,2.266129," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 A a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{8 C a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + 2*A*a*sin(c + d*x)**3/(3*d) + A*a*sin(c + d*x)*cos(c + d*x)**2/d + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 8*C*a*sin(c + d*x)**5/(15*d) + 4*C*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + C*a*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)*cos(c)**2, True))","A",0
2,1,226,0,1.102978," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{A a \sin{\left(c + d x \right)}}{d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) + A*a*sin(c + d*x)/d + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a*sin(c + d*x)**3/(3*d) + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)*cos(c), True))","A",0
3,1,121,0,0.524075," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\begin{cases} A a x + \frac{A a \sin{\left(c + d x \right)}}{d} + \frac{C a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x + A*a*sin(c + d*x)/d + C*a*x*sin(c + d*x)**2/2 + C*a*x*cos(c + d*x)**2/2 + 2*C*a*sin(c + d*x)**3/(3*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d + C*a*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a), True))","A",0
4,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","a \left(\int A \sec{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x), x) + Integral(A*cos(c + d*x)*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(C*cos(c + d*x)**3*sec(c + d*x), x))","F",0
5,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","a \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**2, x) + Integral(A*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**3*sec(c + d*x)**2, x))","F",0
6,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","a \left(\int A \sec^{3}{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**3, x) + Integral(A*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(C*cos(c + d*x)**3*sec(c + d*x)**3, x))","F",0
7,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,592,0,4.679716," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 A a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 C a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 C a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 C a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{16 C a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{8 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{11 C a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{2 C a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{2} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**2*x*sin(c + d*x)**4/8 + 3*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**2*x*sin(c + d*x)**2/2 + 3*A*a**2*x*cos(c + d*x)**4/8 + A*a**2*x*cos(c + d*x)**2/2 + 3*A*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*A*a**2*sin(c + d*x)**3/(3*d) + 5*A*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*A*a**2*sin(c + d*x)*cos(c + d*x)**2/d + A*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 5*C*a**2*x*sin(c + d*x)**6/16 + 15*C*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*C*a**2*x*sin(c + d*x)**4/8 + 15*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*C*a**2*x*cos(c + d*x)**6/16 + 3*C*a**2*x*cos(c + d*x)**4/8 + 5*C*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 16*C*a**2*sin(c + d*x)**5/(15*d) + 5*C*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 8*C*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 11*C*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 2*C*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**2*cos(c)**2, True))","A",0
10,1,350,0,2.481603," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\begin{cases} A a^{2} x \sin^{2}{\left(c + d x \right)} + A a^{2} x \cos^{2}{\left(c + d x \right)} + \frac{2 A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)}}{d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{8 C a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{2 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**2 + A*a**2*x*cos(c + d*x)**2 + 2*A*a**2*sin(c + d*x)**3/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**2/d + A*a**2*sin(c + d*x)*cos(c + d*x)/d + A*a**2*sin(c + d*x)/d + 3*C*a**2*x*sin(c + d*x)**4/4 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*C*a**2*x*cos(c + d*x)**4/4 + 8*C*a**2*sin(c + d*x)**5/(15*d) + 4*C*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 2*C*a**2*sin(c + d*x)**3/(3*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**2*cos(c), True))","A",0
11,1,309,0,1.235404," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + A a^{2} x + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A a^{2} \sin{\left(c + d x \right)}}{d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{C a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{C a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**2/2 + A*a**2*x*cos(c + d*x)**2/2 + A*a**2*x + A*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*a**2*sin(c + d*x)/d + 3*C*a**2*x*sin(c + d*x)**4/8 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + C*a**2*x*sin(c + d*x)**2/2 + 3*C*a**2*x*cos(c + d*x)**4/8 + C*a**2*x*cos(c + d*x)**2/2 + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*C*a**2*sin(c + d*x)**3/(3*d) + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*C*a**2*sin(c + d*x)*cos(c + d*x)**2/d + C*a**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**2, True))","A",0
12,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","a^{2} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 2 A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x), x) + Integral(2*A*cos(c + d*x)*sec(c + d*x), x) + Integral(A*cos(c + d*x)**2*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(2*C*cos(c + d*x)**3*sec(c + d*x), x) + Integral(C*cos(c + d*x)**4*sec(c + d*x), x))","F",0
13,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","a^{2} \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int 2 A \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int A \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x)**2, x) + Integral(2*A*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(A*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(2*C*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**4*sec(c + d*x)**2, x))","F",0
14,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,1,750,0,7.771493," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{9 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 A a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{15 C a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{45 C a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{45 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{15 C a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{16 C a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{15 C a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{33 C a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*A*a**3*x*sin(c + d*x)**4/8 + 9*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**3*x*sin(c + d*x)**2/2 + 9*A*a**3*x*cos(c + d*x)**4/8 + A*a**3*x*cos(c + d*x)**2/2 + 8*A*a**3*sin(c + d*x)**5/(15*d) + 4*A*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*A*a**3*sin(c + d*x)**3/d + A*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*A*a**3*sin(c + d*x)*cos(c + d*x)**2/d + A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 15*C*a**3*x*sin(c + d*x)**6/16 + 45*C*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*C*a**3*x*sin(c + d*x)**4/8 + 45*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 15*C*a**3*x*cos(c + d*x)**6/16 + 3*C*a**3*x*cos(c + d*x)**4/8 + 16*C*a**3*sin(c + d*x)**7/(35*d) + 8*C*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 15*C*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*C*a**3*sin(c + d*x)**5/(5*d) + 2*C*a**3*sin(c + d*x)**3*cos(c + d*x)**4/d + 5*C*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**6/d + 33*C*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**3*cos(c)**2, True))","A",0
19,1,646,0,4.679537," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{A a^{3} \sin{\left(c + d x \right)}}{d} + \frac{5 C a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 C a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 C a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{5 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(c + d*x)**4/8 + 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a**3*x*sin(c + d*x)**2/2 + 3*A*a**3*x*cos(c + d*x)**4/8 + 3*A*a**3*x*cos(c + d*x)**2/2 + 3*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*A*a**3*sin(c + d*x)**3/d + 5*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*A*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + A*a**3*sin(c + d*x)/d + 5*C*a**3*x*sin(c + d*x)**6/16 + 15*C*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*C*a**3*x*sin(c + d*x)**4/8 + 15*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*C*a**3*x*cos(c + d*x)**6/16 + 9*C*a**3*x*cos(c + d*x)**4/8 + 5*C*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*C*a**3*sin(c + d*x)**5/(5*d) + 5*C*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 9*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a**3*sin(c + d*x)**3/(3*d) + 11*C*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**3*cos(c), True))","A",0
20,1,422,0,2.754424," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + A a^{3} x + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)}}{d} + \frac{9 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{C a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{C a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(c + d*x)**2/2 + 3*A*a**3*x*cos(c + d*x)**2/2 + A*a**3*x + 2*A*a**3*sin(c + d*x)**3/(3*d) + A*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*A*a**3*sin(c + d*x)/d + 9*C*a**3*x*sin(c + d*x)**4/8 + 9*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + C*a**3*x*sin(c + d*x)**2/2 + 9*C*a**3*x*cos(c + d*x)**4/8 + C*a**3*x*cos(c + d*x)**2/2 + 8*C*a**3*sin(c + d*x)**5/(15*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a**3*sin(c + d*x)**3/d + C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**2/d + C*a**3*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**3, True))","A",0
21,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","a^{3} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 3 A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 A \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 C \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{5}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(A*sec(c + d*x), x) + Integral(3*A*cos(c + d*x)*sec(c + d*x), x) + Integral(3*A*cos(c + d*x)**2*sec(c + d*x), x) + Integral(A*cos(c + d*x)**3*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(3*C*cos(c + d*x)**3*sec(c + d*x), x) + Integral(3*C*cos(c + d*x)**4*sec(c + d*x), x) + Integral(C*cos(c + d*x)**5*sec(c + d*x), x))","F",0
22,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,1149,0,14.521350," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{5 A a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 A a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 A a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{15 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{5 A a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 A a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{A a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{5 A a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{32 A a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 A a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{16 A a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 A a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 A a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 A a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{4 A a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 A a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{4 A a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{35 C a^{4} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{35 C a^{4} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 C a^{4} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{105 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{45 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 C a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{35 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{45 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{35 C a^{4} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{15 C a^{4} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{3 C a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{35 C a^{4} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{64 C a^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{385 C a^{4} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{32 C a^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{15 C a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{32 C a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{511 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{8 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} + \frac{16 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{93 C a^{4} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{33 C a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{4} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*A*a**4*x*sin(c + d*x)**6/16 + 15*A*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*A*a**4*x*sin(c + d*x)**4/4 + 15*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + A*a**4*x*sin(c + d*x)**2/2 + 5*A*a**4*x*cos(c + d*x)**6/16 + 9*A*a**4*x*cos(c + d*x)**4/4 + A*a**4*x*cos(c + d*x)**2/2 + 5*A*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 32*A*a**4*sin(c + d*x)**5/(15*d) + 5*A*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 16*A*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*A*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*A*a**4*sin(c + d*x)**3/(3*d) + 11*A*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 4*A*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 15*A*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 4*A*a**4*sin(c + d*x)*cos(c + d*x)**2/d + A*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 35*C*a**4*x*sin(c + d*x)**8/128 + 35*C*a**4*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*C*a**4*x*sin(c + d*x)**6/8 + 105*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 45*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*C*a**4*x*sin(c + d*x)**4/8 + 35*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 45*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 3*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 35*C*a**4*x*cos(c + d*x)**8/128 + 15*C*a**4*x*cos(c + d*x)**6/8 + 3*C*a**4*x*cos(c + d*x)**4/8 + 35*C*a**4*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 64*C*a**4*sin(c + d*x)**7/(35*d) + 385*C*a**4*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 32*C*a**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 15*C*a**4*sin(c + d*x)**5*cos(c + d*x)/(8*d) + 32*C*a**4*sin(c + d*x)**5/(15*d) + 511*C*a**4*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 8*C*a**4*sin(c + d*x)**3*cos(c + d*x)**4/d + 5*C*a**4*sin(c + d*x)**3*cos(c + d*x)**3/d + 16*C*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 93*C*a**4*sin(c + d*x)*cos(c + d*x)**7/(128*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**6/d + 33*C*a**4*sin(c + d*x)*cos(c + d*x)**5/(8*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**4*cos(c)**2, True))","A",0
29,1,799,0,8.213030," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + 3 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + 2 A a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 A a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + 2 A a^{4} x \cos^{2}{\left(c + d x \right)} + \frac{8 A a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 A a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 A a^{4} \sin^{3}{\left(c + d x \right)}}{d} + \frac{A a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 A a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{6 A a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{A a^{4} \sin{\left(c + d x \right)}}{d} + \frac{5 C a^{4} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + \frac{15 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + 3 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{5 C a^{4} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{3 C a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{16 C a^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 C a^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{5 C a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{16 C a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{2 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{10 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{8 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{11 C a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{6 C a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{4} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**4*x*sin(c + d*x)**4/2 + 3*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 2*A*a**4*x*sin(c + d*x)**2 + 3*A*a**4*x*cos(c + d*x)**4/2 + 2*A*a**4*x*cos(c + d*x)**2 + 8*A*a**4*sin(c + d*x)**5/(15*d) + 4*A*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*A*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 4*A*a**4*sin(c + d*x)**3/d + A*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*A*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 6*A*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 2*A*a**4*sin(c + d*x)*cos(c + d*x)/d + A*a**4*sin(c + d*x)/d + 5*C*a**4*x*sin(c + d*x)**6/4 + 15*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 3*C*a**4*x*sin(c + d*x)**4/2 + 15*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 3*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 5*C*a**4*x*cos(c + d*x)**6/4 + 3*C*a**4*x*cos(c + d*x)**4/2 + 16*C*a**4*sin(c + d*x)**7/(35*d) + 8*C*a**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 5*C*a**4*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 16*C*a**4*sin(c + d*x)**5/(5*d) + 2*C*a**4*sin(c + d*x)**3*cos(c + d*x)**4/d + 10*C*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 8*C*a**4*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*C*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 2*C*a**4*sin(c + d*x)**3/(3*d) + C*a**4*sin(c + d*x)*cos(c + d*x)**6/d + 11*C*a**4*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 6*C*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + C*a**4*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**4*cos(c), True))","A",0
30,1,707,0,5.060395," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + 3 A a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 A a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + 3 A a^{4} x \cos^{2}{\left(c + d x \right)} + A a^{4} x + \frac{3 A a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{8 A a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 A a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{4 A a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 A a^{4} \sin{\left(c + d x \right)}}{d} + \frac{5 C a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 C a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{15 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{5 C a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 C a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{C a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{5 C a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{32 C a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{16 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 C a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 C a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**4*x*sin(c + d*x)**4/8 + 3*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a**4*x*sin(c + d*x)**2 + 3*A*a**4*x*cos(c + d*x)**4/8 + 3*A*a**4*x*cos(c + d*x)**2 + A*a**4*x + 3*A*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 8*A*a**4*sin(c + d*x)**3/(3*d) + 5*A*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 4*A*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a**4*sin(c + d*x)*cos(c + d*x)/d + 4*A*a**4*sin(c + d*x)/d + 5*C*a**4*x*sin(c + d*x)**6/16 + 15*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*C*a**4*x*sin(c + d*x)**4/4 + 15*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + C*a**4*x*sin(c + d*x)**2/2 + 5*C*a**4*x*cos(c + d*x)**6/16 + 9*C*a**4*x*cos(c + d*x)**4/4 + C*a**4*x*cos(c + d*x)**2/2 + 5*C*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 32*C*a**4*sin(c + d*x)**5/(15*d) + 5*C*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 16*C*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*C*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*C*a**4*sin(c + d*x)**3/(3*d) + 11*C*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**2/d + C*a**4*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a*cos(c) + a)**4, True))","A",0
31,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,1,1795,0,7.585492," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{36 A d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{144 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{216 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{144 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{36 A d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{24 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{168 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{312 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{216 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{48 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{45 C d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{180 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{270 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{180 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{45 C d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{24 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{246 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{374 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{314 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{66 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((36*A*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 144*A*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 216*A*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 144*A*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 36*A*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 24*A*tan(c/2 + d*x/2)**9/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 168*A*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 312*A*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 216*A*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 48*A*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 45*C*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 180*C*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 270*C*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 180*C*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 45*C*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 24*C*tan(c/2 + d*x/2)**9/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 246*C*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 374*C*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 314*C*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 66*C*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a), True))","A",0
40,1,1163,0,4.565545," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} - \frac{6 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{18 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{18 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{6 A d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{30 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{42 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{18 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{9 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{27 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{27 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{9 C d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{48 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{50 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{24 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 18*A*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 18*A*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 6*A*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*A*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 30*A*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 42*A*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 18*A*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 9*C*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 27*C*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 27*C*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 9*C*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*C*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 48*C*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 50*C*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 24*C*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a), True))","A",0
41,1,665,0,2.684197," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{2 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{4 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{2 A d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 C d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{10 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 4*A*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 2*A*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*A*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*A*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*A*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*C*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 6*C*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*C*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*C*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 10*C*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*C*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)/(a*cos(c) + a), True))","A",0
42,1,202,0,1.583151," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{C d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right)}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) + A*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d) - C*d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) - C*d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) + C*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) + 3*C*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*(A + C*cos(c)**2)/(a*cos(c) + a), True))","A",0
43,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x) + 1), x))/a","F",0
44,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**2/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x) + 1), x))/a","F",0
45,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**3/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3/(cos(c + d*x) + 1), x))/a","F",0
46,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**4/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**4/(cos(c + d*x) + 1), x))/a","F",0
47,1,2161,0,17.378525," ","integrate(cos(d*x+c)**4*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{84 A d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{336 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{504 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{336 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{84 A d x}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{4 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{68 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{432 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{800 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{596 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{156 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{165 C d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{660 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{990 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{660 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{165 C d x}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{4 C \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{116 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{894 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{1566 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{1206 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{318 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((84*A*d*x*tan(c/2 + d*x/2)**8/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 336*A*d*x*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 504*A*d*x*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 336*A*d*x*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 84*A*d*x/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 4*A*tan(c/2 + d*x/2)**11/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 68*A*tan(c/2 + d*x/2)**9/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 432*A*tan(c/2 + d*x/2)**7/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 800*A*tan(c/2 + d*x/2)**5/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 596*A*tan(c/2 + d*x/2)**3/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 156*A*tan(c/2 + d*x/2)/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 165*C*d*x*tan(c/2 + d*x/2)**8/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 660*C*d*x*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 990*C*d*x*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 660*C*d*x*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 165*C*d*x/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 4*C*tan(c/2 + d*x/2)**11/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 116*C*tan(c/2 + d*x/2)**9/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 894*C*tan(c/2 + d*x/2)**7/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 1566*C*tan(c/2 + d*x/2)**5/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 1206*C*tan(c/2 + d*x/2)**3/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 318*C*tan(c/2 + d*x/2)/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**4/(a*cos(c) + a)**2, True))","A",0
48,1,1426,0,11.009328," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{12 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{36 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{36 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 A d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{12 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{54 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{68 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 C d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{24 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{138 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{160 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*A*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 36*A*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 36*A*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*A*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - A*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 12*A*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 54*A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 68*A*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*A*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*C*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*C*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - C*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 24*C*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 138*C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 160*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**2, True))","A",0
49,1,845,0,7.005864," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{6 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{12 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{6 A d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{7 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{17 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{9 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{42 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 C d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{19 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{71 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{39 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*A*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 12*A*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 6*A*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + A*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 7*A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 17*A*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 9*A*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*C*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 42*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + C*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 19*C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 71*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 39*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**2, True))","A",0
50,1,335,0,4.028957," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{2 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{3 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 C d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{14 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 2*A*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 3*A*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 14*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**2, True))","A",0
51,1,104,0,2.259644," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} + \frac{C x}{a^{2}} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} - \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**3/(6*a**2*d) + A*tan(c/2 + d*x/2)/(2*a**2*d) + C*x/a**2 + C*tan(c/2 + d*x/2)**3/(6*a**2*d) - 3*C*tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x*(A + C*cos(c)**2)/(a*cos(c) + a)**2, True))","A",0
52,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
53,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
54,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sec^{3}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
55,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,1,1586,0,23.876319," ","integrate(cos(d*x+c)**4*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{180 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{540 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{540 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 A d x}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{21 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{174 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{798 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{975 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{690 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{2070 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{2070 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{690 C d x}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 C \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{41 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{594 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3078 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3675 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{1395 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-180*A*d*x*tan(c/2 + d*x/2)**6/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 540*A*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 540*A*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*A*d*x/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*A*tan(c/2 + d*x/2)**11/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 21*A*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 174*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 798*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 975*A*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*A*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 690*C*d*x*tan(c/2 + d*x/2)**6/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 2070*C*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 2070*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 690*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*C*tan(c/2 + d*x/2)**11/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 41*C*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 594*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3078*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3675*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 1395*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**4/(a*cos(c) + a)**3, True))","A",0
57,1,967,0,15.305867," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{60 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{120 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{60 A d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{14 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{68 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{190 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{105 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{780 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 C d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{34 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{388 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{1310 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{765 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*A*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 120*A*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 60*A*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*A*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 14*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 68*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 190*A*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 105*A*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*C*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 780*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*C*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 34*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 388*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 1310*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 765*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**3, True))","A",0
58,1,422,0,9.497163," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{3 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{7 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{5 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{15 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 C d x}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{27 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{225 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 7*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 5*A*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 15*A*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 27*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 225*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**3, True))","A",0
59,1,128,0,5.785378," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{C x}{a^{3}} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d} - \frac{7 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*tan(c/2 + d*x/2)**5/(20*a**3*d) + A*tan(c/2 + d*x/2)/(4*a**3*d) + C*x/a**3 - C*tan(c/2 + d*x/2)**5/(20*a**3*d) + C*tan(c/2 + d*x/2)**3/(3*a**3*d) - 7*C*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**3, True))","A",0
60,1,136,0,3.686047," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**5/(20*a**3*d) + A*tan(c/2 + d*x/2)**3/(6*a**3*d) + A*tan(c/2 + d*x/2)/(4*a**3*d) + C*tan(c/2 + d*x/2)**5/(20*a**3*d) - C*tan(c/2 + d*x/2)**3/(6*a**3*d) + C*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(A + C*cos(c)**2)/(a*cos(c) + a)**3, True))","A",0
61,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
62,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
63,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,1,1086,0,33.128169," ","integrate(cos(d*x+c)**4*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{840 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{1680 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{840 A d x}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{15 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{75 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{190 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{910 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{2765 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{1575 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{8820 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{17640 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{8820 C d x}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{15 C \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{159 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{1002 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{9114 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{29505 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{17535 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((840*A*d*x*tan(c/2 + d*x/2)**4/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 1680*A*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 840*A*d*x/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 15*A*tan(c/2 + d*x/2)**11/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 75*A*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 190*A*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 910*A*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 2765*A*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 1575*A*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 8820*C*d*x*tan(c/2 + d*x/2)**4/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 17640*C*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 8820*C*d*x/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 15*C*tan(c/2 + d*x/2)**11/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 159*C*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 1002*C*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 9114*C*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 29505*C*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 17535*C*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**4/(a*cos(c) + a)**4, True))","A",0
66,1,462,0,21.157724," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{15 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{48 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{42 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{105 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 C d x}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{15 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{132 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{658 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{4340 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{6825 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*A*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 48*A*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 42*A*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 105*A*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*C*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*C*d*x/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 15*C*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 132*C*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 658*C*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 4340*C*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 6825*C*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**4, True))","A",0
67,1,192,0,13.431827," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{C x}{a^{4}} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{11 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} - \frac{15 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**7/(56*a**4*d) - A*tan(c/2 + d*x/2)**5/(40*a**4*d) - A*tan(c/2 + d*x/2)**3/(24*a**4*d) + A*tan(c/2 + d*x/2)/(8*a**4*d) + C*x/a**4 + C*tan(c/2 + d*x/2)**7/(56*a**4*d) - C*tan(c/2 + d*x/2)**5/(8*a**4*d) + 11*C*tan(c/2 + d*x/2)**3/(24*a**4*d) - 15*C*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**4, True))","A",0
68,1,182,0,9.366496," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} - \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*tan(c/2 + d*x/2)**7/(56*a**4*d) - A*tan(c/2 + d*x/2)**5/(40*a**4*d) + A*tan(c/2 + d*x/2)**3/(24*a**4*d) + A*tan(c/2 + d*x/2)/(8*a**4*d) - C*tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*C*tan(c/2 + d*x/2)**5/(40*a**4*d) - C*tan(c/2 + d*x/2)**3/(8*a**4*d) + C*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**4, True))","A",0
69,1,178,0,6.687265," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*A*tan(c/2 + d*x/2)**5/(40*a**4*d) + A*tan(c/2 + d*x/2)**3/(8*a**4*d) + A*tan(c/2 + d*x/2)/(8*a**4*d) + C*tan(c/2 + d*x/2)**7/(56*a**4*d) - C*tan(c/2 + d*x/2)**5/(40*a**4*d) - C*tan(c/2 + d*x/2)**3/(24*a**4*d) + C*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + C*cos(c)**2)/(a*cos(c) + a)**4, True))","A",0
70,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2), x)","F",0
78,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
79,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)*sec(c + d*x)**2, x)","F",0
80,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**5*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
106,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
107,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
108,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**3/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
109,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**5/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
115,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
116,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
117,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
118,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)/sqrt(cos(c + d*x)), x)","F",0
174,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right)}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)/cos(c + d*x)**(3/2), x)","F",0
175,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right)}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)/cos(c + d*x)**(5/2), x)","F",0
176,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*sqrt(cos(c + d*x))), x)","F",0
201,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(3/2)), x)","F",0
202,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(5/2)), x)","F",0
203,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2)/cos(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
208,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a*(cos(c + d*x) + 1))**(3/2)*cos(c + d*x)**(3/2)), x)","F",0
209,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(cos(c + d*x))/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
213,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,1,173,0,1.792452," ","integrate(cos(d*x+c)**3*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 B x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*B*x*sin(c + d*x)**4/8 + 3*B*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*x*cos(c + d*x)**4/8 + 3*B*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*sin(c + d*x)**5/(15*d) + 4*C*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**3, True))","A",0
217,1,150,0,0.871045," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{2 B \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*B*sin(c + d*x)**3/(3*d) + B*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*x*sin(c + d*x)**4/8 + 3*C*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*x*cos(c + d*x)**4/8 + 3*C*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
218,1,95,0,0.438905," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*x*sin(c + d*x)**2/2 + B*x*cos(c + d*x)**2/2 + B*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*sin(c + d*x)**3/(3*d) + C*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
219,1,63,0,0.218168," ","integrate(B*cos(d*x+c)+C*cos(d*x+c)**2,x)","B \left(\begin{cases} \frac{\sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cos{\left(c \right)} & \text{otherwise} \end{cases}\right) + C \left(\begin{cases} \frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"B*Piecewise((sin(c + d*x)/d, Ne(d, 0)), (x*cos(c), True)) + C*Piecewise((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*cos(c)**2, True))","A",0
220,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x), x)","F",0
221,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2, x)","F",0
222,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**3, x)","F",0
223,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**4, x)","F",0
224,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,1,338,0,2.113427," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 B a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 B a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{B a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{8 C a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*B*a*x*sin(c + d*x)**4/8 + 3*B*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*a*x*cos(c + d*x)**4/8 + 3*B*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a*sin(c + d*x)**3/(3*d) + 5*B*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + B*a*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 8*C*a*sin(c + d*x)**5/(15*d) + 4*C*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + C*a*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a)*cos(c)**2, True))","A",0
227,1,255,0,1.031982," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 B a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 + 2*B*a*sin(c + d*x)**3/(3*d) + B*a*sin(c + d*x)*cos(c + d*x)**2/d + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a*sin(c + d*x)**3/(3*d) + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a)*cos(c), True))","A",0
228,1,170,0,0.514362," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a \sin{\left(c + d x \right)}}{d} + \frac{C a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a*sin(c + d*x)/d + C*a*x*sin(c + d*x)**2/2 + C*a*x*cos(c + d*x)**2/2 + 2*C*a*sin(c + d*x)**3/(3*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d + C*a*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a), True))","A",0
229,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","a \left(\int B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(C*cos(c + d*x)**3*sec(c + d*x), x))","F",0
230,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","a \left(\int B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(B*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**3*sec(c + d*x)**2, x))","F",0
231,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","a \left(\int B \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(B*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(B*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(C*cos(c + d*x)**3*sec(c + d*x)**3, x))","F",0
232,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,1,462,0,2.465697," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 B a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{B a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 B a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 B a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 B a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{8 C a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{2 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*B*a**2*x*sin(c + d*x)**4/8 + 3*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + B*a**2*x*sin(c + d*x)**2/2 + 3*B*a**2*x*cos(c + d*x)**4/8 + B*a**2*x*cos(c + d*x)**2/2 + 3*B*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*B*a**2*sin(c + d*x)**3/(3*d) + 5*B*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*B*a**2*sin(c + d*x)*cos(c + d*x)**2/d + B*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*C*a**2*x*sin(c + d*x)**4/4 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*C*a**2*x*cos(c + d*x)**4/4 + 8*C*a**2*sin(c + d*x)**5/(15*d) + 4*C*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 2*C*a**2*sin(c + d*x)**3/(3*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a)**2*cos(c), True))","A",0
236,1,340,0,1.174767," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} B a^{2} x \sin^{2}{\left(c + d x \right)} + B a^{2} x \cos^{2}{\left(c + d x \right)} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin{\left(c + d x \right)}}{d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{C a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{C a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**2*x*sin(c + d*x)**2 + B*a**2*x*cos(c + d*x)**2 + 2*B*a**2*sin(c + d*x)**3/(3*d) + B*a**2*sin(c + d*x)*cos(c + d*x)**2/d + B*a**2*sin(c + d*x)*cos(c + d*x)/d + B*a**2*sin(c + d*x)/d + 3*C*a**2*x*sin(c + d*x)**4/8 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + C*a**2*x*sin(c + d*x)**2/2 + 3*C*a**2*x*cos(c + d*x)**4/8 + C*a**2*x*cos(c + d*x)**2/2 + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*C*a**2*sin(c + d*x)**3/(3*d) + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*C*a**2*sin(c + d*x)*cos(c + d*x)**2/d + C*a**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a)**2, True))","A",0
237,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","a^{2} \left(\int B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 2 B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(2*B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(B*cos(c + d*x)**3*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(2*C*cos(c + d*x)**3*sec(c + d*x), x) + Integral(C*cos(c + d*x)**4*sec(c + d*x), x))","F",0
238,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","a^{2} \left(\int B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 B \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(B*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(2*B*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(2*C*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**4*sec(c + d*x)**2, x))","F",0
239,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,1,699,0,4.581396," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{9 B a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{B a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 B a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 B a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 B a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 B a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 C a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 C a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 C a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{5 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*B*a**3*x*sin(c + d*x)**4/8 + 9*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + B*a**3*x*sin(c + d*x)**2/2 + 9*B*a**3*x*cos(c + d*x)**4/8 + B*a**3*x*cos(c + d*x)**2/2 + 8*B*a**3*sin(c + d*x)**5/(15*d) + 4*B*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*B*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a**3*sin(c + d*x)**3/d + B*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*B*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*B*a**3*sin(c + d*x)*cos(c + d*x)**2/d + B*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 5*C*a**3*x*sin(c + d*x)**6/16 + 15*C*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*C*a**3*x*sin(c + d*x)**4/8 + 15*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*C*a**3*x*cos(c + d*x)**6/16 + 9*C*a**3*x*cos(c + d*x)**4/8 + 5*C*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*C*a**3*sin(c + d*x)**5/(5*d) + 5*C*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 9*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a**3*sin(c + d*x)**3/(3*d) + 11*C*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a)**3*cos(c), True))","A",0
245,1,532,0,2.634742," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 B a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{5 B a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a^{3} \sin{\left(c + d x \right)}}{d} + \frac{9 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{C a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{C a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*B*a**3*x*sin(c + d*x)**4/8 + 3*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*a**3*x*sin(c + d*x)**2/2 + 3*B*a**3*x*cos(c + d*x)**4/8 + 3*B*a**3*x*cos(c + d*x)**2/2 + 3*B*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a**3*sin(c + d*x)**3/d + 5*B*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*B*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a**3*sin(c + d*x)/d + 9*C*a**3*x*sin(c + d*x)**4/8 + 9*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + C*a**3*x*sin(c + d*x)**2/2 + 9*C*a**3*x*cos(c + d*x)**4/8 + C*a**3*x*cos(c + d*x)**2/2 + 8*C*a**3*sin(c + d*x)**5/(15*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a**3*sin(c + d*x)**3/d + C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**2/d + C*a**3*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*(a*cos(c) + a)**3, True))","A",0
246,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","a^{3} \left(\int B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 B \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 C \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{5}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(3*B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(3*B*cos(c + d*x)**3*sec(c + d*x), x) + Integral(B*cos(c + d*x)**4*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(3*C*cos(c + d*x)**3*sec(c + d*x), x) + Integral(3*C*cos(c + d*x)**4*sec(c + d*x), x) + Integral(C*cos(c + d*x)**5*sec(c + d*x), x))","F",0
247,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,1,1166,0,6.480900," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{9 B d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{27 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{27 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 B d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{6 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{36 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{42 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{12 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{9 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{27 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{27 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{9 C d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{48 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{50 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{24 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*B*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 27*B*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 27*B*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*B*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 6*B*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 36*B*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 42*B*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 12*B*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 9*C*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 27*C*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 27*C*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 9*C*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*C*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 48*C*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 50*C*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 24*C*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a), True))","A",0
254,1,668,0,3.975468," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} - \frac{2 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 B d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{2 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{8 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 C d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{10 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*B*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*B*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*B*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 2*B*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 8*B*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 6*B*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*C*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 6*C*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*C*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*C*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 10*C*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*C*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a), True))","A",0
255,1,265,0,2.297927," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{B d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{C d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) + B*d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) - B*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) - B*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d) - C*d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) - C*d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) + C*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) + 3*C*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)/(a*cos(c) + a), True))","A",0
256,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x) + 1), x))/a","F",0
257,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c)),x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)**2/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x) + 1), x))/a","F",0
258,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c)),x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)**3/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3/(cos(c + d*x) + 1), x))/a","F",0
259,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c)),x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)**4/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**4/(cos(c + d*x) + 1), x))/a","F",0
260,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,1,1430,0,14.641682," ","integrate(cos(d*x+c)**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{21 B d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 B d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{18 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{110 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{39 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 C d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{24 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{138 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{160 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((21*B*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*B*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*B*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*B*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + B*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 18*B*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*B*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 110*B*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 39*B*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*C*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*C*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - C*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 24*C*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 138*C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 160*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**2, True))","A",0
262,1,848,0,9.540936," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{12 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{24 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 B d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{13 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{41 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{42 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 C d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{19 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{71 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{39 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*B*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 24*B*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*B*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - B*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 13*B*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 41*B*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*B*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*C*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 42*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + C*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 19*C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 71*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 39*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**2, True))","A",0
263,1,415,0,6.007647," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{6 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{6 B d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{8 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{9 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 C d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{14 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*B*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 6*B*d*x/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + B*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 8*B*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 9*B*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 14*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**2, True))","A",0
264,1,107,0,3.391552," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} + \frac{C x}{a^{2}} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} - \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*tan(c/2 + d*x/2)**3/(6*a**2*d) + B*tan(c/2 + d*x/2)/(2*a**2*d) + C*x/a**2 + C*tan(c/2 + d*x/2)**3/(6*a**2*d) - 3*C*tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)/(a*cos(c) + a)**2, True))","A",0
265,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
266,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
267,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
268,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,1,971,0,21.209448," ","integrate(cos(d*x+c)**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{180 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{360 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 B d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{24 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{198 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{600 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{780 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 C d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{34 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{388 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{1310 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{765 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-180*B*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 360*B*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*B*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*B*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 24*B*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 198*B*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 600*B*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*B*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*C*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 780*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*C*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 34*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 388*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 1310*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 765*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**3, True))","A",0
270,1,502,0,13.588628," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{60 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{60 B d x}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{17 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{85 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{105 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 C d x}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{27 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{225 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*B*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 60*B*d*x/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*B*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 17*B*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 85*B*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 105*B*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 27*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 225*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**3, True))","A",0
271,1,151,0,8.414155," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{C x}{a^{3}} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d} - \frac{7 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*tan(c/2 + d*x/2)**5/(20*a**3*d) - B*tan(c/2 + d*x/2)**3/(6*a**3*d) + B*tan(c/2 + d*x/2)/(4*a**3*d) + C*x/a**3 - C*tan(c/2 + d*x/2)**5/(20*a**3*d) + C*tan(c/2 + d*x/2)**3/(3*a**3*d) - 7*C*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**3, True))","A",0
272,1,119,0,5.444669," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*tan(c/2 + d*x/2)**5/(20*a**3*d) + B*tan(c/2 + d*x/2)/(4*a**3*d) + C*tan(c/2 + d*x/2)**5/(20*a**3*d) - C*tan(c/2 + d*x/2)**3/(6*a**3*d) + C*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(B*cos(c) + C*cos(c)**2)/(a*cos(c) + a)**3, True))","A",0
273,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
274,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(B*cos(c + d*x)*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
275,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(B + C*cos(c + d*x))*cos(c + d*x), x)","F",0
278,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
281,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,1,321,0,3.445376," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 B \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{B \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 C x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 C x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 C \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 C \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 C \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*x*sin(c + d*x)**4/8 + 3*A*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*x*cos(c + d*x)**4/8 + 3*A*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*B*sin(c + d*x)**5/(15*d) + 4*B*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + B*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*x*sin(c + d*x)**6/16 + 15*C*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*C*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*C*x*cos(c + d*x)**6/16 + 5*C*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*C*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*C*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**4, True))","A",0
291,1,209,0,1.952423," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{2 A \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*sin(c + d*x)**3/(3*d) + A*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*x*sin(c + d*x)**4/8 + 3*B*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*x*cos(c + d*x)**4/8 + 3*B*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*sin(c + d*x)**5/(15*d) + 4*C*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**3, True))","A",0
292,1,197,0,1.033632," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*x*sin(c + d*x)**2/2 + A*x*cos(c + d*x)**2/2 + A*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*sin(c + d*x)**3/(3*d) + B*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*x*sin(c + d*x)**4/8 + 3*C*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*x*cos(c + d*x)**4/8 + 3*C*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
293,1,107,0,0.477044," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A \sin{\left(c + d x \right)}}{d} + \frac{B x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*sin(c + d*x)/d + B*x*sin(c + d*x)**2/2 + B*x*cos(c + d*x)**2/2 + B*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*sin(c + d*x)**3/(3*d) + C*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
294,1,66,0,0.234323," ","integrate(A+B*cos(d*x+c)+C*cos(d*x+c)**2,x)","A x + B \left(\begin{cases} \frac{\sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cos{\left(c \right)} & \text{otherwise} \end{cases}\right) + C \left(\begin{cases} \frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"A*x + B*Piecewise((sin(c + d*x)/d, Ne(d, 0)), (x*cos(c), True)) + C*Piecewise((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*cos(c)**2, True))","A",0
295,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
296,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2, x)","F",0
297,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\int \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3, x)","F",0
298,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\int \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**4, x)","F",0
299,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,1,428,0,2.462173," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 A a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 B a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 B a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{B a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{8 C a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right) \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + 2*A*a*sin(c + d*x)**3/(3*d) + A*a*sin(c + d*x)*cos(c + d*x)**2/d + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*B*a*x*sin(c + d*x)**4/8 + 3*B*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*a*x*cos(c + d*x)**4/8 + 3*B*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a*sin(c + d*x)**3/(3*d) + 5*B*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + B*a*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 8*C*a*sin(c + d*x)**5/(15*d) + 4*C*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + C*a*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + a)*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
302,1,320,0,1.176585," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{A a \sin{\left(c + d x \right)}}{d} + \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 B a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right) \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) + A*a*sin(c + d*x)/d + B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 + 2*B*a*sin(c + d*x)**3/(3*d) + B*a*sin(c + d*x)*cos(c + d*x)**2/d + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a*sin(c + d*x)**3/(3*d) + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a*cos(c) + a)*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
303,1,189,0,0.582811," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} A a x + \frac{A a \sin{\left(c + d x \right)}}{d} + \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a \sin{\left(c + d x \right)}}{d} + \frac{C a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right) \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x + A*a*sin(c + d*x)/d + B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a*sin(c + d*x)/d + C*a*x*sin(c + d*x)**2/2 + C*a*x*cos(c + d*x)**2/2 + 2*C*a*sin(c + d*x)**3/(3*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d + C*a*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)*(A + B*cos(c) + C*cos(c)**2), True))","A",0
304,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","a \left(\int A \sec{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x), x) + Integral(A*cos(c + d*x)*sec(c + d*x), x) + Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(C*cos(c + d*x)**3*sec(c + d*x), x))","F",0
305,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","a \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**2, x) + Integral(A*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**3*sec(c + d*x)**2, x))","F",0
306,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","a \left(\int A \sec^{3}{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**3, x) + Integral(A*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(B*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(B*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(C*cos(c + d*x)**3*sec(c + d*x)**3, x))","F",0
307,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,1,821,0,4.897748," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 A a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 B a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{8 B a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 B a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{5 C a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 C a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 C a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{16 C a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{8 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{11 C a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{2 C a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**2*x*sin(c + d*x)**4/8 + 3*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**2*x*sin(c + d*x)**2/2 + 3*A*a**2*x*cos(c + d*x)**4/8 + A*a**2*x*cos(c + d*x)**2/2 + 3*A*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*A*a**2*sin(c + d*x)**3/(3*d) + 5*A*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*A*a**2*sin(c + d*x)*cos(c + d*x)**2/d + A*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*B*a**2*x*sin(c + d*x)**4/4 + 3*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*B*a**2*x*cos(c + d*x)**4/4 + 8*B*a**2*sin(c + d*x)**5/(15*d) + 4*B*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*B*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 2*B*a**2*sin(c + d*x)**3/(3*d) + B*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + B*a**2*sin(c + d*x)*cos(c + d*x)**2/d + 5*C*a**2*x*sin(c + d*x)**6/16 + 15*C*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*C*a**2*x*sin(c + d*x)**4/8 + 15*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*C*a**2*x*cos(c + d*x)**6/16 + 3*C*a**2*x*cos(c + d*x)**4/8 + 5*C*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 16*C*a**2*sin(c + d*x)**5/(15*d) + 5*C*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 8*C*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 11*C*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 2*C*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + a)**2*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
310,1,570,0,2.800733," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} A a^{2} x \sin^{2}{\left(c + d x \right)} + A a^{2} x \cos^{2}{\left(c + d x \right)} + \frac{2 A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)}}{d} + \frac{3 B a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{B a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 B a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 B a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 B a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{8 C a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{2 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**2 + A*a**2*x*cos(c + d*x)**2 + 2*A*a**2*sin(c + d*x)**3/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**2/d + A*a**2*sin(c + d*x)*cos(c + d*x)/d + A*a**2*sin(c + d*x)/d + 3*B*a**2*x*sin(c + d*x)**4/8 + 3*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + B*a**2*x*sin(c + d*x)**2/2 + 3*B*a**2*x*cos(c + d*x)**4/8 + B*a**2*x*cos(c + d*x)**2/2 + 3*B*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*B*a**2*sin(c + d*x)**3/(3*d) + 5*B*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*B*a**2*sin(c + d*x)*cos(c + d*x)**2/d + B*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*C*a**2*x*sin(c + d*x)**4/4 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*C*a**2*x*cos(c + d*x)**4/4 + 8*C*a**2*sin(c + d*x)**5/(15*d) + 4*C*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 2*C*a**2*sin(c + d*x)**3/(3*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a*cos(c) + a)**2*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
311,1,420,0,1.404609," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + A a^{2} x + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A a^{2} \sin{\left(c + d x \right)}}{d} + B a^{2} x \sin^{2}{\left(c + d x \right)} + B a^{2} x \cos^{2}{\left(c + d x \right)} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin{\left(c + d x \right)}}{d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{C a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{C a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**2/2 + A*a**2*x*cos(c + d*x)**2/2 + A*a**2*x + A*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*a**2*sin(c + d*x)/d + B*a**2*x*sin(c + d*x)**2 + B*a**2*x*cos(c + d*x)**2 + 2*B*a**2*sin(c + d*x)**3/(3*d) + B*a**2*sin(c + d*x)*cos(c + d*x)**2/d + B*a**2*sin(c + d*x)*cos(c + d*x)/d + B*a**2*sin(c + d*x)/d + 3*C*a**2*x*sin(c + d*x)**4/8 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + C*a**2*x*sin(c + d*x)**2/2 + 3*C*a**2*x*cos(c + d*x)**4/8 + C*a**2*x*cos(c + d*x)**2/2 + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*C*a**2*sin(c + d*x)**3/(3*d) + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*C*a**2*sin(c + d*x)*cos(c + d*x)**2/d + C*a**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)**2*(A + B*cos(c) + C*cos(c)**2), True))","A",0
312,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","a^{2} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 2 A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 2 B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x), x) + Integral(2*A*cos(c + d*x)*sec(c + d*x), x) + Integral(A*cos(c + d*x)**2*sec(c + d*x), x) + Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(2*B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(B*cos(c + d*x)**3*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(2*C*cos(c + d*x)**3*sec(c + d*x), x) + Integral(C*cos(c + d*x)**4*sec(c + d*x), x))","F",0
313,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","a^{2} \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int 2 A \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int A \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 B \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x)**2, x) + Integral(2*A*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(A*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(2*B*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(2*C*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(C*cos(c + d*x)**4*sec(c + d*x)**2, x))","F",0
314,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,1,1149,0,8.435919," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{9 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 A a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 B a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 B a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 B a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 B a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 B a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 B a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 B a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{5 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{4 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 B a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 B a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 B a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{45 C a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{45 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{15 C a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{16 C a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{15 C a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{33 C a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{3} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*A*a**3*x*sin(c + d*x)**4/8 + 9*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**3*x*sin(c + d*x)**2/2 + 9*A*a**3*x*cos(c + d*x)**4/8 + A*a**3*x*cos(c + d*x)**2/2 + 8*A*a**3*sin(c + d*x)**5/(15*d) + 4*A*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*A*a**3*sin(c + d*x)**3/d + A*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*A*a**3*sin(c + d*x)*cos(c + d*x)**2/d + A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 5*B*a**3*x*sin(c + d*x)**6/16 + 15*B*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*B*a**3*x*sin(c + d*x)**4/8 + 15*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*B*a**3*x*cos(c + d*x)**6/16 + 9*B*a**3*x*cos(c + d*x)**4/8 + 5*B*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*B*a**3*sin(c + d*x)**5/(5*d) + 5*B*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 4*B*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 9*B*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a**3*sin(c + d*x)**3/(3*d) + 11*B*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*B*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*B*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + B*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 15*C*a**3*x*sin(c + d*x)**6/16 + 45*C*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*C*a**3*x*sin(c + d*x)**4/8 + 45*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 15*C*a**3*x*cos(c + d*x)**6/16 + 3*C*a**3*x*cos(c + d*x)**4/8 + 16*C*a**3*sin(c + d*x)**7/(35*d) + 8*C*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 15*C*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*C*a**3*sin(c + d*x)**5/(5*d) + 2*C*a**3*sin(c + d*x)**3*cos(c + d*x)**4/d + 5*C*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**6/d + 33*C*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + a)**3*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
319,1,932,0,5.176853," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{A a^{3} \sin{\left(c + d x \right)}}{d} + \frac{9 B a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{B a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 B a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 B a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 B a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 B a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 C a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 C a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 C a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{5 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{3} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(c + d*x)**4/8 + 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a**3*x*sin(c + d*x)**2/2 + 3*A*a**3*x*cos(c + d*x)**4/8 + 3*A*a**3*x*cos(c + d*x)**2/2 + 3*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*A*a**3*sin(c + d*x)**3/d + 5*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*A*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + A*a**3*sin(c + d*x)/d + 9*B*a**3*x*sin(c + d*x)**4/8 + 9*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + B*a**3*x*sin(c + d*x)**2/2 + 9*B*a**3*x*cos(c + d*x)**4/8 + B*a**3*x*cos(c + d*x)**2/2 + 8*B*a**3*sin(c + d*x)**5/(15*d) + 4*B*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*B*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a**3*sin(c + d*x)**3/d + B*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*B*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*B*a**3*sin(c + d*x)*cos(c + d*x)**2/d + B*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 5*C*a**3*x*sin(c + d*x)**6/16 + 15*C*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*C*a**3*x*sin(c + d*x)**4/8 + 15*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*C*a**3*x*cos(c + d*x)**6/16 + 9*C*a**3*x*cos(c + d*x)**4/8 + 5*C*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*C*a**3*sin(c + d*x)**5/(5*d) + 5*C*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 9*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a**3*sin(c + d*x)**3/(3*d) + 11*C*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a*cos(c) + a)**3*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
320,1,658,0,2.970146," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + A a^{3} x + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 B a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 B a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{5 B a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a^{3} \sin{\left(c + d x \right)}}{d} + \frac{9 C a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{C a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{9 C a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{C a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{8 C a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 C a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{3} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(c + d*x)**2/2 + 3*A*a**3*x*cos(c + d*x)**2/2 + A*a**3*x + 2*A*a**3*sin(c + d*x)**3/(3*d) + A*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*A*a**3*sin(c + d*x)/d + 3*B*a**3*x*sin(c + d*x)**4/8 + 3*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*a**3*x*sin(c + d*x)**2/2 + 3*B*a**3*x*cos(c + d*x)**4/8 + 3*B*a**3*x*cos(c + d*x)**2/2 + 3*B*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*B*a**3*sin(c + d*x)**3/d + 5*B*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*B*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a**3*sin(c + d*x)/d + 9*C*a**3*x*sin(c + d*x)**4/8 + 9*C*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + C*a**3*x*sin(c + d*x)**2/2 + 9*C*a**3*x*cos(c + d*x)**4/8 + C*a**3*x*cos(c + d*x)**2/2 + 8*C*a**3*sin(c + d*x)**5/(15*d) + 4*C*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*C*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*C*a**3*sin(c + d*x)**3/d + C*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*C*a**3*sin(c + d*x)*cos(c + d*x)**2/d + C*a**3*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)**3*(A + B*cos(c) + C*cos(c)**2), True))","A",0
321,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","a^{3} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 3 A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 A \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 B \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 C \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 C \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int C \cos^{5}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(A*sec(c + d*x), x) + Integral(3*A*cos(c + d*x)*sec(c + d*x), x) + Integral(3*A*cos(c + d*x)**2*sec(c + d*x), x) + Integral(A*cos(c + d*x)**3*sec(c + d*x), x) + Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(3*B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(3*B*cos(c + d*x)**3*sec(c + d*x), x) + Integral(B*cos(c + d*x)**4*sec(c + d*x), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x), x) + Integral(3*C*cos(c + d*x)**3*sec(c + d*x), x) + Integral(3*C*cos(c + d*x)**4*sec(c + d*x), x) + Integral(C*cos(c + d*x)**5*sec(c + d*x), x))","F",0
322,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,1,1640,0,14.528427," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{5 A a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 A a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 A a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{15 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{5 A a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 A a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{A a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{5 A a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{32 A a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 A a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{16 A a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 A a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 A a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 A a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{4 A a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 A a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{4 A a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 B a^{4} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 B a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + \frac{15 B a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + 3 B a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{5 B a^{4} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{3 B a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{16 B a^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 B a^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{5 B a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{16 B a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{2 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{10 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{8 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{11 B a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{6 B a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{B a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{35 C a^{4} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{35 C a^{4} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 C a^{4} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{105 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{45 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 C a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{35 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{45 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{35 C a^{4} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{15 C a^{4} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{3 C a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{35 C a^{4} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{64 C a^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{385 C a^{4} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{32 C a^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{15 C a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{32 C a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{511 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{8 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} + \frac{16 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 C a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{93 C a^{4} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{33 C a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{4} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*A*a**4*x*sin(c + d*x)**6/16 + 15*A*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*A*a**4*x*sin(c + d*x)**4/4 + 15*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + A*a**4*x*sin(c + d*x)**2/2 + 5*A*a**4*x*cos(c + d*x)**6/16 + 9*A*a**4*x*cos(c + d*x)**4/4 + A*a**4*x*cos(c + d*x)**2/2 + 5*A*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 32*A*a**4*sin(c + d*x)**5/(15*d) + 5*A*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 16*A*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*A*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*A*a**4*sin(c + d*x)**3/(3*d) + 11*A*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 4*A*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 15*A*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 4*A*a**4*sin(c + d*x)*cos(c + d*x)**2/d + A*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 5*B*a**4*x*sin(c + d*x)**6/4 + 15*B*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 3*B*a**4*x*sin(c + d*x)**4/2 + 15*B*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 3*B*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 5*B*a**4*x*cos(c + d*x)**6/4 + 3*B*a**4*x*cos(c + d*x)**4/2 + 16*B*a**4*sin(c + d*x)**7/(35*d) + 8*B*a**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 5*B*a**4*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 16*B*a**4*sin(c + d*x)**5/(5*d) + 2*B*a**4*sin(c + d*x)**3*cos(c + d*x)**4/d + 10*B*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 8*B*a**4*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*B*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 2*B*a**4*sin(c + d*x)**3/(3*d) + B*a**4*sin(c + d*x)*cos(c + d*x)**6/d + 11*B*a**4*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 6*B*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + B*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 35*C*a**4*x*sin(c + d*x)**8/128 + 35*C*a**4*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*C*a**4*x*sin(c + d*x)**6/8 + 105*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 45*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*C*a**4*x*sin(c + d*x)**4/8 + 35*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 45*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 3*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 35*C*a**4*x*cos(c + d*x)**8/128 + 15*C*a**4*x*cos(c + d*x)**6/8 + 3*C*a**4*x*cos(c + d*x)**4/8 + 35*C*a**4*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 64*C*a**4*sin(c + d*x)**7/(35*d) + 385*C*a**4*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 32*C*a**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 15*C*a**4*sin(c + d*x)**5*cos(c + d*x)/(8*d) + 32*C*a**4*sin(c + d*x)**5/(15*d) + 511*C*a**4*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 8*C*a**4*sin(c + d*x)**3*cos(c + d*x)**4/d + 5*C*a**4*sin(c + d*x)**3*cos(c + d*x)**3/d + 16*C*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*C*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 93*C*a**4*sin(c + d*x)*cos(c + d*x)**7/(128*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**6/d + 33*C*a**4*sin(c + d*x)*cos(c + d*x)**5/(8*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + a)**4*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
329,1,1258,0,8.821192," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + 3 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + 2 A a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 A a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + 2 A a^{4} x \cos^{2}{\left(c + d x \right)} + \frac{8 A a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 A a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 A a^{4} \sin^{3}{\left(c + d x \right)}}{d} + \frac{A a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 A a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{6 A a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{A a^{4} \sin{\left(c + d x \right)}}{d} + \frac{5 B a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 B a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 B a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{15 B a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 B a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{5 B a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 B a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{B a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{5 B a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{32 B a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{16 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 B a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 B a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 B a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{4 B a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 B a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{4 B a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 C a^{4} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + \frac{15 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + 3 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{5 C a^{4} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{3 C a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{16 C a^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 C a^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{5 C a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{16 C a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{2 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{10 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{8 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{11 C a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{6 C a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{4} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**4*x*sin(c + d*x)**4/2 + 3*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 2*A*a**4*x*sin(c + d*x)**2 + 3*A*a**4*x*cos(c + d*x)**4/2 + 2*A*a**4*x*cos(c + d*x)**2 + 8*A*a**4*sin(c + d*x)**5/(15*d) + 4*A*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*A*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 4*A*a**4*sin(c + d*x)**3/d + A*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*A*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 6*A*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 2*A*a**4*sin(c + d*x)*cos(c + d*x)/d + A*a**4*sin(c + d*x)/d + 5*B*a**4*x*sin(c + d*x)**6/16 + 15*B*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*B*a**4*x*sin(c + d*x)**4/4 + 15*B*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*B*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + B*a**4*x*sin(c + d*x)**2/2 + 5*B*a**4*x*cos(c + d*x)**6/16 + 9*B*a**4*x*cos(c + d*x)**4/4 + B*a**4*x*cos(c + d*x)**2/2 + 5*B*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 32*B*a**4*sin(c + d*x)**5/(15*d) + 5*B*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 16*B*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*B*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*B*a**4*sin(c + d*x)**3/(3*d) + 11*B*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 4*B*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 15*B*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 4*B*a**4*sin(c + d*x)*cos(c + d*x)**2/d + B*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 5*C*a**4*x*sin(c + d*x)**6/4 + 15*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 3*C*a**4*x*sin(c + d*x)**4/2 + 15*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 3*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 5*C*a**4*x*cos(c + d*x)**6/4 + 3*C*a**4*x*cos(c + d*x)**4/2 + 16*C*a**4*sin(c + d*x)**7/(35*d) + 8*C*a**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 5*C*a**4*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 16*C*a**4*sin(c + d*x)**5/(5*d) + 2*C*a**4*sin(c + d*x)**3*cos(c + d*x)**4/d + 10*C*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 8*C*a**4*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*C*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 2*C*a**4*sin(c + d*x)**3/(3*d) + C*a**4*sin(c + d*x)*cos(c + d*x)**6/d + 11*C*a**4*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 6*C*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + C*a**4*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a*cos(c) + a)**4*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
330,1,1005,0,5.337958," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{3 A a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + 3 A a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 A a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + 3 A a^{4} x \cos^{2}{\left(c + d x \right)} + A a^{4} x + \frac{3 A a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{8 A a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 A a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{4 A a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 A a^{4} \sin{\left(c + d x \right)}}{d} + \frac{3 B a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + 3 B a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + 2 B a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 B a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + 2 B a^{4} x \cos^{2}{\left(c + d x \right)} + \frac{8 B a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 B a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 B a^{4} \sin^{3}{\left(c + d x \right)}}{d} + \frac{B a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{6 B a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 B a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{B a^{4} \sin{\left(c + d x \right)}}{d} + \frac{5 C a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 C a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{15 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 C a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{5 C a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 C a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{C a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{5 C a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{32 C a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{16 C a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 C a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 C a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 C a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{4 C a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{4} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**4*x*sin(c + d*x)**4/8 + 3*A*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a**4*x*sin(c + d*x)**2 + 3*A*a**4*x*cos(c + d*x)**4/8 + 3*A*a**4*x*cos(c + d*x)**2 + A*a**4*x + 3*A*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 8*A*a**4*sin(c + d*x)**3/(3*d) + 5*A*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 4*A*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a**4*sin(c + d*x)*cos(c + d*x)/d + 4*A*a**4*sin(c + d*x)/d + 3*B*a**4*x*sin(c + d*x)**4/2 + 3*B*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 2*B*a**4*x*sin(c + d*x)**2 + 3*B*a**4*x*cos(c + d*x)**4/2 + 2*B*a**4*x*cos(c + d*x)**2 + 8*B*a**4*sin(c + d*x)**5/(15*d) + 4*B*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*B*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 4*B*a**4*sin(c + d*x)**3/d + B*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 6*B*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 2*B*a**4*sin(c + d*x)*cos(c + d*x)/d + B*a**4*sin(c + d*x)/d + 5*C*a**4*x*sin(c + d*x)**6/16 + 15*C*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*C*a**4*x*sin(c + d*x)**4/4 + 15*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*C*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + C*a**4*x*sin(c + d*x)**2/2 + 5*C*a**4*x*cos(c + d*x)**6/16 + 9*C*a**4*x*cos(c + d*x)**4/4 + C*a**4*x*cos(c + d*x)**2/2 + 5*C*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 32*C*a**4*sin(c + d*x)**5/(15*d) + 5*C*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 16*C*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*C*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*C*a**4*sin(c + d*x)**3/(3*d) + 11*C*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 15*C*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 4*C*a**4*sin(c + d*x)*cos(c + d*x)**2/d + C*a**4*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)**4*(A + B*cos(c) + C*cos(c)**2), True))","A",0
331,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,1,2688,0,12.677699," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{36 A d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{144 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{216 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{144 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{36 A d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{24 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{168 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{312 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{216 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{48 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{36 B d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{144 B d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{216 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{144 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{36 B d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{24 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{216 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{392 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{296 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{96 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{45 C d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{180 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{270 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{180 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{45 C d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{24 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{246 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{374 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{314 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{66 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((36*A*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 144*A*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 216*A*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 144*A*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 36*A*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 24*A*tan(c/2 + d*x/2)**9/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 168*A*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 312*A*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 216*A*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 48*A*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 36*B*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 144*B*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 216*B*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 144*B*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 36*B*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 24*B*tan(c/2 + d*x/2)**9/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 216*B*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 392*B*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 296*B*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 96*B*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 45*C*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 180*C*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 270*C*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 180*C*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 45*C*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 24*C*tan(c/2 + d*x/2)**9/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 246*C*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 374*C*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 314*C*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 66*C*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a), True))","A",0
340,1,1739,0,8.119787," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} - \frac{6 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{18 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{18 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{6 A d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{30 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{42 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{18 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 B d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{27 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{27 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 B d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{6 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{36 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{42 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{12 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{9 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{27 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{27 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{9 C d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{48 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{50 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{24 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 18*A*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 18*A*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 6*A*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*A*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 30*A*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 42*A*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 18*A*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*B*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 27*B*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 27*B*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*B*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 6*B*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 36*B*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 42*B*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 12*B*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 9*C*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 27*C*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 27*C*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 9*C*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*C*tan(c/2 + d*x/2)**7/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 48*C*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 50*C*tan(c/2 + d*x/2)**3/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 24*C*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a), True))","A",0
341,1,993,0,4.830814," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{2 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{4 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{2 A d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 B d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{2 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{8 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 C d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{10 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 4*A*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 2*A*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*A*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*A*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*A*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*B*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*B*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*B*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 2*B*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 8*B*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 6*B*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*C*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 6*C*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*C*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*C*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 10*C*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*C*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a), True))","A",0
342,1,330,0,2.761299," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{B d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{C d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) + A*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d) + B*d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) + B*d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) - B*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) - B*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d) - C*d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) - C*d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) + C*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) + 3*C*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)/(a*cos(c) + a), True))","A",0
343,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)/(cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x) + 1), x))/a","F",0
344,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**2/(cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**2/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x) + 1), x))/a","F",0
345,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**3/(cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**3/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**3/(cos(c + d*x) + 1), x))/a","F",0
346,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**4/(cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**4/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**4/(cos(c + d*x) + 1), x))/a","F",0
347,1,2134,0,19.097420," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{12 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{36 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{36 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 A d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{12 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{54 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{68 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 B d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 B d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{18 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{110 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{39 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 C d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{24 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{138 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{160 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*A*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 36*A*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 36*A*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*A*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - A*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 12*A*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 54*A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 68*A*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*A*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*B*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*B*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*B*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*B*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + B*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 18*B*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*B*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 110*B*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 39*B*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*C*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*C*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - C*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 24*C*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 138*C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 160*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**2, True))","A",0
348,1,1261,0,13.050003," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{6 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{12 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{6 A d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{7 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{17 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{9 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{24 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 B d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{13 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{41 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{42 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 C d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{19 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{71 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{39 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*A*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 12*A*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 6*A*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + A*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 7*A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 17*A*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 9*A*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*B*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 24*B*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*B*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - B*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 13*B*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 41*B*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*B*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*C*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 42*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + C*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 19*C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 71*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 39*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**2, True))","A",0
349,1,536,0,7.973055," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{2 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{3 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{6 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{6 B d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{8 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{9 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 C d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{14 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 2*A*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 3*A*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 6*B*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 6*B*d*x/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + B*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 8*B*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 9*B*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*C*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*C*d*x/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - C*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 14*C*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*C*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**2, True))","A",0
350,1,148,0,4.514045," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} + \frac{C x}{a^{2}} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} - \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**3/(6*a**2*d) + A*tan(c/2 + d*x/2)/(2*a**2*d) - B*tan(c/2 + d*x/2)**3/(6*a**2*d) + B*tan(c/2 + d*x/2)/(2*a**2*d) + C*x/a**2 + C*tan(c/2 + d*x/2)**3/(6*a**2*d) - 3*C*tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)/(a*cos(c) + a)**2, True))","A",0
351,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
352,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
353,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,1,2373,0,35.736846," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{180 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{540 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{540 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 A d x}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{21 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{174 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{798 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{975 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 B d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{1170 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{1170 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 B d x}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 B \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{31 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{354 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{1698 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{2075 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{765 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{690 C d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{2070 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{2070 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{690 C d x}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 C \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{41 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{594 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3078 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3675 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{1395 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 180 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-180*A*d*x*tan(c/2 + d*x/2)**6/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 540*A*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 540*A*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*A*d*x/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*A*tan(c/2 + d*x/2)**11/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 21*A*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 174*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 798*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 975*A*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*A*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*B*d*x*tan(c/2 + d*x/2)**6/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 1170*B*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 1170*B*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*B*d*x/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*B*tan(c/2 + d*x/2)**11/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 31*B*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 354*B*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 1698*B*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 2075*B*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 765*B*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 690*C*d*x*tan(c/2 + d*x/2)**6/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 2070*C*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 2070*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 690*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*C*tan(c/2 + d*x/2)**11/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 41*C*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 594*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3078*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3675*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 1395*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**6 + 180*a**3*d*tan(c/2 + d*x/2)**4 + 180*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**4/(a*cos(c) + a)**3, True))","A",0
356,1,1445,0,23.821521," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{60 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{120 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{60 A d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{14 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{68 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{190 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{105 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{360 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 B d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{24 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{198 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{600 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{780 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 C d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{34 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{388 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{1310 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{765 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*A*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 120*A*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 60*A*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*A*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 14*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 68*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 190*A*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 105*A*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*B*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 360*B*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*B*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*B*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 24*B*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 198*B*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 600*B*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*B*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*C*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 780*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*C*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 34*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 388*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 1310*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 765*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**3, True))","A",0
357,1,665,0,16.060510," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{3 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{7 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{5 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{15 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{60 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{60 B d x}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{17 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{85 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{105 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{180 C d x}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{3 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{27 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{225 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{375 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 7*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 5*A*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 15*A*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 60*B*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 60*B*d*x/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*B*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 17*B*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 85*B*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 105*B*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*C*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 180*C*d*x/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 3*C*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 27*C*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 225*C*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 375*C*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**3, True))","A",0
358,1,192,0,9.729405," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{C x}{a^{3}} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d} - \frac{7 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*tan(c/2 + d*x/2)**5/(20*a**3*d) + A*tan(c/2 + d*x/2)/(4*a**3*d) + B*tan(c/2 + d*x/2)**5/(20*a**3*d) - B*tan(c/2 + d*x/2)**3/(6*a**3*d) + B*tan(c/2 + d*x/2)/(4*a**3*d) + C*x/a**3 - C*tan(c/2 + d*x/2)**5/(20*a**3*d) + C*tan(c/2 + d*x/2)**3/(3*a**3*d) - 7*C*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**3, True))","A",0
359,1,180,0,6.345860," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} - \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} + \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**5/(20*a**3*d) + A*tan(c/2 + d*x/2)**3/(6*a**3*d) + A*tan(c/2 + d*x/2)/(4*a**3*d) - B*tan(c/2 + d*x/2)**5/(20*a**3*d) + B*tan(c/2 + d*x/2)/(4*a**3*d) + C*tan(c/2 + d*x/2)**5/(20*a**3*d) - C*tan(c/2 + d*x/2)**3/(6*a**3*d) + C*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)/(a*cos(c) + a)**3, True))","A",0
360,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
361,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
362,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,1,1624,0,52.691516," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{840 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{1680 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{840 A d x}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{15 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{75 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{190 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{910 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{2765 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{1575 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 B d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{6720 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 B d x}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{15 B \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{117 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{526 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{3682 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{11165 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{6825 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{8820 C d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{17640 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{8820 C d x}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{15 C \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{159 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{1002 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{9114 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{29505 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{17535 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((840*A*d*x*tan(c/2 + d*x/2)**4/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 1680*A*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 840*A*d*x/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 15*A*tan(c/2 + d*x/2)**11/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 75*A*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 190*A*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 910*A*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 2765*A*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 1575*A*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*B*d*x*tan(c/2 + d*x/2)**4/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 6720*B*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*B*d*x/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 15*B*tan(c/2 + d*x/2)**11/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 117*B*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 526*B*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 3682*B*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 11165*B*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 6825*B*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 8820*C*d*x*tan(c/2 + d*x/2)**4/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 17640*C*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 8820*C*d*x/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 15*C*tan(c/2 + d*x/2)**11/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 159*C*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 1002*C*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 9114*C*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 29505*C*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 17535*C*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**4 + 1680*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**4/(a*cos(c) + a)**4, True))","A",0
365,1,746,0,35.077302," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{15 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{48 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{42 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{105 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{840 B d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{840 B d x}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{15 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{90 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{280 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{1190 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{1575 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 C d x}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{15 C \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{132 C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{658 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{4340 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{6825 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*A*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 48*A*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 42*A*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 105*A*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 840*B*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 840*B*d*x/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 15*B*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 90*B*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 280*B*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 1190*B*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 1575*B*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*C*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*C*d*x/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 15*C*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 132*C*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 658*C*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 4340*C*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 6825*C*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**3/(a*cos(c) + a)**4, True))","A",0
366,1,279,0,22.670228," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} - \frac{B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{C x}{a^{4}} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{11 C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} - \frac{15 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**7/(56*a**4*d) - A*tan(c/2 + d*x/2)**5/(40*a**4*d) - A*tan(c/2 + d*x/2)**3/(24*a**4*d) + A*tan(c/2 + d*x/2)/(8*a**4*d) - B*tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*B*tan(c/2 + d*x/2)**5/(40*a**4*d) - B*tan(c/2 + d*x/2)**3/(8*a**4*d) + B*tan(c/2 + d*x/2)/(8*a**4*d) + C*x/a**4 + C*tan(c/2 + d*x/2)**7/(56*a**4*d) - C*tan(c/2 + d*x/2)**5/(8*a**4*d) + 11*C*tan(c/2 + d*x/2)**3/(24*a**4*d) - 15*C*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2/(a*cos(c) + a)**4, True))","A",0
367,1,267,0,15.468568," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} - \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*tan(c/2 + d*x/2)**7/(56*a**4*d) - A*tan(c/2 + d*x/2)**5/(40*a**4*d) + A*tan(c/2 + d*x/2)**3/(24*a**4*d) + A*tan(c/2 + d*x/2)/(8*a**4*d) + B*tan(c/2 + d*x/2)**7/(56*a**4*d) - B*tan(c/2 + d*x/2)**5/(40*a**4*d) - B*tan(c/2 + d*x/2)**3/(24*a**4*d) + B*tan(c/2 + d*x/2)/(8*a**4*d) - C*tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*C*tan(c/2 + d*x/2)**5/(40*a**4*d) - C*tan(c/2 + d*x/2)**3/(8*a**4*d) + C*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)*cos(c)/(a*cos(c) + a)**4, True))","A",0
368,1,264,0,10.960812," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} - \frac{B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{C \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{C \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right)}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*A*tan(c/2 + d*x/2)**5/(40*a**4*d) + A*tan(c/2 + d*x/2)**3/(8*a**4*d) + A*tan(c/2 + d*x/2)/(8*a**4*d) - B*tan(c/2 + d*x/2)**7/(56*a**4*d) - B*tan(c/2 + d*x/2)**5/(40*a**4*d) + B*tan(c/2 + d*x/2)**3/(24*a**4*d) + B*tan(c/2 + d*x/2)/(8*a**4*d) + C*tan(c/2 + d*x/2)**7/(56*a**4*d) - C*tan(c/2 + d*x/2)**5/(40*a**4*d) - C*tan(c/2 + d*x/2)**3/(24*a**4*d) + C*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + B*cos(c) + C*cos(c)**2)/(a*cos(c) + a)**4, True))","A",0
369,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2), x)","F",0
377,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
378,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2, x)","F",0
379,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
405,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
406,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
407,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
408,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
415,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
416,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
417,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
454,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(cos(c + d*x)), x)","F",0
479,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/cos(c + d*x)**(3/2), x)","F",0
480,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/cos(c + d*x)**(5/2), x)","F",0
481,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*sqrt(cos(c + d*x))), x)","F",0
506,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(3/2)), x)","F",0
507,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
514,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a*(cos(c + d*x) + 1))**(3/2)*cos(c + d*x)**(3/2)), x)","F",0
515,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(cos(c + d*x))/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
519,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,1,279,0,2.215630," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*b*sin(c + d*x)**3/(3*d) + A*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*b*sin(c + d*x)**5/(15*d) + 4*C*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))*cos(c)**2, True))","A",0
523,1,226,0,1.077305," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a \sin{\left(c + d x \right)}}{d} + \frac{A b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*sin(c + d*x)/d + A*b*x*sin(c + d*x)**2/2 + A*b*x*cos(c + d*x)**2/2 + A*b*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*a*sin(c + d*x)**3/(3*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b*x*sin(c + d*x)**4/8 + 3*C*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b*x*cos(c + d*x)**4/8 + 3*C*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))*cos(c), True))","A",0
524,1,121,0,0.523906," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\begin{cases} A a x + \frac{A b \sin{\left(c + d x \right)}}{d} + \frac{C a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x + A*b*sin(c + d*x)/d + C*a*x*sin(c + d*x)**2/2 + C*a*x*cos(c + d*x)**2/2 + C*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*b*sin(c + d*x)**3/(3*d) + C*b*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c)), True))","A",0
525,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))*sec(c + d*x), x)","F",0
526,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
527,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
528,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,1,592,0,4.345321," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 A a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 A a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 C a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{16 C a b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{8 C a b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{2 C a b \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 C b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 C b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 C b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 C b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 C b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{2} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**2/2 + A*a**2*x*cos(c + d*x)**2/2 + A*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 4*A*a*b*sin(c + d*x)**3/(3*d) + 2*A*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*b**2*x*sin(c + d*x)**4/8 + 3*A*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*b**2*x*cos(c + d*x)**4/8 + 3*A*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*C*a**2*x*sin(c + d*x)**4/8 + 3*C*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a**2*x*cos(c + d*x)**4/8 + 3*C*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 16*C*a*b*sin(c + d*x)**5/(15*d) + 8*C*a*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 2*C*a*b*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*b**2*x*sin(c + d*x)**6/16 + 15*C*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*C*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*C*b**2*x*cos(c + d*x)**6/16 + 5*C*b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*C*b**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*C*b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**2*cos(c)**2, True))","A",0
532,1,350,0,2.385857," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{2} \sin{\left(c + d x \right)}}{d} + A a b x \sin^{2}{\left(c + d x \right)} + A a b x \cos^{2}{\left(c + d x \right)} + \frac{A a b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{2 A b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 C a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a b x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 C a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{5 C a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{8 C b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*sin(c + d*x)/d + A*a*b*x*sin(c + d*x)**2 + A*a*b*x*cos(c + d*x)**2 + A*a*b*sin(c + d*x)*cos(c + d*x)/d + 2*A*b**2*sin(c + d*x)**3/(3*d) + A*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 2*C*a**2*sin(c + d*x)**3/(3*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a*b*x*sin(c + d*x)**4/4 + 3*C*a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*C*a*b*x*cos(c + d*x)**4/4 + 3*C*a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 5*C*a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 8*C*b**2*sin(c + d*x)**5/(15*d) + 4*C*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**2*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**2*cos(c), True))","A",0
533,1,309,0,1.242815," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\begin{cases} A a^{2} x + \frac{2 A a b \sin{\left(c + d x \right)}}{d} + \frac{A b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{C a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 C a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 C a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x + 2*A*a*b*sin(c + d*x)/d + A*b**2*x*sin(c + d*x)**2/2 + A*b**2*x*cos(c + d*x)**2/2 + A*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) + C*a**2*x*sin(c + d*x)**2/2 + C*a**2*x*cos(c + d*x)**2/2 + C*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 4*C*a*b*sin(c + d*x)**3/(3*d) + 2*C*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b**2*x*sin(c + d*x)**4/8 + 3*C*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b**2*x*cos(c + d*x)**4/8 + 3*C*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**2, True))","A",0
534,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**2*sec(c + d*x), x)","F",0
535,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**2*sec(c + d*x)**2, x)","F",0
536,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,1,668,0,4.744847," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 A a^{2} b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A a b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 A a b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A b^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A b^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{2} b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{2} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 C a^{2} b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{2} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 C a^{2} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C a b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{4 C a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C b^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 C b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 C b^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 C b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 C b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 C b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sin(c + d*x)/d + 3*A*a**2*b*x*sin(c + d*x)**2/2 + 3*A*a**2*b*x*cos(c + d*x)**2/2 + 3*A*a**2*b*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*a*b**2*sin(c + d*x)**3/d + 3*A*a*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*b**3*x*sin(c + d*x)**4/8 + 3*A*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*b**3*x*cos(c + d*x)**4/8 + 3*A*b**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*b**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*C*a**3*sin(c + d*x)**3/(3*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a**2*b*x*sin(c + d*x)**4/8 + 9*C*a**2*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*C*a**2*b*x*cos(c + d*x)**4/8 + 9*C*a**2*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*C*a**2*b*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*a*b**2*sin(c + d*x)**5/(5*d) + 4*C*a*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*C*a*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*b**3*x*sin(c + d*x)**6/16 + 15*C*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*C*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*C*b**3*x*cos(c + d*x)**6/16 + 5*C*b**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*C*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*C*b**3*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**3*cos(c), True))","A",0
541,1,440,0,2.675078," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2),x)","\begin{cases} A a^{3} x + \frac{3 A a^{2} b \sin{\left(c + d x \right)}}{d} + \frac{3 A a b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C a^{2} b \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 C a^{2} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 C a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 C a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*x + 3*A*a**2*b*sin(c + d*x)/d + 3*A*a*b**2*x*sin(c + d*x)**2/2 + 3*A*a*b**2*x*cos(c + d*x)**2/2 + 3*A*a*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*b**3*sin(c + d*x)**3/(3*d) + A*b**3*sin(c + d*x)*cos(c + d*x)**2/d + C*a**3*x*sin(c + d*x)**2/2 + C*a**3*x*cos(c + d*x)**2/2 + C*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*a**2*b*sin(c + d*x)**3/d + 3*C*a**2*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a*b**2*x*sin(c + d*x)**4/8 + 9*C*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*C*a*b**2*x*cos(c + d*x)**4/8 + 9*C*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*C*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*b**3*sin(c + d*x)**5/(15*d) + 4*C*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**3*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**3, True))","A",0
542,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**3*sec(c + d*x), x)","F",0
543,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,1,850,0,8.040917," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{4} \sin{\left(c + d x \right)}}{d} + 2 A a^{3} b x \sin^{2}{\left(c + d x \right)} + 2 A a^{3} b x \cos^{2}{\left(c + d x \right)} + \frac{2 A a^{3} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 A a^{2} b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{6 A a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a b^{3} x \sin^{4}{\left(c + d x \right)}}{2} + 3 A a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 A a b^{3} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 A a b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 A a b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{8 A b^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A b^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A b^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{2 C a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a^{3} b x \sin^{4}{\left(c + d x \right)}}{2} + 3 C a^{3} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 C a^{3} b x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 C a^{3} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 C a^{3} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{16 C a^{2} b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{8 C a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{6 C a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a b^{3} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 C a b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{15 C a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + \frac{5 C a b^{3} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{5 C a b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{10 C a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{16 C b^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 C b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 C b^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{C b^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{4} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*sin(c + d*x)/d + 2*A*a**3*b*x*sin(c + d*x)**2 + 2*A*a**3*b*x*cos(c + d*x)**2 + 2*A*a**3*b*sin(c + d*x)*cos(c + d*x)/d + 4*A*a**2*b**2*sin(c + d*x)**3/d + 6*A*a**2*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a*b**3*x*sin(c + d*x)**4/2 + 3*A*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*A*a*b**3*x*cos(c + d*x)**4/2 + 3*A*a*b**3*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*A*a*b**3*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 8*A*b**4*sin(c + d*x)**5/(15*d) + 4*A*b**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*b**4*sin(c + d*x)*cos(c + d*x)**4/d + 2*C*a**4*sin(c + d*x)**3/(3*d) + C*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a**3*b*x*sin(c + d*x)**4/2 + 3*C*a**3*b*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*C*a**3*b*x*cos(c + d*x)**4/2 + 3*C*a**3*b*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*C*a**3*b*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 16*C*a**2*b**2*sin(c + d*x)**5/(5*d) + 8*C*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 6*C*a**2*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a*b**3*x*sin(c + d*x)**6/4 + 15*C*a*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 15*C*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 5*C*a*b**3*x*cos(c + d*x)**6/4 + 5*C*a*b**3*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 10*C*a*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 11*C*a*b**3*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 16*C*b**4*sin(c + d*x)**7/(35*d) + 8*C*b**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*C*b**4*sin(c + d*x)**3*cos(c + d*x)**4/d + C*b**4*sin(c + d*x)*cos(c + d*x)**6/d, Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**4*cos(c), True))","A",0
550,1,748,0,5.199864," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2),x)","\begin{cases} A a^{4} x + \frac{4 A a^{3} b \sin{\left(c + d x \right)}}{d} + 3 A a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} + 3 A a^{2} b^{2} x \cos^{2}{\left(c + d x \right)} + \frac{3 A a^{2} b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{8 A a b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 A a b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A b^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{8 C a^{3} b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 C a^{3} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{9 C a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{9 C a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{9 C a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{15 C a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{32 C a b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{16 C a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{4 C a b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 C b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 C b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 C b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 C b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 C b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(A + C \cos^{2}{\left(c \right)}\right) \left(a + b \cos{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*x + 4*A*a**3*b*sin(c + d*x)/d + 3*A*a**2*b**2*x*sin(c + d*x)**2 + 3*A*a**2*b**2*x*cos(c + d*x)**2 + 3*A*a**2*b**2*sin(c + d*x)*cos(c + d*x)/d + 8*A*a*b**3*sin(c + d*x)**3/(3*d) + 4*A*a*b**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*b**4*x*sin(c + d*x)**4/8 + 3*A*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*b**4*x*cos(c + d*x)**4/8 + 3*A*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a**4*x*sin(c + d*x)**2/2 + C*a**4*x*cos(c + d*x)**2/2 + C*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 8*C*a**3*b*sin(c + d*x)**3/(3*d) + 4*C*a**3*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a**2*b**2*x*sin(c + d*x)**4/4 + 9*C*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 9*C*a**2*b**2*x*cos(c + d*x)**4/4 + 9*C*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 15*C*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 32*C*a*b**3*sin(c + d*x)**5/(15*d) + 16*C*a*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 4*C*a*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*b**4*x*sin(c + d*x)**6/16 + 15*C*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*C*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*C*b**4*x*cos(c + d*x)**6/16 + 5*C*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*C*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*C*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(A + C*cos(c)**2)*(a + b*cos(c))**4, True))","A",0
551,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,1,321,0,2.385894," ","integrate((a+b*cos(d*x+c))**3*(a**2-b**2*cos(d*x+c)**2),x)","\begin{cases} a^{5} x + \frac{3 a^{4} b \sin{\left(c + d x \right)}}{d} + a^{3} b^{2} x \sin^{2}{\left(c + d x \right)} + a^{3} b^{2} x \cos^{2}{\left(c + d x \right)} + \frac{a^{3} b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{4 a^{2} b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{2 a^{2} b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{9 a b^{4} x \sin^{4}{\left(c + d x \right)}}{8} - \frac{9 a b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} - \frac{9 a b^{4} x \cos^{4}{\left(c + d x \right)}}{8} - \frac{9 a b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{15 a b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{8 b^{5} \sin^{5}{\left(c + d x \right)}}{15 d} - \frac{4 b^{5} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{b^{5} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{3} \left(a^{2} - b^{2} \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x + 3*a**4*b*sin(c + d*x)/d + a**3*b**2*x*sin(c + d*x)**2 + a**3*b**2*x*cos(c + d*x)**2 + a**3*b**2*sin(c + d*x)*cos(c + d*x)/d - 4*a**2*b**3*sin(c + d*x)**3/(3*d) - 2*a**2*b**3*sin(c + d*x)*cos(c + d*x)**2/d - 9*a*b**4*x*sin(c + d*x)**4/8 - 9*a*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 - 9*a*b**4*x*cos(c + d*x)**4/8 - 9*a*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 15*a*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 8*b**5*sin(c + d*x)**5/(15*d) - 4*b**5*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - b**5*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**3*(a**2 - b**2*cos(c)**2), True))","A",0
560,1,190,0,1.089897," ","integrate((a+b*cos(d*x+c))**2*(a**2-b**2*cos(d*x+c)**2),x)","\begin{cases} a^{4} x + \frac{2 a^{3} b \sin{\left(c + d x \right)}}{d} - \frac{4 a b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{2 a b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{3 b^{4} x \sin^{4}{\left(c + d x \right)}}{8} - \frac{3 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} - \frac{3 b^{4} x \cos^{4}{\left(c + d x \right)}}{8} - \frac{3 b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{5 b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \left(a^{2} - b^{2} \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 2*a**3*b*sin(c + d*x)/d - 4*a*b**3*sin(c + d*x)**3/(3*d) - 2*a*b**3*sin(c + d*x)*cos(c + d*x)**2/d - 3*b**4*x*sin(c + d*x)**4/8 - 3*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 - 3*b**4*x*cos(c + d*x)**4/8 - 3*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 5*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**2*(a**2 - b**2*cos(c)**2), True))","A",0
561,1,131,0,0.540545," ","integrate((a+b*cos(d*x+c))*(a**2-b**2*cos(d*x+c)**2),x)","\begin{cases} a^{3} x + \frac{a^{2} b \sin{\left(c + d x \right)}}{d} - \frac{a b^{2} x \sin^{2}{\left(c + d x \right)}}{2} - \frac{a b^{2} x \cos^{2}{\left(c + d x \right)}}{2} - \frac{a b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{2 b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(a^{2} - b^{2} \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + a**2*b*sin(c + d*x)/d - a*b**2*x*sin(c + d*x)**2/2 - a*b**2*x*cos(c + d*x)**2/2 - a*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) - 2*b**3*sin(c + d*x)**3/(3*d) - b**3*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))*(a**2 - b**2*cos(c)**2), True))","A",0
562,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,1,2518,0,129.159235," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + C \cos^{2}{\left(c \right)}\right)}{\cos{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{A}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{C d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{C d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{3 C \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{C}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: a = - b \\\frac{A x + \frac{C x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + C \cos^{2}{\left(c \right)}\right)}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} + \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} - \frac{C d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} - \frac{C d x}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} + \frac{C \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} + \frac{3 C \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} & \text{for}\: a = b \\\frac{A b^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{A b^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{A b^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{A b^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{C a^{2} d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{C a^{2} d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{C a^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{C a^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{C a^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{C a^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{C a b d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{C a b d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{2 C a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{2 C b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + C*cos(c)**2)/cos(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (A*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + A/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + C*d*x*tan(c/2 + d*x/2)**3/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + C*d*x*tan(c/2 + d*x/2)/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + 3*C*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + C/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)), Eq(a, -b)), ((A*x + C*x*sin(c + d*x)**2/2 + C*x*cos(c + d*x)**2/2 + C*sin(c + d*x)*cos(c + d*x)/(2*d))/a, Eq(b, 0)), (x*(A + C*cos(c)**2)/(a + b*cos(c)), Eq(d, 0)), (A*tan(c/2 + d*x/2)**3/(b*d*tan(c/2 + d*x/2)**2 + b*d) + A*tan(c/2 + d*x/2)/(b*d*tan(c/2 + d*x/2)**2 + b*d) - C*d*x*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**2 + b*d) - C*d*x/(b*d*tan(c/2 + d*x/2)**2 + b*d) + C*tan(c/2 + d*x/2)**3/(b*d*tan(c/2 + d*x/2)**2 + b*d) + 3*C*tan(c/2 + d*x/2)/(b*d*tan(c/2 + d*x/2)**2 + b*d), Eq(a, b)), (A*b**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + A*b**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - A*b**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - A*b**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - C*a**2*d*x*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - C*a**2*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + C*a**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + C*a**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - C*a**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - C*a**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + C*a*b*d*x*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + C*a*b*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + 2*C*a*b*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - 2*C*b**2*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
566,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
567,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
568,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
569,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**4/(a + b*cos(c + d*x)), x)","F",0
570,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x))**2, x)","F",0
575,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x))**2, x)","F",0
576,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a + b*cos(c + d*x))**2, x)","F",0
577,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x))**3, x)","F",0
583,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x))**3, x)","F",0
584,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,1,1039,0,125.897348," ","integrate((1-cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(1 - \cos^{2}{\left(c \right)}\right)}{\cos{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{x}{b} - \frac{\sin{\left(c + d x \right)}}{b d} & \text{for}\: a = - b \\\frac{- \frac{x \sin^{2}{\left(c + d x \right)}}{2} - \frac{x \cos^{2}{\left(c + d x \right)}}{2} + x - \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \left(1 - \cos^{2}{\left(c \right)}\right)}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{x}{b} - \frac{\sin{\left(c + d x \right)}}{b d} & \text{for}\: a = b \\\frac{a d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{2 b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(1 - cos(c)**2)/cos(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-x/b - sin(c + d*x)/(b*d), Eq(a, -b)), ((-x*sin(c + d*x)**2/2 - x*cos(c + d*x)**2/2 + x - sin(c + d*x)*cos(c + d*x)/(2*d))/a, Eq(b, 0)), (x*(1 - cos(c)**2)/(a + b*cos(c)), Eq(d, 0)), (x/b - sin(c + d*x)/(b*d), Eq(a, b)), (a*d*x*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) + a*d*x*sqrt(-a/(a - b) - b/(a - b))/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) - 2*b*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) - b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) - b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) + b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))) + b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + b**2*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
597,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c)),x)","- \int \left(- \frac{\sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)/(a + b*cos(c + d*x)), x) - Integral(cos(c + d*x)**2*sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
598,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","- \int \left(- \frac{\sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)**2/(a + b*cos(c + d*x)), x) - Integral(cos(c + d*x)**2*sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
599,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","- \int \left(- \frac{\sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)**3/(a + b*cos(c + d*x)), x) - Integral(cos(c + d*x)**2*sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
600,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","- \int \left(- \frac{\sec^{4}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)**4/(a + b*cos(c + d*x)), x) - Integral(cos(c + d*x)**2*sec(c + d*x)**4/(a + b*cos(c + d*x)), x)","F",0
601,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","- \int \left(- \frac{\sec{\left(c + d x \right)}}{a^{2} + 2 a b \cos{\left(c + d x \right)} + b^{2} \cos^{2}{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a^{2} + 2 a b \cos{\left(c + d x \right)} + b^{2} \cos^{2}{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)/(a**2 + 2*a*b*cos(c + d*x) + b**2*cos(c + d*x)**2), x) - Integral(cos(c + d*x)**2*sec(c + d*x)/(a**2 + 2*a*b*cos(c + d*x) + b**2*cos(c + d*x)**2), x)","F",0
607,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","- \int \left(- \frac{\sec^{2}{\left(c + d x \right)}}{a^{2} + 2 a b \cos{\left(c + d x \right)} + b^{2} \cos^{2}{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a^{2} + 2 a b \cos{\left(c + d x \right)} + b^{2} \cos^{2}{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)**2/(a**2 + 2*a*b*cos(c + d*x) + b**2*cos(c + d*x)**2), x) - Integral(cos(c + d*x)**2*sec(c + d*x)**2/(a**2 + 2*a*b*cos(c + d*x) + b**2*cos(c + d*x)**2), x)","F",0
608,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","- \int \left(- \frac{\sec^{3}{\left(c + d x \right)}}{a^{2} + 2 a b \cos{\left(c + d x \right)} + b^{2} \cos^{2}{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{a^{2} + 2 a b \cos{\left(c + d x \right)} + b^{2} \cos^{2}{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)**3/(a**2 + 2*a*b*cos(c + d*x) + b**2*cos(c + d*x)**2), x) - Integral(cos(c + d*x)**2*sec(c + d*x)**3/(a**2 + 2*a*b*cos(c + d*x) + b**2*cos(c + d*x)**2), x)","F",0
609,-1,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**3,x)","- \int \left(- \frac{\sec{\left(c + d x \right)}}{a^{3} + 3 a^{2} b \cos{\left(c + d x \right)} + 3 a b^{2} \cos^{2}{\left(c + d x \right)} + b^{3} \cos^{3}{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a^{3} + 3 a^{2} b \cos{\left(c + d x \right)} + 3 a b^{2} \cos^{2}{\left(c + d x \right)} + b^{3} \cos^{3}{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)/(a**3 + 3*a**2*b*cos(c + d*x) + 3*a*b**2*cos(c + d*x)**2 + b**3*cos(c + d*x)**3), x) - Integral(cos(c + d*x)**2*sec(c + d*x)/(a**3 + 3*a**2*b*cos(c + d*x) + 3*a*b**2*cos(c + d*x)**2 + b**3*cos(c + d*x)**3), x)","F",0
616,0,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","- \int \left(- \frac{\sec^{2}{\left(c + d x \right)}}{a^{3} + 3 a^{2} b \cos{\left(c + d x \right)} + 3 a b^{2} \cos^{2}{\left(c + d x \right)} + b^{3} \cos^{3}{\left(c + d x \right)}}\right)\, dx - \int \frac{\cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a^{3} + 3 a^{2} b \cos{\left(c + d x \right)} + 3 a b^{2} \cos^{2}{\left(c + d x \right)} + b^{3} \cos^{3}{\left(c + d x \right)}}\, dx"," ",0,"-Integral(-sec(c + d*x)**2/(a**3 + 3*a**2*b*cos(c + d*x) + 3*a*b**2*cos(c + d*x)**2 + b**3*cos(c + d*x)**3), x) - Integral(cos(c + d*x)**2*sec(c + d*x)**2/(a**3 + 3*a**2*b*cos(c + d*x) + 3*a*b**2*cos(c + d*x)**2 + b**3*cos(c + d*x)**3), x)","F",0
617,-1,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate((1-cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,1,32,0,0.682292," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\begin{cases} a x - \frac{b \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(a^{2} - b^{2} \cos^{2}{\left(c \right)}\right)}{a + b \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x - b*sin(c + d*x)/d, Ne(d, 0)), (x*(a**2 - b**2*cos(c)**2)/(a + b*cos(c)), True))","A",0
620,-1,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x)), x)","F",0
626,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)*(a+b*cos(d*x+c))**(1/2),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))*sec(c + d*x), x)","F",0
627,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2*(a+b*cos(d*x+c))**(1/2),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
628,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(a**2-b**2*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
647,0,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2),x)","\int \left(a - b \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a - b*cos(c + d*x))*(a + b*cos(c + d*x))**(3/2), x)","F",0
648,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/sqrt(a + b*cos(c + d*x)), x)","F",0
652,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
653,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/sqrt(a + b*cos(c + d*x)), x)","F",0
654,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**3/sqrt(a + b*cos(c + d*x)), x)","F",0
655,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
657,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
658,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
659,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
660,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x))**(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x))**(3/2), x)","F",0
662,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a + b*cos(c + d*x))**(3/2), x)","F",0
663,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
665,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
666,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
667,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
668,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
669,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
670,0,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\int \left(a - b \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((a - b*cos(c + d*x))*sqrt(a + b*cos(c + d*x)), x)","F",0
671,0,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{a - b \cos{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a - b*cos(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
672,-1,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
673,-1,0,0,0.000000," ","integrate((a**2-b**2*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
674,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
675,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
680,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
681,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
682,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
683,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
684,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
685,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
687,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
688,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
701,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
702,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
703,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
704,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
723,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
729,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
730,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(5/2), x)","F",0
731,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
737,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
738,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
751,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
752,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
754,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
756,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
758,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(5/2), x)","F",0
763,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
768,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
770,1,255,0,1.137798," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*b*sin(c + d*x)**3/(3*d) + B*b*sin(c + d*x)*cos(c + d*x)**2/d + 2*C*a*sin(c + d*x)**3/(3*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b*x*sin(c + d*x)**4/8 + 3*C*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b*x*cos(c + d*x)**4/8 + 3*C*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))*(B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
771,1,170,0,0.582014," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a \sin{\left(c + d x \right)}}{d} + \frac{B b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{C a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*sin(c + d*x)/d + B*b*x*sin(c + d*x)**2/2 + B*b*x*cos(c + d*x)**2/2 + B*b*sin(c + d*x)*cos(c + d*x)/(2*d) + C*a*x*sin(c + d*x)**2/2 + C*a*x*cos(c + d*x)**2/2 + C*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*b*sin(c + d*x)**3/(3*d) + C*b*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))*(B*cos(c) + C*cos(c)**2), True))","A",0
772,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*(a + b*cos(c + d*x))*cos(c + d*x)*sec(c + d*x), x)","F",0
773,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*(a + b*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2, x)","F",0
774,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*(a + b*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**3, x)","F",0
775,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
776,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
777,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,1,462,0,2.910323," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 B a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 B a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 C a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a b x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 C a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{5 C a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{8 C b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**2*x*sin(c + d*x)**2/2 + B*a**2*x*cos(c + d*x)**2/2 + B*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 4*B*a*b*sin(c + d*x)**3/(3*d) + 2*B*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*b**2*x*sin(c + d*x)**4/8 + 3*B*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*b**2*x*cos(c + d*x)**4/8 + 3*B*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*C*a**2*sin(c + d*x)**3/(3*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a*b*x*sin(c + d*x)**4/4 + 3*C*a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*C*a*b*x*cos(c + d*x)**4/4 + 3*C*a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 5*C*a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 8*C*b**2*sin(c + d*x)**5/(15*d) + 4*C*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**2*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**2*(B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
779,1,340,0,1.353494," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a^{2} \sin{\left(c + d x \right)}}{d} + B a b x \sin^{2}{\left(c + d x \right)} + B a b x \cos^{2}{\left(c + d x \right)} + \frac{B a b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{2 B b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 C a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 C a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**2*sin(c + d*x)/d + B*a*b*x*sin(c + d*x)**2 + B*a*b*x*cos(c + d*x)**2 + B*a*b*sin(c + d*x)*cos(c + d*x)/d + 2*B*b**2*sin(c + d*x)**3/(3*d) + B*b**2*sin(c + d*x)*cos(c + d*x)**2/d + C*a**2*x*sin(c + d*x)**2/2 + C*a**2*x*cos(c + d*x)**2/2 + C*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 4*C*a*b*sin(c + d*x)**3/(3*d) + 2*C*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b**2*x*sin(c + d*x)**4/8 + 3*C*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b**2*x*cos(c + d*x)**4/8 + 3*C*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**2*(B*cos(c) + C*cos(c)**2), True))","A",0
780,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2} \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*(a + b*cos(c + d*x))**2*cos(c + d*x)*sec(c + d*x), x)","F",0
781,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2} \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*(a + b*cos(c + d*x))**2*cos(c + d*x)*sec(c + d*x)**2, x)","F",0
782,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
783,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
784,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
785,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
786,1,552,0,3.090079," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{B a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 B a^{2} b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B a b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 B a b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B b^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B b^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C a^{2} b \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 C a^{2} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 C a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 C a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{3} \left(B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**3*sin(c + d*x)/d + 3*B*a**2*b*x*sin(c + d*x)**2/2 + 3*B*a**2*b*x*cos(c + d*x)**2/2 + 3*B*a**2*b*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*a*b**2*sin(c + d*x)**3/d + 3*B*a*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*b**3*x*sin(c + d*x)**4/8 + 3*B*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*b**3*x*cos(c + d*x)**4/8 + 3*B*b**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*b**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a**3*x*sin(c + d*x)**2/2 + C*a**3*x*cos(c + d*x)**2/2 + C*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*a**2*b*sin(c + d*x)**3/d + 3*C*a**2*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a*b**2*x*sin(c + d*x)**4/8 + 9*C*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*C*a*b**2*x*cos(c + d*x)**4/8 + 9*C*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*C*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*b**3*sin(c + d*x)**5/(15*d) + 4*C*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**3*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**3*(B*cos(c) + C*cos(c)**2), True))","A",0
787,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{3} \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*(a + b*cos(c + d*x))**3*cos(c + d*x)*sec(c + d*x), x)","F",0
788,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
789,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
790,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
791,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
792,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
793,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
794,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
795,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
796,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c)),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
798,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
799,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
800,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**4/(a + b*cos(c + d*x)), x)","F",0
801,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
802,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)/(a + b*cos(c + d*x))**2, x)","F",0
805,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2/(a + b*cos(c + d*x))**2, x)","F",0
806,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**3/(a + b*cos(c + d*x))**2, x)","F",0
807,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)/(a + b*cos(c + d*x))**3, x)","F",0
812,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2/(a + b*cos(c + d*x))**3, x)","F",0
813,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*cos(c + d*x), x)","F",0
816,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*cos(c + d*x)*sec(c + d*x), x)","F",0
817,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2, x)","F",0
818,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
824,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
837,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
838,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2/sqrt(a + b*cos(c + d*x)), x)","F",0
839,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**3/sqrt(a + b*cos(c + d*x)), x)","F",0
840,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
843,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)/(a + b*cos(c + d*x))**(3/2), x)","F",0
845,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**2/(a + b*cos(c + d*x))**(3/2), x)","F",0
846,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sec(c + d*x)**3/(a + b*cos(c + d*x))**(3/2), x)","F",0
847,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x)), x)","F",0
899,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(a + b*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
900,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
901,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
913,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
914,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
915,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
916,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
917,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
922,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(cos(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
923,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{B + C \cos{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
924,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{B + C \cos{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
925,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
928,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
929,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
930,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{B + C \cos{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))/((a + b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
931,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
932,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
933,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
934,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)**(3/2)/(a + b*cos(c + d*x))**(5/2), x)","F",0
935,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(5/2), x)","F",0
936,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
937,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
938,1,428,0,2.543351," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 B a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 C a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*b*sin(c + d*x)**3/(3*d) + A*b*sin(c + d*x)*cos(c + d*x)**2/d + 2*B*a*sin(c + d*x)**3/(3*d) + B*a*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*b*x*sin(c + d*x)**4/8 + 3*B*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*b*x*cos(c + d*x)**4/8 + 3*B*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*b*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*C*a*x*sin(c + d*x)**4/8 + 3*C*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*a*x*cos(c + d*x)**4/8 + 3*C*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*b*sin(c + d*x)**5/(15*d) + 4*C*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))*(A + B*cos(c) + C*cos(c)**2)*cos(c)**2, True))","A",0
939,1,320,0,1.221361," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a \sin{\left(c + d x \right)}}{d} + \frac{A b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 C a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*sin(c + d*x)/d + A*b*x*sin(c + d*x)**2/2 + A*b*x*cos(c + d*x)**2/2 + A*b*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*b*sin(c + d*x)**3/(3*d) + B*b*sin(c + d*x)*cos(c + d*x)**2/d + 2*C*a*sin(c + d*x)**3/(3*d) + C*a*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b*x*sin(c + d*x)**4/8 + 3*C*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b*x*cos(c + d*x)**4/8 + 3*C*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
940,1,189,0,0.599140," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} A a x + \frac{A b \sin{\left(c + d x \right)}}{d} + \frac{B a \sin{\left(c + d x \right)}}{d} + \frac{B b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{C a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x + A*b*sin(c + d*x)/d + B*a*sin(c + d*x)/d + B*b*x*sin(c + d*x)**2/2 + B*b*x*cos(c + d*x)**2/2 + B*b*sin(c + d*x)*cos(c + d*x)/(2*d) + C*a*x*sin(c + d*x)**2/2 + C*a*x*cos(c + d*x)**2/2 + C*a*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*b*sin(c + d*x)**3/(3*d) + C*b*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))*(A + B*cos(c) + C*cos(c)**2), True))","A",0
941,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
942,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2, x)","F",0
943,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3, x)","F",0
944,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
945,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
946,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
947,1,570,0,3.151410," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{2} \sin{\left(c + d x \right)}}{d} + A a b x \sin^{2}{\left(c + d x \right)} + A a b x \cos^{2}{\left(c + d x \right)} + \frac{A a b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{2 A b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 B a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 B a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 C a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 C a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 C a b x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 C a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{5 C a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{8 C b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*sin(c + d*x)/d + A*a*b*x*sin(c + d*x)**2 + A*a*b*x*cos(c + d*x)**2 + A*a*b*sin(c + d*x)*cos(c + d*x)/d + 2*A*b**2*sin(c + d*x)**3/(3*d) + A*b**2*sin(c + d*x)*cos(c + d*x)**2/d + B*a**2*x*sin(c + d*x)**2/2 + B*a**2*x*cos(c + d*x)**2/2 + B*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 4*B*a*b*sin(c + d*x)**3/(3*d) + 2*B*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*b**2*x*sin(c + d*x)**4/8 + 3*B*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*b**2*x*cos(c + d*x)**4/8 + 3*B*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*C*a**2*sin(c + d*x)**3/(3*d) + C*a**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a*b*x*sin(c + d*x)**4/4 + 3*C*a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*C*a*b*x*cos(c + d*x)**4/4 + 3*C*a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 5*C*a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 8*C*b**2*sin(c + d*x)**5/(15*d) + 4*C*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**2*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**2*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
948,1,420,0,1.550140," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} A a^{2} x + \frac{2 A a b \sin{\left(c + d x \right)}}{d} + \frac{A b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a^{2} \sin{\left(c + d x \right)}}{d} + B a b x \sin^{2}{\left(c + d x \right)} + B a b x \cos^{2}{\left(c + d x \right)} + \frac{B a b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{2 B b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{C a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 C a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 C a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x + 2*A*a*b*sin(c + d*x)/d + A*b**2*x*sin(c + d*x)**2/2 + A*b**2*x*cos(c + d*x)**2/2 + A*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a**2*sin(c + d*x)/d + B*a*b*x*sin(c + d*x)**2 + B*a*b*x*cos(c + d*x)**2 + B*a*b*sin(c + d*x)*cos(c + d*x)/d + 2*B*b**2*sin(c + d*x)**3/(3*d) + B*b**2*sin(c + d*x)*cos(c + d*x)**2/d + C*a**2*x*sin(c + d*x)**2/2 + C*a**2*x*cos(c + d*x)**2/2 + C*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 4*C*a*b*sin(c + d*x)**3/(3*d) + 2*C*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b**2*x*sin(c + d*x)**4/8 + 3*C*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b**2*x*cos(c + d*x)**4/8 + 3*C*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**2*(A + B*cos(c) + C*cos(c)**2), True))","A",0
949,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
950,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2, x)","F",0
951,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
952,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
953,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
954,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
955,1,966,0,6.084913," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 A a^{2} b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A a b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 A a b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A b^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A b^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{B a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B a^{2} b \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 B a^{2} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 B a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 B a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 B a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 B a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 B a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 B b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{B b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{2 C a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{2} b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{2} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 C a^{2} b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 C a^{2} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 C a^{2} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C a b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{4 C a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C b^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 C b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 C b^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 C b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 C b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 C b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{3} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sin(c + d*x)/d + 3*A*a**2*b*x*sin(c + d*x)**2/2 + 3*A*a**2*b*x*cos(c + d*x)**2/2 + 3*A*a**2*b*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*a*b**2*sin(c + d*x)**3/d + 3*A*a*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*b**3*x*sin(c + d*x)**4/8 + 3*A*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*b**3*x*cos(c + d*x)**4/8 + 3*A*b**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*b**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + B*a**3*x*sin(c + d*x)**2/2 + B*a**3*x*cos(c + d*x)**2/2 + B*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*a**2*b*sin(c + d*x)**3/d + 3*B*a**2*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*B*a*b**2*x*sin(c + d*x)**4/8 + 9*B*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*B*a*b**2*x*cos(c + d*x)**4/8 + 9*B*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*B*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*B*b**3*sin(c + d*x)**5/(15*d) + 4*B*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + B*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 2*C*a**3*sin(c + d*x)**3/(3*d) + C*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a**2*b*x*sin(c + d*x)**4/8 + 9*C*a**2*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*C*a**2*b*x*cos(c + d*x)**4/8 + 9*C*a**2*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*C*a**2*b*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*a*b**2*sin(c + d*x)**5/(5*d) + 4*C*a*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*C*a*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*b**3*x*sin(c + d*x)**6/16 + 15*C*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*C*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*C*b**3*x*cos(c + d*x)**6/16 + 5*C*b**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*C*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*C*b**3*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*cos(c))**3*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
956,1,685,0,3.510567," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} A a^{3} x + \frac{3 A a^{2} b \sin{\left(c + d x \right)}}{d} + \frac{3 A a b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 B a^{2} b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a^{2} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B a b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 B a b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B b^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B b^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{C a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C a^{2} b \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 C a^{2} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 C a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 C a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{3} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*x + 3*A*a**2*b*sin(c + d*x)/d + 3*A*a*b**2*x*sin(c + d*x)**2/2 + 3*A*a*b**2*x*cos(c + d*x)**2/2 + 3*A*a*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*b**3*sin(c + d*x)**3/(3*d) + A*b**3*sin(c + d*x)*cos(c + d*x)**2/d + B*a**3*sin(c + d*x)/d + 3*B*a**2*b*x*sin(c + d*x)**2/2 + 3*B*a**2*b*x*cos(c + d*x)**2/2 + 3*B*a**2*b*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*a*b**2*sin(c + d*x)**3/d + 3*B*a*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*b**3*x*sin(c + d*x)**4/8 + 3*B*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*b**3*x*cos(c + d*x)**4/8 + 3*B*b**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*b**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + C*a**3*x*sin(c + d*x)**2/2 + C*a**3*x*cos(c + d*x)**2/2 + C*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*a**2*b*sin(c + d*x)**3/d + 3*C*a**2*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a*b**2*x*sin(c + d*x)**4/8 + 9*C*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*C*a*b**2*x*cos(c + d*x)**4/8 + 9*C*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*C*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*b**3*sin(c + d*x)**5/(15*d) + 4*C*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**3*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**3*(A + B*cos(c) + C*cos(c)**2), True))","A",0
957,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{3} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
958,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
959,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
960,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
961,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
962,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
963,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
964,1,1334,0,10.602411," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} \frac{A a^{4} \sin{\left(c + d x \right)}}{d} + 2 A a^{3} b x \sin^{2}{\left(c + d x \right)} + 2 A a^{3} b x \cos^{2}{\left(c + d x \right)} + \frac{2 A a^{3} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 A a^{2} b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{6 A a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A a b^{3} x \sin^{4}{\left(c + d x \right)}}{2} + 3 A a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 A a b^{3} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 A a b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 A a b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{8 A b^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A b^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A b^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{B a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{8 B a^{3} b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 B a^{3} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 B a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{9 B a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{9 B a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{9 B a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{15 B a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{32 B a b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{16 B a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{4 B a b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 B b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 B b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 B b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 B b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 B b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 B b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{2 C a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C a^{3} b x \sin^{4}{\left(c + d x \right)}}{2} + 3 C a^{3} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 C a^{3} b x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 C a^{3} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 C a^{3} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{16 C a^{2} b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{8 C a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{6 C a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C a b^{3} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 C a b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{15 C a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + \frac{5 C a b^{3} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{5 C a b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{10 C a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{11 C a b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{16 C b^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 C b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 C b^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{C b^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{4} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*sin(c + d*x)/d + 2*A*a**3*b*x*sin(c + d*x)**2 + 2*A*a**3*b*x*cos(c + d*x)**2 + 2*A*a**3*b*sin(c + d*x)*cos(c + d*x)/d + 4*A*a**2*b**2*sin(c + d*x)**3/d + 6*A*a**2*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*a*b**3*x*sin(c + d*x)**4/2 + 3*A*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*A*a*b**3*x*cos(c + d*x)**4/2 + 3*A*a*b**3*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*A*a*b**3*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 8*A*b**4*sin(c + d*x)**5/(15*d) + 4*A*b**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*b**4*sin(c + d*x)*cos(c + d*x)**4/d + B*a**4*x*sin(c + d*x)**2/2 + B*a**4*x*cos(c + d*x)**2/2 + B*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 8*B*a**3*b*sin(c + d*x)**3/(3*d) + 4*B*a**3*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*B*a**2*b**2*x*sin(c + d*x)**4/4 + 9*B*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 9*B*a**2*b**2*x*cos(c + d*x)**4/4 + 9*B*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 15*B*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 32*B*a*b**3*sin(c + d*x)**5/(15*d) + 16*B*a*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 4*B*a*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*b**4*x*sin(c + d*x)**6/16 + 15*B*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*B*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*B*b**4*x*cos(c + d*x)**6/16 + 5*B*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*B*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*B*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 2*C*a**4*sin(c + d*x)**3/(3*d) + C*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*a**3*b*x*sin(c + d*x)**4/2 + 3*C*a**3*b*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*C*a**3*b*x*cos(c + d*x)**4/2 + 3*C*a**3*b*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*C*a**3*b*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 16*C*a**2*b**2*sin(c + d*x)**5/(5*d) + 8*C*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 6*C*a**2*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*a*b**3*x*sin(c + d*x)**6/4 + 15*C*a*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 15*C*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 5*C*a*b**3*x*cos(c + d*x)**6/4 + 5*C*a*b**3*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 10*C*a*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 11*C*a*b**3*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 16*C*b**4*sin(c + d*x)**7/(35*d) + 8*C*b**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*C*b**4*sin(c + d*x)**3*cos(c + d*x)**4/d + C*b**4*sin(c + d*x)*cos(c + d*x)**6/d, Ne(d, 0)), (x*(a + b*cos(c))**4*(A + B*cos(c) + C*cos(c)**2)*cos(c), True))","A",0
965,1,1066,0,6.719232," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\begin{cases} A a^{4} x + \frac{4 A a^{3} b \sin{\left(c + d x \right)}}{d} + 3 A a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} + 3 A a^{2} b^{2} x \cos^{2}{\left(c + d x \right)} + \frac{3 A a^{2} b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{8 A a b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 A a b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 A b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A b^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{B a^{4} \sin{\left(c + d x \right)}}{d} + 2 B a^{3} b x \sin^{2}{\left(c + d x \right)} + 2 B a^{3} b x \cos^{2}{\left(c + d x \right)} + \frac{2 B a^{3} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 B a^{2} b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{6 B a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B a b^{3} x \sin^{4}{\left(c + d x \right)}}{2} + 3 B a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 B a b^{3} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 B a b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 B a b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{8 B b^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B b^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{B b^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{C a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{8 C a^{3} b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 C a^{3} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{9 C a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{9 C a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{9 C a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{15 C a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{32 C a b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{16 C a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{4 C a b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 C b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 C b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 C b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 C b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 C b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 C b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 C b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{4} \left(A + B \cos{\left(c \right)} + C \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*x + 4*A*a**3*b*sin(c + d*x)/d + 3*A*a**2*b**2*x*sin(c + d*x)**2 + 3*A*a**2*b**2*x*cos(c + d*x)**2 + 3*A*a**2*b**2*sin(c + d*x)*cos(c + d*x)/d + 8*A*a*b**3*sin(c + d*x)**3/(3*d) + 4*A*a*b**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*A*b**4*x*sin(c + d*x)**4/8 + 3*A*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*b**4*x*cos(c + d*x)**4/8 + 3*A*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) + B*a**4*sin(c + d*x)/d + 2*B*a**3*b*x*sin(c + d*x)**2 + 2*B*a**3*b*x*cos(c + d*x)**2 + 2*B*a**3*b*sin(c + d*x)*cos(c + d*x)/d + 4*B*a**2*b**2*sin(c + d*x)**3/d + 6*B*a**2*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*a*b**3*x*sin(c + d*x)**4/2 + 3*B*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*B*a*b**3*x*cos(c + d*x)**4/2 + 3*B*a*b**3*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*B*a*b**3*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 8*B*b**4*sin(c + d*x)**5/(15*d) + 4*B*b**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + B*b**4*sin(c + d*x)*cos(c + d*x)**4/d + C*a**4*x*sin(c + d*x)**2/2 + C*a**4*x*cos(c + d*x)**2/2 + C*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 8*C*a**3*b*sin(c + d*x)**3/(3*d) + 4*C*a**3*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a**2*b**2*x*sin(c + d*x)**4/4 + 9*C*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 9*C*a**2*b**2*x*cos(c + d*x)**4/4 + 9*C*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 15*C*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 32*C*a*b**3*sin(c + d*x)**5/(15*d) + 16*C*a*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 4*C*a*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*C*b**4*x*sin(c + d*x)**6/16 + 15*C*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*C*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*C*b**4*x*cos(c + d*x)**6/16 + 5*C*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*C*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*C*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*cos(c))**4*(A + B*cos(c) + C*cos(c)**2), True))","A",0
966,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
967,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
968,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
969,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
970,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
971,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
972,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
973,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
974,1,619,0,3.165392," ","integrate((a+b*cos(d*x+c))**3*(a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2),x)","\begin{cases} B a^{4} b x + \frac{4 B a^{3} b^{2} \sin{\left(c + d x \right)}}{d} + 3 B a^{2} b^{3} x \sin^{2}{\left(c + d x \right)} + 3 B a^{2} b^{3} x \cos^{2}{\left(c + d x \right)} + \frac{3 B a^{2} b^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{8 B a b^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 B a b^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B b^{5} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{5} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 B b^{5} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 B b^{5} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 B b^{5} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - C a^{5} x - \frac{3 C a^{4} b \sin{\left(c + d x \right)}}{d} - C a^{3} b^{2} x \sin^{2}{\left(c + d x \right)} - C a^{3} b^{2} x \cos^{2}{\left(c + d x \right)} - \frac{C a^{3} b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 C a^{2} b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 C a^{2} b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 C a b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 C a b^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 C a b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 C a b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 C b^{5} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 C b^{5} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{C b^{5} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{3} \left(B a b + B b^{2} \cos{\left(c \right)} - C a^{2} + C b^{2} \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**4*b*x + 4*B*a**3*b**2*sin(c + d*x)/d + 3*B*a**2*b**3*x*sin(c + d*x)**2 + 3*B*a**2*b**3*x*cos(c + d*x)**2 + 3*B*a**2*b**3*sin(c + d*x)*cos(c + d*x)/d + 8*B*a*b**4*sin(c + d*x)**3/(3*d) + 4*B*a*b**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*b**5*x*sin(c + d*x)**4/8 + 3*B*b**5*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*B*b**5*x*cos(c + d*x)**4/8 + 3*B*b**5*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*B*b**5*sin(c + d*x)*cos(c + d*x)**3/(8*d) - C*a**5*x - 3*C*a**4*b*sin(c + d*x)/d - C*a**3*b**2*x*sin(c + d*x)**2 - C*a**3*b**2*x*cos(c + d*x)**2 - C*a**3*b**2*sin(c + d*x)*cos(c + d*x)/d + 4*C*a**2*b**3*sin(c + d*x)**3/(3*d) + 2*C*a**2*b**3*sin(c + d*x)*cos(c + d*x)**2/d + 9*C*a*b**4*x*sin(c + d*x)**4/8 + 9*C*a*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*C*a*b**4*x*cos(c + d*x)**4/8 + 9*C*a*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*C*a*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*C*b**5*sin(c + d*x)**5/(15*d) + 4*C*b**5*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + C*b**5*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**3*(B*a*b + B*b**2*cos(c) - C*a**2 + C*b**2*cos(c)**2), True))","A",0
975,1,357,0,1.359243," ","integrate((a+b*cos(d*x+c))**2*(a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2),x)","\begin{cases} B a^{3} b x + \frac{3 B a^{2} b^{2} \sin{\left(c + d x \right)}}{d} + \frac{3 B a b^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 B a b^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a b^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 B b^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B b^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - C a^{4} x - \frac{2 C a^{3} b \sin{\left(c + d x \right)}}{d} + \frac{4 C a b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 C a b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 C b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 C b^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 C b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 C b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \left(B a b + B b^{2} \cos{\left(c \right)} - C a^{2} + C b^{2} \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**3*b*x + 3*B*a**2*b**2*sin(c + d*x)/d + 3*B*a*b**3*x*sin(c + d*x)**2/2 + 3*B*a*b**3*x*cos(c + d*x)**2/2 + 3*B*a*b**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*B*b**4*sin(c + d*x)**3/(3*d) + B*b**4*sin(c + d*x)*cos(c + d*x)**2/d - C*a**4*x - 2*C*a**3*b*sin(c + d*x)/d + 4*C*a*b**3*sin(c + d*x)**3/(3*d) + 2*C*a*b**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*C*b**4*x*sin(c + d*x)**4/8 + 3*C*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*C*b**4*x*cos(c + d*x)**4/8 + 3*C*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*C*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**2*(B*a*b + B*b**2*cos(c) - C*a**2 + C*b**2*cos(c)**2), True))","A",0
976,1,241,0,0.672253," ","integrate((a+b*cos(d*x+c))*(a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2),x)","\begin{cases} B a^{2} b x + \frac{2 B a b^{2} \sin{\left(c + d x \right)}}{d} + \frac{B b^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B b^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B b^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - C a^{3} x - \frac{C a^{2} b \sin{\left(c + d x \right)}}{d} + \frac{C a b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{C a b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{C a b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 C b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{C b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \left(B a b + B b^{2} \cos{\left(c \right)} - C a^{2} + C b^{2} \cos^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**2*b*x + 2*B*a*b**2*sin(c + d*x)/d + B*b**3*x*sin(c + d*x)**2/2 + B*b**3*x*cos(c + d*x)**2/2 + B*b**3*sin(c + d*x)*cos(c + d*x)/(2*d) - C*a**3*x - C*a**2*b*sin(c + d*x)/d + C*a*b**2*x*sin(c + d*x)**2/2 + C*a*b**2*x*cos(c + d*x)**2/2 + C*a*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*C*b**3*sin(c + d*x)**3/(3*d) + C*b**3*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))*(B*a*b + B*b**2*cos(c) - C*a**2 + C*b**2*cos(c)**2), True))","A",0
977,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
978,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
979,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
980,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
981,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
982,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
983,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
984,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**4/(a + b*cos(c + d*x)), x)","F",0
985,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
986,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
987,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
988,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
989,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
990,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x))**2, x)","F",0
991,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x))**2, x)","F",0
992,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a + b*cos(c + d*x))**2, x)","F",0
993,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
994,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
995,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
996,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
997,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
998,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x))**3, x)","F",0
999,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x))**3, x)","F",0
1000,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1001,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1002,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1003,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1004,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1005,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1006,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1007,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1008,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1009,1,58,0,0.686687," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\begin{cases} B b x - C a x + \frac{C b \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a b + B b^{2} \cos{\left(c \right)} - C a^{2} + C b^{2} \cos^{2}{\left(c \right)}\right)}{a + b \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*b*x - C*a*x + C*b*sin(c + d*x)/d, Ne(d, 0)), (x*(B*a*b + B*b**2*cos(c) - C*a**2 + C*b**2*cos(c)**2)/(a + b*cos(c)), True))","A",0
1010,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1011,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1012,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1013,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1014,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1015,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1016,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2), x)","F",0
1017,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x), x)","F",0
1018,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2, x)","F",0
1019,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1020,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1022,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1023,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1024,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1027,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1030,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1031,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1032,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1033,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1034,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1035,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1036,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1037,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1038,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1039,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2),x)","- \int C a^{2} \sqrt{a + b \cos{\left(c + d x \right)}}\, dx - \int \left(- B a b \sqrt{a + b \cos{\left(c + d x \right)}}\right)\, dx - \int \left(- B b^{2} \sqrt{a + b \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)}\right)\, dx - \int \left(- C b^{2} \sqrt{a + b \cos{\left(c + d x \right)}} \cos^{2}{\left(c + d x \right)}\right)\, dx"," ",0,"-Integral(C*a**2*sqrt(a + b*cos(c + d*x)), x) - Integral(-B*a*b*sqrt(a + b*cos(c + d*x)), x) - Integral(-B*b**2*sqrt(a + b*cos(c + d*x))*cos(c + d*x), x) - Integral(-C*b**2*sqrt(a + b*cos(c + d*x))*cos(c + d*x)**2, x)","F",0
1040,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1041,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1042,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(a + b*cos(c + d*x)), x)","F",0
1043,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
1044,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/sqrt(a + b*cos(c + d*x)), x)","F",0
1045,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3/sqrt(a + b*cos(c + d*x)), x)","F",0
1046,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**4/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1047,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1048,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1049,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1050,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)/(a + b*cos(c + d*x))**(3/2), x)","F",0
1051,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**2/(a + b*cos(c + d*x))**(3/2), x)","F",0
1052,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sec(c + d*x)**3/(a + b*cos(c + d*x))**(3/2), x)","F",0
1053,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1054,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1055,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1056,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1057,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1058,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**2/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1059,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**3/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1060,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1061,0,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","- \int \left(- B b \sqrt{a + b \cos{\left(c + d x \right)}}\right)\, dx - \int C a \sqrt{a + b \cos{\left(c + d x \right)}}\, dx - \int \left(- C b \sqrt{a + b \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)}\right)\, dx"," ",0,"-Integral(-B*b*sqrt(a + b*cos(c + d*x)), x) - Integral(C*a*sqrt(a + b*cos(c + d*x)), x) - Integral(-C*b*sqrt(a + b*cos(c + d*x))*cos(c + d*x), x)","F",0
1062,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1063,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1064,-1,0,0,0.000000," ","integrate((a*b*B-a**2*C+b**2*B*cos(d*x+c)+b**2*C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1067,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1068,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1069,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1070,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1071,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1072,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1073,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1074,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1075,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1076,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1077,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1078,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1079,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1080,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1081,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1082,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1083,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1084,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1085,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1086,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1087,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1089,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1090,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1091,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1092,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1093,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1094,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1095,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1096,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1097,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1098,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1099,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1100,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1101,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1103,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1104,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1105,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1106,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1107,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1108,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1109,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1111,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1112,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1113,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1115,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1116,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1117,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(cos(c + d*x)), x)","F",0
1118,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/cos(c + d*x)**(3/2), x)","F",0
1119,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/cos(c + d*x)**(5/2), x)","F",0
1120,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1121,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1122,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1123,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1124,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1125,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1127,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1128,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1129,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1130,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1131,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1132,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1133,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1134,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1135,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1136,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1137,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1138,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
1139,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
1140,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1141,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1142,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(9/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1143,-1,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1144,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c)+2*b*cos(d*x+c)**2)/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{a \cos{\left(c + d x \right)} + a + 2 b \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a + 2*b*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
1145,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1146,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1147,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
1148,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1149,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1150,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1152,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(5/2), x)","F",0
1153,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1156,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1157,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1158,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1159,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1160,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1161,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1163,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1164,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","a \left(\int A \sqrt{\sec{\left(c + d x \right)}}\, dx + \int A \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(A*sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**3*sqrt(sec(c + d*x)), x))","F",0
1165,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","a \left(\int \frac{A}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{A \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a*(Integral(A/sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**3/sqrt(sec(c + d*x)), x))","F",0
1166,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","a \left(\int \frac{A}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{A \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(A/sec(c + d*x)**(3/2), x) + Integral(A*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**3/sec(c + d*x)**(3/2), x))","F",0
1167,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1169,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1170,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1171,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1172,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","a^{2} \left(\int A \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 2 A \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int A \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a**2*(Integral(A*sqrt(sec(c + d*x)), x) + Integral(2*A*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(2*C*cos(c + d*x)**3*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**4*sqrt(sec(c + d*x)), x))","F",0
1173,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","a^{2} \left(\int \frac{A}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{2 A \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{A \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{2 C \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{4}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**2*(Integral(A/sqrt(sec(c + d*x)), x) + Integral(2*A*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(2*C*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**4/sqrt(sec(c + d*x)), x))","F",0
1174,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","a^{2} \left(\int \frac{A}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{2 A \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{A \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{2 C \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{4}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a**2*(Integral(A/sec(c + d*x)**(3/2), x) + Integral(2*A*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(A*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(2*C*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**4/sec(c + d*x)**(3/2), x))","F",0
1175,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1176,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1177,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1178,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1179,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1180,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1181,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1182,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","a^{3} \left(\int \frac{A}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 A \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 A \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{A \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 C \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 C \cos^{4}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{5}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**3*(Integral(A/sqrt(sec(c + d*x)), x) + Integral(3*A*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(3*A*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(3*C*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(3*C*cos(c + d*x)**4/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**5/sqrt(sec(c + d*x)), x))","F",0
1183,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","a^{3} \left(\int \frac{A}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 A \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 A \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{A \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 C \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 C \cos^{4}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{5}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a**3*(Integral(A/sec(c + d*x)**(3/2), x) + Integral(3*A*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(3*A*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(A*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(3*C*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(3*C*cos(c + d*x)**4/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**5/sec(c + d*x)**(3/2), x))","F",0
1184,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1185,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1186,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1187,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sqrt{\sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sqrt(sec(c + d*x))/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x))/(cos(c + d*x) + 1), x))/a","F",0
1188,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\frac{\int \frac{A}{\cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a}"," ",0,"(Integral(A/(cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x) + Integral(C*cos(c + d*x)**2/(cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x))/a","F",0
1189,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\frac{\int \frac{A}{\cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"(Integral(A/(cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x) + Integral(C*cos(c + d*x)**2/(cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x))/a","F",0
1190,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1191,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1192,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1193,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sqrt{\sec{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sqrt(sec(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
1194,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\frac{\int \frac{A}{\cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"(Integral(A/(cos(c + d*x)**2*sqrt(sec(c + d*x)) + 2*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x) + Integral(C*cos(c + d*x)**2/(cos(c + d*x)**2*sqrt(sec(c + d*x)) + 2*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x))/a**2","F",0
1195,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1196,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1197,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1198,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1199,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sqrt{\sec{\left(c + d x \right)}}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A*sqrt(sec(c + d*x))/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x))/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
1200,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1201,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1202,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1203,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1204,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1205,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1206,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1207,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1208,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1209,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)*sec(d*x+c)**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x)), x)","F",0
1210,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1211,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + C \cos^{2}{\left(c + d x \right)}\right)}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + C*cos(c + d*x)**2)/sec(c + d*x)**(3/2), x)","F",0
1212,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1213,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1214,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1215,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1216,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1217,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1218,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1219,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1220,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1221,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1222,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1223,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1224,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1225,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1226,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1227,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1228,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1229,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1232,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1234,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1235,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
1237,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*sqrt(sec(c + d*x))), x)","F",0
1238,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x)**(3/2)), x)","F",0
1239,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1243,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
1244,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
1245,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1246,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1248,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1250,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1251,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1252,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1253,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1254,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1256,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1257,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\int \left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)*sqrt(sec(c + d*x)), x)","F",0
1258,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)/sqrt(sec(c + d*x)), x)","F",0
1259,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(B + C \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((B + C*cos(c + d*x))*cos(c + d*x)/sec(c + d*x)**(3/2), x)","F",0
1260,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1261,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1262,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1263,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\int \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x)), x)","F",0
1264,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1265,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sec(c + d*x)**(3/2), x)","F",0
1266,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1267,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1268,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1269,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1270,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","a \left(\int A \sqrt{\sec{\left(c + d x \right)}}\, dx + \int A \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int B \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(A*sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**3*sqrt(sec(c + d*x)), x))","F",0
1271,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","a \left(\int \frac{A}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{A \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a*(Integral(A/sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**3/sqrt(sec(c + d*x)), x))","F",0
1272,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","a \left(\int \frac{A}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{A \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(A/sec(c + d*x)**(3/2), x) + Integral(A*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(B*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(B*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**3/sec(c + d*x)**(3/2), x))","F",0
1273,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1274,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1275,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1276,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1277,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1278,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","a^{2} \left(\int A \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 2 A \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int A \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int B \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 2 B \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int B \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 2 C \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int C \cos^{4}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a**2*(Integral(A*sqrt(sec(c + d*x)), x) + Integral(2*A*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(2*B*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)**3*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(2*C*cos(c + d*x)**3*sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**4*sqrt(sec(c + d*x)), x))","F",0
1279,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","a^{2} \left(\int \frac{A}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{2 A \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{A \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{2 B \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{2 C \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{4}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**2*(Integral(A/sqrt(sec(c + d*x)), x) + Integral(2*A*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(2*B*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(2*C*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**4/sqrt(sec(c + d*x)), x))","F",0
1280,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","a^{2} \left(\int \frac{A}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{2 A \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{A \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{2 B \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{2 C \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{4}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a**2*(Integral(A/sec(c + d*x)**(3/2), x) + Integral(2*A*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(A*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(B*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(2*B*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(B*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(2*C*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**4/sec(c + d*x)**(3/2), x))","F",0
1281,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1282,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1283,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1284,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1285,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1286,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1287,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1288,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","a^{3} \left(\int \frac{A}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 A \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 A \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{A \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 B \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 B \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos^{4}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 C \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 C \cos^{4}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{5}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**3*(Integral(A/sqrt(sec(c + d*x)), x) + Integral(3*A*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(3*A*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(A*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(3*B*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(3*B*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(B*cos(c + d*x)**4/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(3*C*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(3*C*cos(c + d*x)**4/sqrt(sec(c + d*x)), x) + Integral(C*cos(c + d*x)**5/sqrt(sec(c + d*x)), x))","F",0
1289,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","a^{3} \left(\int \frac{A}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 A \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 A \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{A \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 B \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 B \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos^{4}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 C \cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 C \cos^{4}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{5}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a**3*(Integral(A/sec(c + d*x)**(3/2), x) + Integral(3*A*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(3*A*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(A*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(B*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(3*B*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(3*B*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(B*cos(c + d*x)**4/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(3*C*cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(3*C*cos(c + d*x)**4/sec(c + d*x)**(3/2), x) + Integral(C*cos(c + d*x)**5/sec(c + d*x)**(3/2), x))","F",0
1290,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1291,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1292,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1293,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{A \sqrt{\sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sqrt(sec(c + d*x))/(cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sqrt(sec(c + d*x))/(cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x))/(cos(c + d*x) + 1), x))/a","F",0
1294,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\frac{\int \frac{A}{\cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a}"," ",0,"(Integral(A/(cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x) + Integral(B*cos(c + d*x)/(cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x) + Integral(C*cos(c + d*x)**2/(cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x))/a","F",0
1295,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\frac{\int \frac{A}{\cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"(Integral(A/(cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x) + Integral(B*cos(c + d*x)/(cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x) + Integral(C*cos(c + d*x)**2/(cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x))/a","F",0
1296,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sqrt{\sec{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sqrt(sec(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sqrt(sec(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
1300,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\frac{\int \frac{A}{\cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{B \cos{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"(Integral(A/(cos(c + d*x)**2*sqrt(sec(c + d*x)) + 2*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x) + Integral(B*cos(c + d*x)/(cos(c + d*x)**2*sqrt(sec(c + d*x)) + 2*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x) + Integral(C*cos(c + d*x)**2/(cos(c + d*x)**2*sqrt(sec(c + d*x)) + 2*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x))/a**2","F",0
1301,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1302,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1303,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1304,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1305,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sqrt{\sec{\left(c + d x \right)}}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{B \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx + \int \frac{C \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A*sqrt(sec(c + d*x))/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sqrt(sec(c + d*x))/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x) + Integral(C*cos(c + d*x)**2*sqrt(sec(c + d*x))/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
1306,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1307,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1308,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1309,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1310,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1311,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1315,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x)), x)","F",0
1316,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1317,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sec(c + d*x)**(3/2), x)","F",0
1318,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1319,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1320,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1321,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1322,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1323,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1324,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1325,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1326,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1331,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1332,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1334,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1335,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1336,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1337,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1338,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1339,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1340,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1341,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1342,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
1343,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/(sqrt(a*(cos(c + d*x) + 1))*sqrt(sec(c + d*x))), x)","F",0
1344,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1345,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))*sqrt(sec(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
1346,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1347,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1348,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1349,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1350,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
1351,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
1352,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1353,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1354,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1355,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1356,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1357,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1358,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1359,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1360,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1361,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1362,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1363,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1364,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))*sqrt(sec(c + d*x)), x)","F",0
1365,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))/sqrt(sec(c + d*x)), x)","F",0
1366,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))/sec(c + d*x)**(3/2), x)","F",0
1367,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1368,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1369,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1370,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1371,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1372,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**2*sqrt(sec(c + d*x)), x)","F",0
1373,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**2/sqrt(sec(c + d*x)), x)","F",0
1374,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{2}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**2/sec(c + d*x)**(3/2), x)","F",0
1375,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1376,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1377,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1378,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1379,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1380,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1381,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{3}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**3/sqrt(sec(c + d*x)), x)","F",0
1382,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{3}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*(a + b*cos(c + d*x))**3/sec(c + d*x)**(3/2), x)","F",0
1383,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1384,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1385,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1386,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1387,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1388,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1389,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1390,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1391,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1392,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1393,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1394,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x)), x)","F",0
1395,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
1396,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right) \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))*sec(c + d*x)**(3/2)), x)","F",0
1397,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1398,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1399,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1400,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**2, x)","F",0
1401,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))**2*sqrt(sec(c + d*x))), x)","F",0
1402,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1403,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1404,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1405,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1406,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**3, x)","F",0
1407,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1408,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1409,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1410,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1411,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1412,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1413,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1414,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1415,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1416,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)*sec(d*x+c)**(1/2),x)","\int \left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x)), x)","F",0
1417,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))/sqrt(sec(c + d*x)), x)","F",0
1418,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(a + b*cos(c + d*x))/sec(c + d*x)**(3/2), x)","F",0
1419,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1420,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1421,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1422,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1423,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1424,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1425,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1426,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1427,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1428,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1429,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1430,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1431,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1432,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1433,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1434,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1435,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1436,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1437,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1438,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
1439,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
1440,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1441,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1442,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1443,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
1444,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
1445,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1446,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1447,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1448,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1449,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1450,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1451,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1452,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1453,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1454,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1455,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x)), x)","F",0
1456,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right) \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1457,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right) \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sec(c + d*x)**(3/2), x)","F",0
1458,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1459,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1460,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1461,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1462,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1463,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x)), x)","F",0
1464,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{2} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1465,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{2} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sec(c + d*x)**(3/2), x)","F",0
1466,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1467,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1468,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1469,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1470,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1471,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1472,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{3} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1473,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1474,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1475,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1476,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1477,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1478,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1479,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1480,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1481,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1482,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1483,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1484,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1485,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x)), x)","F",0
1486,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
1487,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right) \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))*sec(c + d*x)**(3/2)), x)","F",0
1488,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1489,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1490,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1491,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**2, x)","F",0
1492,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))**2*sqrt(sec(c + d*x))), x)","F",0
1493,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1494,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1495,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1496,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1497,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1498,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1499,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1500,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1501,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1502,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1503,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1504,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1505,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1506,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1507,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)*sec(d*x+c)**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x)), x)","F",0
1508,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sqrt(sec(c + d*x)), x)","F",0
1509,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right)}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)**2)/sec(c + d*x)**(3/2), x)","F",0
1510,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1511,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1512,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1513,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1514,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1515,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1516,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1517,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1518,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1519,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1520,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1521,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1522,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1523,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1524,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1525,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(9/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1526,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1527,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1528,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1529,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
1530,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/(sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
1531,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1532,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x)), x)","F",0
1533,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1534,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1535,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1536,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
1537,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)} + C \cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x) + C*cos(c + d*x)**2)/((a + b*cos(c + d*x))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
1538,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1539,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1540,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1541,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)**2)*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
