1,1,333,0,2.158621," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\begin{cases} \frac{3 A a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 A a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{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{8 B a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 B a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{B a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B a \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 \cos{\left(c \right)} + a\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a*x*sin(c + d*x)**4/8 + 3*A*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a*x*cos(c + d*x)**4/8 + 3*A*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*A*a*sin(c + d*x)**3/(3*d) + 5*A*a*sin(c + d*x)*cos(c + d*x)**3/(8*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 + 8*B*a*sin(c + d*x)**5/(15*d) + 4*B*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*B*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + B*a*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*a*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)*cos(c)**3, True))","A",0
2,1,252,0,1.048886," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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*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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)*cos(c)**2, True))","A",0
3,1,168,0,0.532822," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)*cos(c), True))","A",0
4,1,94,0,0.248900," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a), True))","A",0
5,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*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\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))","F",0
6,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*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\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))","F",0
7,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*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\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))","F",0
8,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","a \left(\int A \sec^{4}{\left(c + d x \right)}\, dx + \int A \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int B \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int B \cos^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**4, x) + Integral(A*cos(c + d*x)*sec(c + d*x)**4, x) + Integral(B*cos(c + d*x)*sec(c + d*x)**4, x) + Integral(B*cos(c + d*x)**2*sec(c + d*x)**4, x))","F",0
9,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,600,0,4.338657," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)),x)","\begin{cases} \frac{3 A a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{8 A a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 A a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \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^{4}{\left(c + d x \right)}}{d} + \frac{5 A a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{5 B a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 B a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 B a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 B a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 B a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 B a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{16 B a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{8 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)}}{8 d} + \frac{11 B a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{2 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)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\left(c \right)}\right) \left(a \cos{\left(c \right)} + a\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**2*x*sin(c + d*x)**4/4 + 3*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*A*a**2*x*cos(c + d*x)**4/4 + 8*A*a**2*sin(c + d*x)**5/(15*d) + 4*A*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*A*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 2*A*a**2*sin(c + d*x)**3/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*A*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**2/d + 5*B*a**2*x*sin(c + d*x)**6/16 + 15*B*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*B*a**2*x*sin(c + d*x)**4/8 + 15*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*B*a**2*x*cos(c + d*x)**6/16 + 3*B*a**2*x*cos(c + d*x)**4/8 + 5*B*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 16*B*a**2*sin(c + d*x)**5/(15*d) + 5*B*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 8*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)/(8*d) + 11*B*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 2*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/(8*d), Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**2*cos(c)**3, True))","A",0
11,1,459,0,2.580393," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**2*cos(c)**2, True))","A",0
12,1,338,0,1.229162," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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*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), Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**2*cos(c), True))","A",0
13,1,199,0,0.636524," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**2, True))","A",0
14,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*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\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))","F",0
15,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*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\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))","F",0
16,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","a^{2} \left(\int A \sec^{3}{\left(c + d x \right)}\, dx + \int 2 A \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int A \cos^{2}{\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 2 B \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \cos^{3}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x)**3, x) + Integral(2*A*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(A*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(B*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(2*B*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(B*cos(c + d*x)**3*sec(c + d*x)**3, x))","F",0
17,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,1,695,0,4.834415," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**3*cos(c)**2, True))","A",0
20,1,530,0,2.812861," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)),x)","\begin{cases} \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A a^{3} x \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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**3*cos(c), True))","A",0
21,1,371,0,1.324919," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**3, True))","A",0
22,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*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\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))","F",0
23,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","a^{3} \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int 3 A \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 A \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int A \cos^{3}{\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 3 B \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 B \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \cos^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(A*sec(c + d*x)**2, x) + Integral(3*A*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(3*A*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(A*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(3*B*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(3*B*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(B*cos(c + d*x)**4*sec(c + d*x)**2, x))","F",0
24,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**3,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+B*cos(d*x+c))*sec(d*x+c)**4,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+B*cos(d*x+c))*sec(d*x+c)**5,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+B*cos(d*x+c))*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,960,0,8.007691," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**4*cos(c)**2, True))","A",0
29,1,765,0,4.830695," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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*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), Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**4*cos(c), True))","A",0
30,1,544,0,3.023858," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a*cos(c) + a)**4, True))","A",0
31,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c),x)","a^{4} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 4 A \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 6 A \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 4 A \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \cos^{4}{\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 4 B \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 6 B \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 4 B \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \cos^{5}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**4*(Integral(A*sec(c + d*x), x) + Integral(4*A*cos(c + d*x)*sec(c + d*x), x) + Integral(6*A*cos(c + d*x)**2*sec(c + d*x), x) + Integral(4*A*cos(c + d*x)**3*sec(c + d*x), x) + Integral(A*cos(c + d*x)**4*sec(c + d*x), x) + Integral(B*cos(c + d*x)*sec(c + d*x), x) + Integral(4*B*cos(c + d*x)**2*sec(c + d*x), x) + Integral(6*B*cos(c + d*x)**3*sec(c + d*x), x) + Integral(4*B*cos(c + d*x)**4*sec(c + d*x), x) + Integral(B*cos(c + d*x)**5*sec(c + d*x), x))","F",0
32,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*(A+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,1,1794,0,7.461697," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(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{216 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{392 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{296 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{96 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 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{180 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{270 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{180 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{45 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{246 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{374 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{314 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{66 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos^{4}{\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) + 216*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) + 392*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) + 296*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) + 96*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*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) + 180*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) + 270*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) + 180*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) + 45*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) - 246*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) - 374*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) - 314*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) - 66*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**4/(a*cos(c) + a), True))","A",0
39,1,1161,0,4.506639," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{9 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{27 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{27 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{9 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{36 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{12 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{48 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{50 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{24 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*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) + 27*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) + 27*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) + 9*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) - 36*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) - 12*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) + 48*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) + 50*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) + 24*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**3/(a*cos(c) + a), True))","A",0
40,1,665,0,3.232446," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(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{8 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{6 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 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{6 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{3 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{10 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{4 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos^{2}{\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) + 8*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) + 6*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*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) + 6*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) + 3*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) - 10*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) - 4*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**2/(a*cos(c) + a), True))","A",0
41,1,264,0,1.706922," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{A 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{A d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \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{3 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) + A*d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) - 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) + 3*B*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))*cos(c)/(a*cos(c) + a), True))","A",0
42,1,49,0,0.861057," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d} + \frac{B x}{a} - \frac{B \tan{\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)}\right)}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*tan(c/2 + d*x/2)/(a*d) + B*x/a - B*tan(c/2 + d*x/2)/(a*d), Ne(d, 0)), (x*(A + B*cos(c))/(a*cos(c) + a), True))","A",0
43,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a","F",0
44,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a","F",0
45,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a","F",0
46,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a","F",0
47,1,1425,0,10.807435," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{21 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{63 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{63 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{21 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{18 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{90 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{110 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{39 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 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{90 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{90 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{30 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{24 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{138 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{160 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{63 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((21*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) + 63*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) + 63*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) + 21*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) - 18*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) - 90*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) - 110*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) - 39*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*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) - 90*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) - 90*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) - 30*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) + 24*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) + 138*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) + 160*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) + 63*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**4/(a*cos(c) + a)**2, True))","A",0
48,1,843,0,6.980120," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{12 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{24 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{12 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{13 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{41 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{27 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 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{42 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{21 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{19 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{71 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{39 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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)**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*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) - 12*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) + 13*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) + 41*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) + 27*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*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) + 42*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) + 21*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) - 19*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) - 71*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) - 39*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**3/(a*cos(c) + a)**2, True))","A",0
49,1,411,0,4.163670," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{6 A 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 A d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \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{8 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{9 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 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{12 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{14 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{27 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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)**2/(6*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)**2 + 6*a**2*d) + A*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 8*A*tan(c/2 + d*x/2)**3/(6*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)**2 + 6*a**2*d) - 12*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) - 12*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) + 14*B*tan(c/2 + d*x/2)**3/(6*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)**2 + 6*a**2*d), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**2/(a*cos(c) + a)**2, True))","A",0
50,1,105,0,2.334027," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(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 x}{a^{2}} + \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} - \frac{3 B \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)}\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)**3/(6*a**2*d) + A*tan(c/2 + d*x/2)/(2*a**2*d) + B*x/a**2 + B*tan(c/2 + d*x/2)**3/(6*a**2*d) - 3*B*tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)/(a*cos(c) + a)**2, True))","A",0
51,1,94,0,1.741713," ","integrate((A+B*cos(d*x+c))/(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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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), Ne(d, 0)), (x*(A + B*cos(c))/(a*cos(c) + a)**2, True))","A",0
52,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a**2","F",0
53,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a**2","F",0
54,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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{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}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
55,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**4/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{A \sec^{4}{\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^{4}{\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)**4/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x) + Integral(B*cos(c + d*x)*sec(c + d*x)**4/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x))/a**2","F",0
56,1,1584,0,25.371873," ","integrate(cos(d*x+c)**5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{390 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{1170 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{1170 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{390 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{31 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{354 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{1698 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{2075 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{765 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 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{2070 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{2070 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{690 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{41 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{594 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{3078 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{3675 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{1395 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((390*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) + 1170*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) + 1170*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) + 390*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) + 31*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) - 354*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) - 1698*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) - 2075*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) - 765*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*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) - 2070*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) - 2070*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) - 690*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) - 41*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) + 594*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) + 3078*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) + 3675*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) + 1395*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**5/(a*cos(c) + a)**3, True))","A",0
57,1,966,0,15.908159," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{180 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{360 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{180 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{24 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{198 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{600 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{375 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 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{780 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{390 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{34 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{388 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{1310 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{765 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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)**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*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) - 180*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) - 24*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) + 198*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) + 600*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) + 375*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*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) + 780*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) + 390*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) + 34*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) - 388*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) - 1310*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) - 765*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**4/(a*cos(c) + a)**3, True))","A",0
58,1,496,0,9.802338," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{60 A 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 A d x}{60 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \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{17 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{85 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{105 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 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{180 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{27 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{225 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{375 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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)**2/(60*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)**2 + 60*a**3*d) - 3*A*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 17*A*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 85*A*tan(c/2 + d*x/2)**3/(60*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)**2 + 60*a**3*d) - 180*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) - 180*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) - 27*B*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 225*B*tan(c/2 + d*x/2)**3/(60*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)**2 + 60*a**3*d), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**3/(a*cos(c) + a)**3, True))","A",0
59,1,148,0,5.797875," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(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 x}{a^{3}} - \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)}}{3 a^{3} d} - \frac{7 B \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)}\right) \cos^{2}{\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)**3/(6*a**3*d) + A*tan(c/2 + d*x/2)/(4*a**3*d) + B*x/a**3 - B*tan(c/2 + d*x/2)**5/(20*a**3*d) + B*tan(c/2 + d*x/2)**3/(3*a**3*d) - 7*B*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**2/(a*cos(c) + a)**3, True))","A",0
60,1,117,0,3.721951," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)/(a*cos(c) + a)**3, True))","A",0
61,1,114,0,2.537390," ","integrate((A+B*cos(d*x+c))/(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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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), Ne(d, 0)), (x*(A + B*cos(c))/(a*cos(c) + a)**3, True))","A",0
62,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a**3","F",0
63,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a**3","F",0
64,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{A \sec^{3}{\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^{3}{\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)**3/(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)**3/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x))/a**3","F",0
65,1,1085,0,33.041320," ","integrate(cos(d*x+c)**5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{3360 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{6720 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{3360 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{117 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{526 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{3682 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{11165 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{6825 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 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{17640 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{8820 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{159 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{1002 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{9114 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{29505 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{17535 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3360*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) - 6720*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) - 3360*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) + 117*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) - 526*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) + 3682*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) + 11165*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) + 6825*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*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) + 17640*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) + 8820*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) - 159*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) + 1002*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) - 9114*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) - 29505*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) - 17535*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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**5/(a*cos(c) + a)**4, True))","A",0
66,1,578,0,21.681982," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{840 A 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 A d x}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \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{90 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{280 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{1190 A \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 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 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{3360 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{132 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{658 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{4340 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{6825 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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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)**2/(840*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)**2 + 840*a**4*d) + 15*A*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 90*A*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 280*A*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 1190*A*tan(c/2 + d*x/2)**3/(840*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)**2 + 840*a**4*d) - 3360*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) - 3360*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) + 132*B*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 658*B*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 4340*B*tan(c/2 + d*x/2)**3/(840*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)**2 + 840*a**4*d), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**4/(a*cos(c) + a)**4, True))","A",0
67,1,192,0,13.269747," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(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 x}{a^{4}} + \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)}}{8 a^{4} d} + \frac{11 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} - \frac{15 B \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)}\right) \cos^{3}{\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) + 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*x/a**4 + B*tan(c/2 + d*x/2)**7/(56*a**4*d) - B*tan(c/2 + d*x/2)**5/(8*a**4*d) + 11*B*tan(c/2 + d*x/2)**3/(24*a**4*d) - 15*B*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**3/(a*cos(c) + a)**4, True))","A",0
68,1,182,0,9.236634," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)**2/(a*cos(c) + a)**4, True))","A",0
69,1,178,0,6.689023," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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), Ne(d, 0)), (x*(A + B*cos(c))*cos(c)/(a*cos(c) + a)**4, True))","A",0
70,1,177,0,4.874605," ","integrate((A+B*cos(d*x+c))/(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} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\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), Ne(d, 0)), (x*(A + B*cos(c))/(a*cos(c) + a)**4, True))","A",0
71,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(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+B*cos(d*x+c))*sec(d*x+c)**2/(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+B*cos(d*x+c))*sec(d*x+c)**3/(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+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(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)}\right) \cos{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))*cos(c + d*x), x)","F",0
77,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(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)}\right)\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x)), x)","F",0
78,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*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)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))*sec(c + d*x), x)","F",0
79,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*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)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
80,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
81,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),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+B*cos(d*x+c)),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+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\int \left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*(A + B*cos(c + d*x)), x)","F",0
86,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*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+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),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+B*cos(d*x+c))*sec(d*x+c),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+B*cos(d*x+c))*sec(d*x+c)**2,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+B*cos(d*x+c))*sec(d*x+c)**3,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+B*cos(d*x+c))*sec(d*x+c)**4,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+B*cos(d*x+c))*sec(d*x+c)**5,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+B*cos(d*x+c))*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*cos(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
103,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\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))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
104,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
105,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**2/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
106,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**3/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
107,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \cos{\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))*cos(c + d*x)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
111,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{A + B \cos{\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))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
112,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
113,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**2/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
114,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**3/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
115,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(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((A+B*cos(d*x+c))*sec(d*x+c)/(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((A+B*cos(d*x+c))*sec(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+B*cos(d*x+c))*sec(d*x+c)**3/(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(cos(d*x+c)**(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((a+a*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
132,-1,0,0,0.000000," ","integrate((a+a*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
133,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),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+B*cos(d*x+c))/cos(d*x+c)**(7/2),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+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),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+B*cos(d*x+c))/cos(d*x+c)**(9/2),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+B*cos(d*x+c))/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(9/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(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)**(5/2)*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(1/2)*(A+B*cos(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)}\right) \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))*sqrt(cos(c + d*x)), x)","F",0
169,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/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)}\right)}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
170,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/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)}\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))/cos(c + d*x)**(3/2), x)","F",0
171,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/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)}\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))/cos(c + d*x)**(5/2), x)","F",0
172,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \cos{\left(c + d x \right)}\right)}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*(A + B*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
177,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \cos{\left(c + d x \right)}\right)}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*(A + B*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
178,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \cos{\left(c + d x \right)}\right)}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*(A + B*cos(c + d*x))/cos(c + d*x)**(5/2), x)","F",0
179,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),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+B*cos(d*x+c))/cos(d*x+c)**(9/2),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+B*cos(d*x+c))/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),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+B*cos(d*x+c))/cos(d*x+c)**(11/2),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+B*cos(d*x+c))/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sqrt{\cos{\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))*sqrt(cos(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
193,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/(sqrt(a*(cos(c + d*x) + 1))*sqrt(cos(c + d*x))), x)","F",0
194,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(3/2)), x)","F",0
195,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\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{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sqrt(cos(c + d*x))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
199,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
200,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/((a*(cos(c + d*x) + 1))**(3/2)*cos(c + d*x)**(3/2)), x)","F",0
201,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \cos^{\frac{3}{2}}{\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))*cos(c + d*x)**(3/2)/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
204,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + B \cos{\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))*sqrt(cos(c + d*x))/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
205,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,1,252,0,1.043666," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))*cos(c)**2, True))","A",0
216,1,168,0,0.514144," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))*cos(c), True))","A",0
217,1,94,0,0.247798," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c)), True))","A",0
218,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*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)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))*sec(c + d*x), x)","F",0
219,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*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)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
220,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*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)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
221,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))*sec(c + d*x)**4, x)","F",0
222,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,1,459,0,2.471383," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)),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{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{3 B a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 B a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 B a b x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 B a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{5 B a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{8 B b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{B 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) \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) + 2*B*a**2*sin(c + d*x)**3/(3*d) + B*a**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*a*b*x*sin(c + d*x)**4/4 + 3*B*a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*B*a*b*x*cos(c + d*x)**4/4 + 3*B*a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 5*B*a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 8*B*b**2*sin(c + d*x)**5/(15*d) + 4*B*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + B*b**2*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**2*cos(c)**2, True))","A",0
224,1,338,0,1.187241," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**2*cos(c), True))","A",0
225,1,199,0,0.590235," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**2, True))","A",0
226,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*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)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**2*sec(c + d*x), x)","F",0
227,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*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)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**2*sec(c + d*x)**2, x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*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)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**2*sec(c + d*x)**3, x)","F",0
229,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,1,721,0,4.621147," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)),x)","\begin{cases} \frac{A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 A a^{2} b \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 A a^{2} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 A a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 A a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 A a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 A a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 A a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 A b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{2 B a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 B a^{2} b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 B a^{2} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 B a^{2} b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 B a^{2} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 B a^{2} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 B a b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{4 B a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 B a b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B b^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 B b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 B b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 B b^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 B b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 B b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 B 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) \left(a + b \cos{\left(c \right)}\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*x*sin(c + d*x)**2/2 + A*a**3*x*cos(c + d*x)**2/2 + A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*A*a**2*b*sin(c + d*x)**3/d + 3*A*a**2*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*A*a*b**2*x*sin(c + d*x)**4/8 + 9*A*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*A*a*b**2*x*cos(c + d*x)**4/8 + 9*A*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*A*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*A*b**3*sin(c + d*x)**5/(15*d) + 4*A*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 2*B*a**3*sin(c + d*x)**3/(3*d) + B*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 9*B*a**2*b*x*sin(c + d*x)**4/8 + 9*B*a**2*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*B*a**2*b*x*cos(c + d*x)**4/8 + 9*B*a**2*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*B*a**2*b*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*B*a*b**2*sin(c + d*x)**5/(5*d) + 4*B*a*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*B*a*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*b**3*x*sin(c + d*x)**6/16 + 15*B*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*B*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*B*b**3*x*cos(c + d*x)**6/16 + 5*B*b**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*B*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*B*b**3*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**3*cos(c)**2, True))","A",0
232,1,551,0,2.758478," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**3*cos(c), True))","A",0
233,1,386,0,1.317489," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**3, True))","A",0
234,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*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)}\right)^{3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**3*sec(c + d*x), x)","F",0
235,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*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)}\right)^{3} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**3*sec(c + d*x)**2, x)","F",0
236,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,1,1017,0,8.195593," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)),x)","\begin{cases} \frac{A a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{8 A a^{3} b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 A a^{3} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 A a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{9 A a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{9 A a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{9 A a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{15 A a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{32 A a b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{16 A a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{4 A a b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 A b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 A b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 A b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 A b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 A b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 A b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 A b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 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^{2}{\left(c + d x \right)}}{d} + \frac{3 B a^{3} b x \sin^{4}{\left(c + d x \right)}}{2} + 3 B a^{3} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 B a^{3} b x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 B a^{3} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 B a^{3} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{16 B a^{2} b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{8 B a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{6 B a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 B a b^{3} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 B a b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{15 B a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + \frac{5 B a b^{3} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{5 B a b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{10 B a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{11 B a b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{16 B b^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 B b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 B b^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{B 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) \left(a + b \cos{\left(c \right)}\right)^{4} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*x*sin(c + d*x)**2/2 + A*a**4*x*cos(c + d*x)**2/2 + A*a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 8*A*a**3*b*sin(c + d*x)**3/(3*d) + 4*A*a**3*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*A*a**2*b**2*x*sin(c + d*x)**4/4 + 9*A*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 9*A*a**2*b**2*x*cos(c + d*x)**4/4 + 9*A*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 15*A*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 32*A*a*b**3*sin(c + d*x)**5/(15*d) + 16*A*a*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 4*A*a*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*A*b**4*x*sin(c + d*x)**6/16 + 15*A*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*A*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*A*b**4*x*cos(c + d*x)**6/16 + 5*A*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*A*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*A*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 2*B*a**4*sin(c + d*x)**3/(3*d) + B*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*B*a**3*b*x*sin(c + d*x)**4/2 + 3*B*a**3*b*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*B*a**3*b*x*cos(c + d*x)**4/2 + 3*B*a**3*b*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*B*a**3*b*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 16*B*a**2*b**2*sin(c + d*x)**5/(5*d) + 8*B*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 6*B*a**2*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*B*a*b**3*x*sin(c + d*x)**6/4 + 15*B*a*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 15*B*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 5*B*a*b**3*x*cos(c + d*x)**6/4 + 5*B*a*b**3*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 10*B*a*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 11*B*a*b**3*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 16*B*b**4*sin(c + d*x)**7/(35*d) + 8*B*b**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*B*b**4*sin(c + d*x)**3*cos(c + d*x)**4/d + B*b**4*sin(c + d*x)*cos(c + d*x)**6/d, Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**4*cos(c)**2, True))","A",0
241,1,811,0,4.989742," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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 + 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), Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**4*cos(c), True))","A",0
242,1,580,0,2.832969," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\x \left(A + B \cos{\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) + 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, Ne(d, 0)), (x*(A + B*cos(c))*(a + b*cos(c))**4, True))","A",0
243,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*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)}\right)^{4} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**4*sec(c + d*x), x)","F",0
244,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*(A+B*cos(d*x+c))*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,1,3225,0,118.447464," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\begin{cases} \tilde{\infty} x \left(A + B \cos{\left(c \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{A 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{A 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{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{B 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{B 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 B \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{B}{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{\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}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \cos{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{A 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{A d x}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} - \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{B 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{B d x}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} + \frac{B \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 B \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 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{A 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{A a 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)}}{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 a b \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 a 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)}}{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 a b \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} 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{A b^{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{B 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{B 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{B 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{B 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{B 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{B 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{B 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{B 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 B 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 B 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 + B*cos(c)), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (A*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)) + A*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)) + 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)) + B*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)) + B*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*B*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + B/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)), Eq(a, -b)), ((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))/a, Eq(b, 0)), (x*(A + B*cos(c))*cos(c)/(a + b*cos(c)), Eq(d, 0)), (A*d*x*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**2 + b*d) + A*d*x/(b*d*tan(c/2 + d*x/2)**2 + b*d) - 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) - B*d*x*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**2 + b*d) - B*d*x/(b*d*tan(c/2 + d*x/2)**2 + b*d) + B*tan(c/2 + d*x/2)**3/(b*d*tan(c/2 + d*x/2)**2 + b*d) + 3*B*tan(c/2 + d*x/2)/(b*d*tan(c/2 + d*x/2)**2 + b*d), Eq(a, b)), (A*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))) + A*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))) - A*a*b*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*a*b*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*a*b*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*a*b*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*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))) - A*b**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))) - B*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))) - B*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))) + B*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))) + B*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))) - B*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))) - B*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))) + B*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))) + B*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*B*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*B*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
253,1,524,0,24.723802," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \cos{\left(c \right)}\right)}{\cos{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{A}{b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{B x}{b} + \frac{B}{b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: a = - b \\\frac{A x + \frac{B \sin{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right)}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d} + \frac{B x}{b} - \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d} & \text{for}\: a = b \\\frac{A b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{A b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B a d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{B a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{B b d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*cos(c))/cos(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (A/(b*d*tan(c/2 + d*x/2)) + B*x/b + B/(b*d*tan(c/2 + d*x/2)), Eq(a, -b)), ((A*x + B*sin(c + d*x)/d)/a, Eq(b, 0)), (x*(A + B*cos(c))/(a + b*cos(c)), Eq(d, 0)), (A*tan(c/2 + d*x/2)/(b*d) + B*x/b - B*tan(c/2 + d*x/2)/(b*d), Eq(a, b)), (A*b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) - A*b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) + B*a*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) - B*a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) + B*a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) - B*b*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
254,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
255,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
256,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
257,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)**4/(a + b*cos(c + d*x)), x)","F",0
258,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/(a + b*cos(c + d*x))**2, x)","F",0
263,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)**2/(a + b*cos(c + d*x))**2, x)","F",0
264,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)**3/(a + b*cos(c + d*x))**2, x)","F",0
265,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/(a + b*cos(c + d*x))**3, x)","F",0
271,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)**2/(a + b*cos(c + d*x))**3, x)","F",0
272,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{3}{\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))*sec(c + d*x)**3/(a + b*cos(c + d*x))**3, x)","F",0
273,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**4,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)/(a + b*cos(c + d*x))**4, x)","F",0
279,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c))**4,x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)**2/(a + b*cos(c + d*x))**4, x)","F",0
280,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,1,56,0,1.259502," ","integrate(cos(d*x+c)**3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \cos{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{a + b \cos{\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, Ne(d, 0)), (x*(B*a + B*b*cos(c))*cos(c)**3/(a + b*cos(c)), True))","A",0
282,1,68,0,0.886429," ","integrate(cos(d*x+c)**2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),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} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \cos{\left(c \right)}\right) \cos^{2}{\left(c \right)}}{a + b \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), Ne(d, 0)), (x*(B*a + B*b*cos(c))*cos(c)**2/(a + b*cos(c)), True))","A",0
283,1,31,0,0.601953," ","integrate(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{B \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \cos{\left(c \right)}\right) \cos{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*sin(c + d*x)/d, Ne(d, 0)), (x*(B*a + B*b*cos(c))*cos(c)/(a + b*cos(c)), True))","A",0
284,1,2,0,0.127077," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","B x"," ",0,"B*x","A",0
285,1,39,0,3.814609," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{B \log{\left(\tan{\left(c + d x \right)} + \sec{\left(c + d x \right)} \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \cos{\left(c \right)}\right) \sec{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*log(tan(c + d*x) + sec(c + d*x))/d, Ne(d, 0)), (x*(B*a + B*b*cos(c))*sec(c)/(a + b*cos(c)), True))","A",0
286,1,32,0,3.097226," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{B \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \cos{\left(c \right)}\right) \sec^{2}{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*tan(c + d*x)/d, Ne(d, 0)), (x*(B*a + B*b*cos(c))*sec(c)**2/(a + b*cos(c)), True))","A",0
287,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","B \int \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"B*Integral(sec(c + d*x)**3, x)","F",0
288,1,42,0,17.646591," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{B \left(\frac{\tan^{3}{\left(c + d x \right)}}{3} + \tan{\left(c + d x \right)}\right)}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \cos{\left(c \right)}\right) \sec^{4}{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*(tan(c + d*x)**3/3 + tan(c + d*x))/d, Ne(d, 0)), (x*(B*a + B*b*cos(c))*sec(c)**4/(a + b*cos(c)), True))","A",0
289,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","B \int \frac{\sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
294,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","B \int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
295,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","B \int \frac{\sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
296,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\int \left(A + B \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((A + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*cos(c + d*x), x)","F",0
299,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),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
300,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \left(A + B \cos{\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 + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*sec(c + d*x), x)","F",0
301,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\int \left(A + B \cos{\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 + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
302,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \sqrt{a + b \cos{\left(c + d x \right)}} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
303,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),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
307,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*cos(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
322,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),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
323,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
324,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**2/sqrt(a + b*cos(c + d*x)), x)","F",0
325,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**3/sqrt(a + b*cos(c + d*x)), x)","F",0
326,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\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))*sec(c + d*x)/(a + b*cos(c + d*x))**(3/2), x)","F",0
331,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**2/(a + b*cos(c + d*x))**(3/2), x)","F",0
332,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sec(c + d*x)**3/(a + b*cos(c + d*x))**(3/2), x)","F",0
333,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/sqrt(a + b*cos(c + d*x)), x)","F",0
342,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{\sec{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(sec(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
343,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
346,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-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)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**2*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate((a+b*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
356,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**3*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\int \left(A + B \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((A + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x)), x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\int \frac{\left(A + B \cos{\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 + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(5/2), x)","F",0
400,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/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)^{\frac{3}{2}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**(3/2)/sqrt(cos(c + d*x)), x)","F",0
405,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(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)}\right)^{\frac{3}{2}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**(3/2)/cos(c + d*x)**(3/2), x)","F",0
406,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**(3/2)/cos(c + d*x)**(5/2), x)","F",0
407,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(3/2*b*B/a+B*cos(d*x+c))/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)**(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*sqrt(cos(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
422,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
423,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
424,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
428,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{A + B \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((A + B*cos(c + d*x))/((a + b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
429,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*cos(c + d*x)**(3/2)/(a + b*cos(c + d*x))**(5/2), x)","F",0
433,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\left(A + B \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((A + B*cos(c + d*x))*sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(5/2), x)","F",0
434,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(cos(c + d*x)**(3/2)/sqrt(a + b*cos(c + d*x)), x)","F",0
438,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(sqrt(cos(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
439,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
440,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
441,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(2+3*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{3 \cos{\left(c + d x \right)} + 2} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(3*cos(c + d*x) + 2)*cos(c + d*x)**(3/2)), x)","F",0
442,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(-2+3*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{3 \cos{\left(c + d x \right)} - 2} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(3*cos(c + d*x) - 2)*cos(c + d*x)**(3/2)), x)","F",0
443,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(2-3*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{2 - 3 \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(2 - 3*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
444,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(-2-3*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{- 3 \cos{\left(c + d x \right)} - 2} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(-3*cos(c + d*x) - 2)*cos(c + d*x)**(3/2)), x)","F",0
445,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(3+2*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{2 \cos{\left(c + d x \right)} + 3} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(2*cos(c + d*x) + 3)*cos(c + d*x)**(3/2)), x)","F",0
446,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(3-2*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{3 - 2 \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(3 - 2*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
447,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(-3+2*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{2 \cos{\left(c + d x \right)} - 3} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(2*cos(c + d*x) - 3)*cos(c + d*x)**(3/2)), x)","F",0
448,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)**(3/2)/(-3-2*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} + 1}{\sqrt{- 2 \cos{\left(c + d x \right)} - 3} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((cos(c + d*x) + 1)/(sqrt(-2*cos(c + d*x) - 3)*cos(c + d*x)**(3/2)), x)","F",0
449,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(a+b*cos(f*x+e))**n*(A+B*cos(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(a+b*cos(f*x+e))**4*(A+B*cos(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(a+b*cos(f*x+e))**3*(A+B*cos(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(a+b*cos(f*x+e))**2*(A+B*cos(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,0,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x)","\int \left(c \cos{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right) \left(a + b \cos{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((c*cos(e + f*x))**m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x)), x)","F",0
454,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(a+b*cos(f*x+e))**(3/2)*(A+B*cos(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,0,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(A+B*cos(f*x+e))*(a+b*cos(f*x+e))**(1/2),x)","\int \left(c \cos{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right) \sqrt{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c*cos(e + f*x))**m*(A + B*cos(e + f*x))*sqrt(a + b*cos(e + f*x)), x)","F",0
457,0,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))**(1/2),x)","\int \frac{\left(c \cos{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right)}{\sqrt{a + b \cos{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c*cos(e + f*x))**m*(A + B*cos(e + f*x))/sqrt(a + b*cos(e + f*x)), x)","F",0
458,0,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))**(3/2),x)","\int \frac{\left(c \cos{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right)}{\left(a + b \cos{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*cos(e + f*x))**m*(A + B*cos(e + f*x))/(a + b*cos(e + f*x))**(3/2), x)","F",0
459,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*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\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))","F",0
463,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/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\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))","F",0
464,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/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\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))","F",0
465,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate((a+a*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
467,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))*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\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))","F",0
469,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*(A+B*cos(d*x+c))/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\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))","F",0
470,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(1/2),x)","a^{3} \left(\int A \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 3 A \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 3 A \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int A \cos^{3}{\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 3 B \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 3 B \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int B \cos^{4}{\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))","F",0
475,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*(A+B*cos(d*x+c))/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\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))","F",0
476,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a","F",0
479,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(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}{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))/a","F",0
480,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(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}{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))/a","F",0
481,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a**2","F",0
484,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(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}{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))/a**2","F",0
485,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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}{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))/a**3","F",0
489,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(11/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(9/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(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 + B \cos{\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))*sqrt(sec(c + d*x)), x)","F",0
499,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(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)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*(A + B*cos(c + d*x))/sqrt(sec(c + d*x)), x)","F",0
500,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(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)}\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))/sec(c + d*x)**(3/2), x)","F",0
501,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(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))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(11/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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) \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))*sqrt(sec(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
526,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/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)}}{\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))/(sqrt(a*(cos(c + d*x) + 1))*sqrt(sec(c + d*x))), x)","F",0
527,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\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 + B*cos(c + d*x))/(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x)**(3/2)), x)","F",0
528,0,0,0,0.000000," ","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
529,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
533,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sqrt(sec(c + d*x))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
534,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(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)}}{\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))/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
535,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*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)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))*sqrt(sec(c + d*x)), x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/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)}\right)}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))/sqrt(sec(c + d*x)), x)","F",0
555,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/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)}\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))/sec(c + d*x)**(3/2), x)","F",0
556,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((a+b*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
558,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))*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)}\right)^{2} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**2*sqrt(sec(c + d*x)), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(A+B*cos(d*x+c))/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)}\right)^{2}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**2/sqrt(sec(c + d*x)), x)","F",0
561,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))*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)}\right)^{3} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**3*sqrt(sec(c + d*x)), x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(A+B*cos(d*x+c))/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)}\right)^{3}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**3/sqrt(sec(c + d*x)), x)","F",0
567,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\int \frac{\left(A + B \cos{\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))*sqrt(sec(c + d*x))/(a + b*cos(c + d*x)), x)","F",0
570,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\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))/((a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
571,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\int \frac{A + B \cos{\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))/((a + b*cos(c + d*x))*sec(c + d*x)**(3/2)), x)","F",0
572,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(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+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(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+B*cos(d*x+c))*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)}\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))*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**2, x)","F",0
575,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\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))/((a + b*cos(c + d*x))**2*sqrt(sec(c + d*x))), x)","F",0
576,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\int \frac{\left(A + B \cos{\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 + B*cos(c + d*x))*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**3, x)","F",0
580,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","B \int \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sqrt(sec(c + d*x)), x)","F",0
587,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)**(1/2),x)","B \int \frac{1}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/sqrt(sec(c + d*x)), x)","F",0
588,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)**(3/2),x)","B \int \frac{1}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sec(c + d*x)**(-3/2), x)","F",0
589,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(9/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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
595,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\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
596,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\left(A + B \cos{\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 + B*cos(c + d*x))*sqrt(a + b*cos(c + d*x))/sec(c + d*x)**(3/2), x)","F",0
597,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sqrt(sec(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
618,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\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))/(sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
619,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}} \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(sqrt(a + b*cos(c + d*x))*sec(c + d*x)**(3/2)), x)","F",0
620,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*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)}\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))*sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
623,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(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)}}{\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))/((a + b*cos(c + d*x))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
624,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","B \int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(sqrt(sec(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
633,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","B \int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
634,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate((a+b*cos(f*x+e))**n*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate((a+b*cos(f*x+e))**4*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))**3*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\int \left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right) \left(a + b \cos{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))**3, x)","F",0
638,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))**2*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\int \left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right) \left(a + b \cos{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))**2, x)","F",0
639,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\int \left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right) \left(a + b \cos{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x)), x)","F",0
640,0,0,0,0.000000," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))**m/(a+b*cos(f*x+e)),x)","\int \frac{\left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right)}{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))/(a + b*cos(e + f*x)), x)","F",0
641,-1,0,0,0.000000," ","integrate((a+b*cos(f*x+e))**(3/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))**(1/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))**m,x)","\int \left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right) \sqrt{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))*sqrt(a + b*cos(e + f*x)), x)","F",0
643,0,0,0,0.000000," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))**m/(a+b*cos(f*x+e))**(1/2),x)","\int \frac{\left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right)}{\sqrt{a + b \cos{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))/sqrt(a + b*cos(e + f*x)), x)","F",0
644,0,0,0,0.000000," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))**m/(a+b*cos(f*x+e))**(3/2),x)","\int \frac{\left(c \sec{\left(e + f x \right)}\right)^{m} \left(A + B \cos{\left(e + f x \right)}\right)}{\left(a + b \cos{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*sec(e + f*x))**m*(A + B*cos(e + f*x))/(a + b*cos(e + f*x))**(3/2), x)","F",0
