1,1,311,0,3.430388," ","integrate((d*x+c)**4*sin(b*x+a),x)","\begin{cases} - \frac{c^{4} \cos{\left(a + b x \right)}}{b} - \frac{4 c^{3} d x \cos{\left(a + b x \right)}}{b} - \frac{6 c^{2} d^{2} x^{2} \cos{\left(a + b x \right)}}{b} - \frac{4 c d^{3} x^{3} \cos{\left(a + b x \right)}}{b} - \frac{d^{4} x^{4} \cos{\left(a + b x \right)}}{b} + \frac{4 c^{3} d \sin{\left(a + b x \right)}}{b^{2}} + \frac{12 c^{2} d^{2} x \sin{\left(a + b x \right)}}{b^{2}} + \frac{12 c d^{3} x^{2} \sin{\left(a + b x \right)}}{b^{2}} + \frac{4 d^{4} x^{3} \sin{\left(a + b x \right)}}{b^{2}} + \frac{12 c^{2} d^{2} \cos{\left(a + b x \right)}}{b^{3}} + \frac{24 c d^{3} x \cos{\left(a + b x \right)}}{b^{3}} + \frac{12 d^{4} x^{2} \cos{\left(a + b x \right)}}{b^{3}} - \frac{24 c d^{3} \sin{\left(a + b x \right)}}{b^{4}} - \frac{24 d^{4} x \sin{\left(a + b x \right)}}{b^{4}} - \frac{24 d^{4} \cos{\left(a + b x \right)}}{b^{5}} & \text{for}\: b \neq 0 \\\left(c^{4} x + 2 c^{3} d x^{2} + 2 c^{2} d^{2} x^{3} + c d^{3} x^{4} + \frac{d^{4} x^{5}}{5}\right) \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**4*cos(a + b*x)/b - 4*c**3*d*x*cos(a + b*x)/b - 6*c**2*d**2*x**2*cos(a + b*x)/b - 4*c*d**3*x**3*cos(a + b*x)/b - d**4*x**4*cos(a + b*x)/b + 4*c**3*d*sin(a + b*x)/b**2 + 12*c**2*d**2*x*sin(a + b*x)/b**2 + 12*c*d**3*x**2*sin(a + b*x)/b**2 + 4*d**4*x**3*sin(a + b*x)/b**2 + 12*c**2*d**2*cos(a + b*x)/b**3 + 24*c*d**3*x*cos(a + b*x)/b**3 + 12*d**4*x**2*cos(a + b*x)/b**3 - 24*c*d**3*sin(a + b*x)/b**4 - 24*d**4*x*sin(a + b*x)/b**4 - 24*d**4*cos(a + b*x)/b**5, Ne(b, 0)), ((c**4*x + 2*c**3*d*x**2 + 2*c**2*d**2*x**3 + c*d**3*x**4 + d**4*x**5/5)*sin(a), True))","A",0
2,1,202,0,1.609256," ","integrate((d*x+c)**3*sin(b*x+a),x)","\begin{cases} - \frac{c^{3} \cos{\left(a + b x \right)}}{b} - \frac{3 c^{2} d x \cos{\left(a + b x \right)}}{b} - \frac{3 c d^{2} x^{2} \cos{\left(a + b x \right)}}{b} - \frac{d^{3} x^{3} \cos{\left(a + b x \right)}}{b} + \frac{3 c^{2} d \sin{\left(a + b x \right)}}{b^{2}} + \frac{6 c d^{2} x \sin{\left(a + b x \right)}}{b^{2}} + \frac{3 d^{3} x^{2} \sin{\left(a + b x \right)}}{b^{2}} + \frac{6 c d^{2} \cos{\left(a + b x \right)}}{b^{3}} + \frac{6 d^{3} x \cos{\left(a + b x \right)}}{b^{3}} - \frac{6 d^{3} \sin{\left(a + b x \right)}}{b^{4}} & \text{for}\: b \neq 0 \\\left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**3*cos(a + b*x)/b - 3*c**2*d*x*cos(a + b*x)/b - 3*c*d**2*x**2*cos(a + b*x)/b - d**3*x**3*cos(a + b*x)/b + 3*c**2*d*sin(a + b*x)/b**2 + 6*c*d**2*x*sin(a + b*x)/b**2 + 3*d**3*x**2*sin(a + b*x)/b**2 + 6*c*d**2*cos(a + b*x)/b**3 + 6*d**3*x*cos(a + b*x)/b**3 - 6*d**3*sin(a + b*x)/b**4, Ne(b, 0)), ((c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4)*sin(a), True))","A",0
3,1,112,0,0.727993," ","integrate((d*x+c)**2*sin(b*x+a),x)","\begin{cases} - \frac{c^{2} \cos{\left(a + b x \right)}}{b} - \frac{2 c d x \cos{\left(a + b x \right)}}{b} - \frac{d^{2} x^{2} \cos{\left(a + b x \right)}}{b} + \frac{2 c d \sin{\left(a + b x \right)}}{b^{2}} + \frac{2 d^{2} x \sin{\left(a + b x \right)}}{b^{2}} + \frac{2 d^{2} \cos{\left(a + b x \right)}}{b^{3}} & \text{for}\: b \neq 0 \\\left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**2*cos(a + b*x)/b - 2*c*d*x*cos(a + b*x)/b - d**2*x**2*cos(a + b*x)/b + 2*c*d*sin(a + b*x)/b**2 + 2*d**2*x*sin(a + b*x)/b**2 + 2*d**2*cos(a + b*x)/b**3, Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a), True))","A",0
4,1,46,0,0.246405," ","integrate((d*x+c)*sin(b*x+a),x)","\begin{cases} - \frac{c \cos{\left(a + b x \right)}}{b} - \frac{d x \cos{\left(a + b x \right)}}{b} + \frac{d \sin{\left(a + b x \right)}}{b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*cos(a + b*x)/b - d*x*cos(a + b*x)/b + d*sin(a + b*x)/b**2, Ne(b, 0)), ((c*x + d*x**2/2)*sin(a), True))","A",0
5,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c),x)","\int \frac{\sin{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x), x)","F",0
6,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c)**2,x)","\int \frac{\sin{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x)**2, x)","F",0
7,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c)**3,x)","\int \frac{\sin{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x)**3, x)","F",0
8,1,660,0,6.325265," ","integrate((d*x+c)**4*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{4} x \sin^{2}{\left(a + b x \right)}}{2} + \frac{c^{4} x \cos^{2}{\left(a + b x \right)}}{2} + c^{3} d x^{2} \sin^{2}{\left(a + b x \right)} + c^{3} d x^{2} \cos^{2}{\left(a + b x \right)} + c^{2} d^{2} x^{3} \sin^{2}{\left(a + b x \right)} + c^{2} d^{2} x^{3} \cos^{2}{\left(a + b x \right)} + \frac{c d^{3} x^{4} \sin^{2}{\left(a + b x \right)}}{2} + \frac{c d^{3} x^{4} \cos^{2}{\left(a + b x \right)}}{2} + \frac{d^{4} x^{5} \sin^{2}{\left(a + b x \right)}}{10} + \frac{d^{4} x^{5} \cos^{2}{\left(a + b x \right)}}{10} - \frac{c^{4} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{2 c^{3} d x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{3 c^{2} d^{2} x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c d^{3} x^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{d^{4} x^{4} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{c^{3} d \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{3 c^{2} d^{2} x \sin^{2}{\left(a + b x \right)}}{2 b^{2}} - \frac{3 c^{2} d^{2} x \cos^{2}{\left(a + b x \right)}}{2 b^{2}} + \frac{3 c d^{3} x^{2} \sin^{2}{\left(a + b x \right)}}{2 b^{2}} - \frac{3 c d^{3} x^{2} \cos^{2}{\left(a + b x \right)}}{2 b^{2}} + \frac{d^{4} x^{3} \sin^{2}{\left(a + b x \right)}}{2 b^{2}} - \frac{d^{4} x^{3} \cos^{2}{\left(a + b x \right)}}{2 b^{2}} + \frac{3 c^{2} d^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{3}} + \frac{3 c d^{3} x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{3}} + \frac{3 d^{4} x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{3}} + \frac{3 c d^{3} \cos^{2}{\left(a + b x \right)}}{2 b^{4}} - \frac{3 d^{4} x \sin^{2}{\left(a + b x \right)}}{4 b^{4}} + \frac{3 d^{4} x \cos^{2}{\left(a + b x \right)}}{4 b^{4}} - \frac{3 d^{4} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{5}} & \text{for}\: b \neq 0 \\\left(c^{4} x + 2 c^{3} d x^{2} + 2 c^{2} d^{2} x^{3} + c d^{3} x^{4} + \frac{d^{4} x^{5}}{5}\right) \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x*sin(a + b*x)**2/2 + c**4*x*cos(a + b*x)**2/2 + c**3*d*x**2*sin(a + b*x)**2 + c**3*d*x**2*cos(a + b*x)**2 + c**2*d**2*x**3*sin(a + b*x)**2 + c**2*d**2*x**3*cos(a + b*x)**2 + c*d**3*x**4*sin(a + b*x)**2/2 + c*d**3*x**4*cos(a + b*x)**2/2 + d**4*x**5*sin(a + b*x)**2/10 + d**4*x**5*cos(a + b*x)**2/10 - c**4*sin(a + b*x)*cos(a + b*x)/(2*b) - 2*c**3*d*x*sin(a + b*x)*cos(a + b*x)/b - 3*c**2*d**2*x**2*sin(a + b*x)*cos(a + b*x)/b - 2*c*d**3*x**3*sin(a + b*x)*cos(a + b*x)/b - d**4*x**4*sin(a + b*x)*cos(a + b*x)/(2*b) - c**3*d*cos(a + b*x)**2/b**2 + 3*c**2*d**2*x*sin(a + b*x)**2/(2*b**2) - 3*c**2*d**2*x*cos(a + b*x)**2/(2*b**2) + 3*c*d**3*x**2*sin(a + b*x)**2/(2*b**2) - 3*c*d**3*x**2*cos(a + b*x)**2/(2*b**2) + d**4*x**3*sin(a + b*x)**2/(2*b**2) - d**4*x**3*cos(a + b*x)**2/(2*b**2) + 3*c**2*d**2*sin(a + b*x)*cos(a + b*x)/(2*b**3) + 3*c*d**3*x*sin(a + b*x)*cos(a + b*x)/b**3 + 3*d**4*x**2*sin(a + b*x)*cos(a + b*x)/(2*b**3) + 3*c*d**3*cos(a + b*x)**2/(2*b**4) - 3*d**4*x*sin(a + b*x)**2/(4*b**4) + 3*d**4*x*cos(a + b*x)**2/(4*b**4) - 3*d**4*sin(a + b*x)*cos(a + b*x)/(4*b**5), Ne(b, 0)), ((c**4*x + 2*c**3*d*x**2 + 2*c**2*d**2*x**3 + c*d**3*x**4 + d**4*x**5/5)*sin(a)**2, True))","A",0
9,1,456,0,3.448622," ","integrate((d*x+c)**3*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{3} x \sin^{2}{\left(a + b x \right)}}{2} + \frac{c^{3} x \cos^{2}{\left(a + b x \right)}}{2} + \frac{3 c^{2} d x^{2} \sin^{2}{\left(a + b x \right)}}{4} + \frac{3 c^{2} d x^{2} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c d^{2} x^{3} \sin^{2}{\left(a + b x \right)}}{2} + \frac{c d^{2} x^{3} \cos^{2}{\left(a + b x \right)}}{2} + \frac{d^{3} x^{4} \sin^{2}{\left(a + b x \right)}}{8} + \frac{d^{3} x^{4} \cos^{2}{\left(a + b x \right)}}{8} - \frac{c^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{3 c^{2} d x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{3 c d^{2} x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{d^{3} x^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{3 c^{2} d \cos^{2}{\left(a + b x \right)}}{4 b^{2}} + \frac{3 c d^{2} x \sin^{2}{\left(a + b x \right)}}{4 b^{2}} - \frac{3 c d^{2} x \cos^{2}{\left(a + b x \right)}}{4 b^{2}} + \frac{3 d^{3} x^{2} \sin^{2}{\left(a + b x \right)}}{8 b^{2}} - \frac{3 d^{3} x^{2} \cos^{2}{\left(a + b x \right)}}{8 b^{2}} + \frac{3 c d^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{3}} + \frac{3 d^{3} x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{3}} + \frac{3 d^{3} \cos^{2}{\left(a + b x \right)}}{8 b^{4}} & \text{for}\: b \neq 0 \\\left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*x*sin(a + b*x)**2/2 + c**3*x*cos(a + b*x)**2/2 + 3*c**2*d*x**2*sin(a + b*x)**2/4 + 3*c**2*d*x**2*cos(a + b*x)**2/4 + c*d**2*x**3*sin(a + b*x)**2/2 + c*d**2*x**3*cos(a + b*x)**2/2 + d**3*x**4*sin(a + b*x)**2/8 + d**3*x**4*cos(a + b*x)**2/8 - c**3*sin(a + b*x)*cos(a + b*x)/(2*b) - 3*c**2*d*x*sin(a + b*x)*cos(a + b*x)/(2*b) - 3*c*d**2*x**2*sin(a + b*x)*cos(a + b*x)/(2*b) - d**3*x**3*sin(a + b*x)*cos(a + b*x)/(2*b) - 3*c**2*d*cos(a + b*x)**2/(4*b**2) + 3*c*d**2*x*sin(a + b*x)**2/(4*b**2) - 3*c*d**2*x*cos(a + b*x)**2/(4*b**2) + 3*d**3*x**2*sin(a + b*x)**2/(8*b**2) - 3*d**3*x**2*cos(a + b*x)**2/(8*b**2) + 3*c*d**2*sin(a + b*x)*cos(a + b*x)/(4*b**3) + 3*d**3*x*sin(a + b*x)*cos(a + b*x)/(4*b**3) + 3*d**3*cos(a + b*x)**2/(8*b**4), Ne(b, 0)), ((c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4)*sin(a)**2, True))","A",0
10,1,264,0,1.571277," ","integrate((d*x+c)**2*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{2} x \sin^{2}{\left(a + b x \right)}}{2} + \frac{c^{2} x \cos^{2}{\left(a + b x \right)}}{2} + \frac{c d x^{2} \sin^{2}{\left(a + b x \right)}}{2} + \frac{c d x^{2} \cos^{2}{\left(a + b x \right)}}{2} + \frac{d^{2} x^{3} \sin^{2}{\left(a + b x \right)}}{6} + \frac{d^{2} x^{3} \cos^{2}{\left(a + b x \right)}}{6} - \frac{c^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{c d x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{d^{2} x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{c d \cos^{2}{\left(a + b x \right)}}{2 b^{2}} + \frac{d^{2} x \sin^{2}{\left(a + b x \right)}}{4 b^{2}} - \frac{d^{2} x \cos^{2}{\left(a + b x \right)}}{4 b^{2}} + \frac{d^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{3}} & \text{for}\: b \neq 0 \\\left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*x*sin(a + b*x)**2/2 + c**2*x*cos(a + b*x)**2/2 + c*d*x**2*sin(a + b*x)**2/2 + c*d*x**2*cos(a + b*x)**2/2 + d**2*x**3*sin(a + b*x)**2/6 + d**2*x**3*cos(a + b*x)**2/6 - c**2*sin(a + b*x)*cos(a + b*x)/(2*b) - c*d*x*sin(a + b*x)*cos(a + b*x)/b - d**2*x**2*sin(a + b*x)*cos(a + b*x)/(2*b) - c*d*cos(a + b*x)**2/(2*b**2) + d**2*x*sin(a + b*x)**2/(4*b**2) - d**2*x*cos(a + b*x)**2/(4*b**2) + d**2*sin(a + b*x)*cos(a + b*x)/(4*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**2, True))","A",0
11,1,126,0,0.671699," ","integrate((d*x+c)*sin(b*x+a)**2,x)","\begin{cases} \frac{c x \sin^{2}{\left(a + b x \right)}}{2} + \frac{c x \cos^{2}{\left(a + b x \right)}}{2} + \frac{d x^{2} \sin^{2}{\left(a + b x \right)}}{4} + \frac{d x^{2} \cos^{2}{\left(a + b x \right)}}{4} - \frac{c \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{d x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{d \cos^{2}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x*sin(a + b*x)**2/2 + c*x*cos(a + b*x)**2/2 + d*x**2*sin(a + b*x)**2/4 + d*x**2*cos(a + b*x)**2/4 - c*sin(a + b*x)*cos(a + b*x)/(2*b) - d*x*sin(a + b*x)*cos(a + b*x)/(2*b) - d*cos(a + b*x)**2/(4*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**2, True))","A",0
12,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c),x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**2/(c + d*x), x)","F",0
13,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**2/(c + d*x)**2, x)","F",0
14,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**3,x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**2/(c + d*x)**3, x)","F",0
15,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**4,x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)**2/(c + d*x)**4, x)","F",0
16,1,772,0,10.994729," ","integrate((d*x+c)**4*sin(b*x+a)**3,x)","\begin{cases} - \frac{c^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c^{4} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{4 c^{3} d x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{8 c^{3} d x \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{6 c^{2} d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{4 c^{2} d^{2} x^{2} \cos^{3}{\left(a + b x \right)}}{b} - \frac{4 c d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{8 c d^{3} x^{3} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{d^{4} x^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 d^{4} x^{4} \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{28 c^{3} d \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{8 c^{3} d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{28 c^{2} d^{2} x \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{8 c^{2} d^{2} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{28 c d^{3} x^{2} \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{8 c d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{28 d^{4} x^{3} \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{8 d^{4} x^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{28 c^{2} d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{80 c^{2} d^{2} \cos^{3}{\left(a + b x \right)}}{9 b^{3}} + \frac{56 c d^{3} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{160 c d^{3} x \cos^{3}{\left(a + b x \right)}}{9 b^{3}} + \frac{28 d^{4} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{80 d^{4} x^{2} \cos^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{488 c d^{3} \sin^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{160 c d^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{4}} - \frac{488 d^{4} x \sin^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{160 d^{4} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{4}} - \frac{488 d^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{27 b^{5}} - \frac{1456 d^{4} \cos^{3}{\left(a + b x \right)}}{81 b^{5}} & \text{for}\: b \neq 0 \\\left(c^{4} x + 2 c^{3} d x^{2} + 2 c^{2} d^{2} x^{3} + c d^{3} x^{4} + \frac{d^{4} x^{5}}{5}\right) \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**4*sin(a + b*x)**2*cos(a + b*x)/b - 2*c**4*cos(a + b*x)**3/(3*b) - 4*c**3*d*x*sin(a + b*x)**2*cos(a + b*x)/b - 8*c**3*d*x*cos(a + b*x)**3/(3*b) - 6*c**2*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)/b - 4*c**2*d**2*x**2*cos(a + b*x)**3/b - 4*c*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)/b - 8*c*d**3*x**3*cos(a + b*x)**3/(3*b) - d**4*x**4*sin(a + b*x)**2*cos(a + b*x)/b - 2*d**4*x**4*cos(a + b*x)**3/(3*b) + 28*c**3*d*sin(a + b*x)**3/(9*b**2) + 8*c**3*d*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 28*c**2*d**2*x*sin(a + b*x)**3/(3*b**2) + 8*c**2*d**2*x*sin(a + b*x)*cos(a + b*x)**2/b**2 + 28*c*d**3*x**2*sin(a + b*x)**3/(3*b**2) + 8*c*d**3*x**2*sin(a + b*x)*cos(a + b*x)**2/b**2 + 28*d**4*x**3*sin(a + b*x)**3/(9*b**2) + 8*d**4*x**3*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 28*c**2*d**2*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 80*c**2*d**2*cos(a + b*x)**3/(9*b**3) + 56*c*d**3*x*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 160*c*d**3*x*cos(a + b*x)**3/(9*b**3) + 28*d**4*x**2*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 80*d**4*x**2*cos(a + b*x)**3/(9*b**3) - 488*c*d**3*sin(a + b*x)**3/(27*b**4) - 160*c*d**3*sin(a + b*x)*cos(a + b*x)**2/(9*b**4) - 488*d**4*x*sin(a + b*x)**3/(27*b**4) - 160*d**4*x*sin(a + b*x)*cos(a + b*x)**2/(9*b**4) - 488*d**4*sin(a + b*x)**2*cos(a + b*x)/(27*b**5) - 1456*d**4*cos(a + b*x)**3/(81*b**5), Ne(b, 0)), ((c**4*x + 2*c**3*d*x**2 + 2*c**2*d**2*x**3 + c*d**3*x**4 + d**4*x**5/5)*sin(a)**3, True))","A",0
17,1,495,0,5.737352," ","integrate((d*x+c)**3*sin(b*x+a)**3,x)","\begin{cases} - \frac{c^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c^{3} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{3 c^{2} d x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c^{2} d x \cos^{3}{\left(a + b x \right)}}{b} - \frac{3 c d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c d^{2} x^{2} \cos^{3}{\left(a + b x \right)}}{b} - \frac{d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 d^{3} x^{3} \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{7 c^{2} d \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 c^{2} d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{14 c d^{2} x \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 c d^{2} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{7 d^{3} x^{2} \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{14 c d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{40 c d^{2} \cos^{3}{\left(a + b x \right)}}{9 b^{3}} + \frac{14 d^{3} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{40 d^{3} x \cos^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{122 d^{3} \sin^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{40 d^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{4}} & \text{for}\: b \neq 0 \\\left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**3*sin(a + b*x)**2*cos(a + b*x)/b - 2*c**3*cos(a + b*x)**3/(3*b) - 3*c**2*d*x*sin(a + b*x)**2*cos(a + b*x)/b - 2*c**2*d*x*cos(a + b*x)**3/b - 3*c*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)/b - 2*c*d**2*x**2*cos(a + b*x)**3/b - d**3*x**3*sin(a + b*x)**2*cos(a + b*x)/b - 2*d**3*x**3*cos(a + b*x)**3/(3*b) + 7*c**2*d*sin(a + b*x)**3/(3*b**2) + 2*c**2*d*sin(a + b*x)*cos(a + b*x)**2/b**2 + 14*c*d**2*x*sin(a + b*x)**3/(3*b**2) + 4*c*d**2*x*sin(a + b*x)*cos(a + b*x)**2/b**2 + 7*d**3*x**2*sin(a + b*x)**3/(3*b**2) + 2*d**3*x**2*sin(a + b*x)*cos(a + b*x)**2/b**2 + 14*c*d**2*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 40*c*d**2*cos(a + b*x)**3/(9*b**3) + 14*d**3*x*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 40*d**3*x*cos(a + b*x)**3/(9*b**3) - 122*d**3*sin(a + b*x)**3/(27*b**4) - 40*d**3*sin(a + b*x)*cos(a + b*x)**2/(9*b**4), Ne(b, 0)), ((c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4)*sin(a)**3, True))","A",0
18,1,284,0,3.043058," ","integrate((d*x+c)**2*sin(b*x+a)**3,x)","\begin{cases} - \frac{c^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c^{2} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c d x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{4 c d x \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 d^{2} x^{2} \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{14 c d \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{4 c d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{14 d^{2} x \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{4 d^{2} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{14 d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{3}} + \frac{40 d^{2} \cos^{3}{\left(a + b x \right)}}{27 b^{3}} & \text{for}\: b \neq 0 \\\left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**2*sin(a + b*x)**2*cos(a + b*x)/b - 2*c**2*cos(a + b*x)**3/(3*b) - 2*c*d*x*sin(a + b*x)**2*cos(a + b*x)/b - 4*c*d*x*cos(a + b*x)**3/(3*b) - d**2*x**2*sin(a + b*x)**2*cos(a + b*x)/b - 2*d**2*x**2*cos(a + b*x)**3/(3*b) + 14*c*d*sin(a + b*x)**3/(9*b**2) + 4*c*d*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 14*d**2*x*sin(a + b*x)**3/(9*b**2) + 4*d**2*x*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 14*d**2*sin(a + b*x)**2*cos(a + b*x)/(9*b**3) + 40*d**2*cos(a + b*x)**3/(27*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**3, True))","A",0
19,1,126,0,1.254977," ","integrate((d*x+c)*sin(b*x+a)**3,x)","\begin{cases} - \frac{c \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 c \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{d x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 d x \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{7 d \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{2 d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*sin(a + b*x)**2*cos(a + b*x)/b - 2*c*cos(a + b*x)**3/(3*b) - d*x*sin(a + b*x)**2*cos(a + b*x)/b - 2*d*x*cos(a + b*x)**3/(3*b) + 7*d*sin(a + b*x)**3/(9*b**2) + 2*d*sin(a + b*x)*cos(a + b*x)**2/(3*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**3, True))","A",0
20,0,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c),x)","\int \frac{\sin^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**3/(c + d*x), x)","F",0
21,0,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\sin^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**3/(c + d*x)**2, x)","F",0
22,0,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c)**3,x)","\int \frac{\sin^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**3/(c + d*x)**3, x)","F",0
23,0,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a),x)","\int \left(c + d x\right)^{3} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*csc(a + b*x), x)","F",0
24,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a),x)","\int \left(c + d x\right)^{2} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x), x)","F",0
25,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a),x)","\int \left(c + d x\right) \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x), x)","F",0
26,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*x+c),x)","\int \frac{\csc{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)/(c + d*x), x)","F",0
27,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*x+c)**2,x)","\int \frac{\csc{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)/(c + d*x)**2, x)","F",0
28,0,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*csc(a + b*x)**2, x)","F",0
29,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)**2, x)","F",0
30,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**2,x)","\int \left(c + d x\right) \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**2, x)","F",0
31,0,0,0,0.000000," ","integrate(csc(b*x+a)**2/(d*x+c),x)","\int \frac{\csc^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**2/(c + d*x), x)","F",0
32,0,0,0,0.000000," ","integrate(csc(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\csc^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**2/(c + d*x)**2, x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**3,x)","\int \left(c + d x\right)^{3} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*csc(a + b*x)**3, x)","F",0
34,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)**3, x)","F",0
35,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**3,x)","\int \left(c + d x\right) \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**3, x)","F",0
36,0,0,0,0.000000," ","integrate(csc(b*x+a)**3/(d*x+c),x)","\int \frac{\csc^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**3/(c + d*x), x)","F",0
37,0,0,0,0.000000," ","integrate(csc(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\csc^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**3/(c + d*x)**2, x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)**(5/2)*sin(b*x+a),x)","\int \left(c + d x\right)^{\frac{5}{2}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(5/2)*sin(a + b*x), x)","F",0
39,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*sin(b*x+a),x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x), x)","F",0
40,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*sin(b*x+a),x)","\int \sqrt{c + d x} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x), x)","F",0
41,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c)**(1/2),x)","\int \frac{\sin{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(sin(a + b*x)/sqrt(c + d*x), x)","F",0
42,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c)**(3/2),x)","\int \frac{\sin{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x)**(3/2), x)","F",0
43,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c)**(5/2),x)","\int \frac{\sin{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x)**(5/2), x)","F",0
44,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x+c)**(7/2),x)","\int \frac{\sin{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x)**(7/2), x)","F",0
45,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)**2, x)","F",0
47,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2, x)","F",0
48,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**(1/2),x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(sin(a + b*x)**2/sqrt(c + d*x), x)","F",0
49,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**(3/2),x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)**2/(c + d*x)**(3/2), x)","F",0
50,0,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**(5/2),x)","\int \frac{\sin^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)**2/(c + d*x)**(5/2), x)","F",0
51,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*sin(b*x+a)**3,x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)**3, x)","F",0
55,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*sin(b*x+a)**3,x)","\int \sqrt{c + d x} \sin^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**3, x)","F",0
56,0,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c)**(1/2),x)","\int \frac{\sin^{3}{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(sin(a + b*x)**3/sqrt(c + d*x), x)","F",0
57,0,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c)**(3/2),x)","\int \frac{\sin^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)**3/(c + d*x)**(3/2), x)","F",0
58,0,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c)**(5/2),x)","\int \frac{\sin^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(a + b*x)**3/(c + d*x)**(5/2), x)","F",0
59,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,1,117,0,21.826881," ","integrate((d*x)**(3/2)*sin(f*x),x)","- \frac{7 d^{\frac{3}{2}} x^{\frac{3}{2}} \cos{\left(f x \right)} \Gamma\left(\frac{7}{4}\right)}{4 f \Gamma\left(\frac{11}{4}\right)} + \frac{21 d^{\frac{3}{2}} \sqrt{x} \sin{\left(f x \right)} \Gamma\left(\frac{7}{4}\right)}{8 f^{2} \Gamma\left(\frac{11}{4}\right)} - \frac{21 \sqrt{2} \sqrt{\pi} d^{\frac{3}{2}} S\left(\frac{\sqrt{2} \sqrt{f} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{7}{4}\right)}{16 f^{\frac{5}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"-7*d**(3/2)*x**(3/2)*cos(f*x)*gamma(7/4)/(4*f*gamma(11/4)) + 21*d**(3/2)*sqrt(x)*sin(f*x)*gamma(7/4)/(8*f**2*gamma(11/4)) - 21*sqrt(2)*sqrt(pi)*d**(3/2)*fresnels(sqrt(2)*sqrt(f)*sqrt(x)/sqrt(pi))*gamma(7/4)/(16*f**(5/2)*gamma(11/4))","A",0
61,1,85,0,2.102463," ","integrate((d*x)**(1/2)*sin(f*x),x)","- \frac{5 \sqrt{d} \sqrt{x} \cos{\left(f x \right)} \Gamma\left(\frac{5}{4}\right)}{4 f \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} \sqrt{d} C\left(\frac{\sqrt{2} \sqrt{f} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 f^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"-5*sqrt(d)*sqrt(x)*cos(f*x)*gamma(5/4)/(4*f*gamma(9/4)) + 5*sqrt(2)*sqrt(pi)*sqrt(d)*fresnelc(sqrt(2)*sqrt(f)*sqrt(x)/sqrt(pi))*gamma(5/4)/(8*f**(3/2)*gamma(9/4))","A",0
62,1,54,0,1.161704," ","integrate(sin(f*x)/(d*x)**(1/2),x)","\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} \sqrt{f} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{4 \sqrt{d} \sqrt{f} \Gamma\left(\frac{7}{4}\right)}"," ",0,"3*sqrt(2)*sqrt(pi)*fresnels(sqrt(2)*sqrt(f)*sqrt(x)/sqrt(pi))*gamma(3/4)/(4*sqrt(d)*sqrt(f)*gamma(7/4))","A",0
63,1,80,0,3.424922," ","integrate(sin(f*x)/(d*x)**(3/2),x)","\frac{\sqrt{2} \sqrt{\pi} \sqrt{f} C\left(\frac{\sqrt{2} \sqrt{f} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 d^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)} - \frac{\sin{\left(f x \right)} \Gamma\left(\frac{1}{4}\right)}{2 d^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(2)*sqrt(pi)*sqrt(f)*fresnelc(sqrt(2)*sqrt(f)*sqrt(x)/sqrt(pi))*gamma(1/4)/(2*d**(3/2)*gamma(5/4)) - sin(f*x)*gamma(1/4)/(2*d**(3/2)*sqrt(x)*gamma(5/4))","A",0
64,1,114,0,24.496284," ","integrate(sin(f*x)/(d*x)**(5/2),x)","\frac{\sqrt{2} \sqrt{\pi} f^{\frac{3}{2}} S\left(\frac{\sqrt{2} \sqrt{f} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(- \frac{1}{4}\right)}{3 d^{\frac{5}{2}} \Gamma\left(\frac{3}{4}\right)} + \frac{f \cos{\left(f x \right)} \Gamma\left(- \frac{1}{4}\right)}{3 d^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{\sin{\left(f x \right)} \Gamma\left(- \frac{1}{4}\right)}{6 d^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(2)*sqrt(pi)*f**(3/2)*fresnels(sqrt(2)*sqrt(f)*sqrt(x)/sqrt(pi))*gamma(-1/4)/(3*d**(5/2)*gamma(3/4)) + f*cos(f*x)*gamma(-1/4)/(3*d**(5/2)*sqrt(x)*gamma(3/4)) + sin(f*x)*gamma(-1/4)/(6*d**(5/2)*x**(3/2)*gamma(3/4))","A",0
65,0,0,0,0.000000," ","integrate(csc(b*x+a)*(d*x+c)**(1/2),x)","\int \sqrt{c + d x} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*csc(a + b*x), x)","F",0
66,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*x+c)**(1/2),x)","\int \frac{\csc{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(csc(a + b*x)/sqrt(c + d*x), x)","F",0
67,0,0,0,0.000000," ","integrate(x/sin(f*x+e)**(3/2)+x*sin(f*x+e)**(1/2),x)","\int \frac{x \left(\sin^{2}{\left(e + f x \right)} + 1\right)}{\sin^{\frac{3}{2}}{\left(e + f x \right)}}\, dx"," ",0,"Integral(x*(sin(e + f*x)**2 + 1)/sin(e + f*x)**(3/2), x)","F",0
68,0,0,0,0.000000," ","integrate(x**2/sin(f*x+e)**(3/2)+x**2*sin(f*x+e)**(1/2),x)","\int \frac{x^{2} \left(\sin^{2}{\left(e + f x \right)} + 1\right)}{\sin^{\frac{3}{2}}{\left(e + f x \right)}}\, dx"," ",0,"Integral(x**2*(sin(e + f*x)**2 + 1)/sin(e + f*x)**(3/2), x)","F",0
69,0,0,0,0.000000," ","integrate(x/sin(f*x+e)**(5/2)-1/3*x/sin(f*x+e)**(1/2),x)","- \frac{\int \left(- \frac{3 x}{\sin^{\frac{5}{2}}{\left(e + f x \right)}}\right)\, dx + \int \frac{x}{\sqrt{\sin{\left(e + f x \right)}}}\, dx}{3}"," ",0,"-(Integral(-3*x/sin(e + f*x)**(5/2), x) + Integral(x/sqrt(sin(e + f*x)), x))/3","F",0
70,0,0,0,0.000000," ","integrate(x/sin(f*x+e)**(7/2)+3/5*x*sin(f*x+e)**(1/2),x)","\frac{\int \frac{5 x}{\sin^{\frac{7}{2}}{\left(e + f x \right)}}\, dx + \int 3 x \sqrt{\sin{\left(e + f x \right)}}\, dx}{5}"," ",0,"(Integral(5*x/sin(e + f*x)**(7/2), x) + Integral(3*x*sqrt(sin(e + f*x)), x))/5","F",0
71,0,0,0,0.000000," ","integrate((d*x+c)**m*(b*sin(f*x+e))**n,x)","\int \left(b \sin{\left(e + f x \right)}\right)^{n} \left(c + d x\right)^{m}\, dx"," ",0,"Integral((b*sin(e + f*x))**n*(c + d*x)**m, x)","F",0
72,0,0,0,0.000000," ","integrate((d*x+c)**m*sin(b*x+a)**3,x)","\int \left(c + d x\right)^{m} \sin^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)**3, x)","F",0
73,0,0,0,0.000000," ","integrate((d*x+c)**m*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)**2, x)","F",0
74,0,0,0,0.000000," ","integrate((d*x+c)**m*sin(b*x+a),x)","\int \left(c + d x\right)^{m} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x), x)","F",0
75,0,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a),x)","\int \left(c + d x\right)^{m} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*csc(a + b*x), x)","F",0
76,0,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*csc(a + b*x)**2, x)","F",0
77,0,0,0,0.000000," ","integrate(x**(3+m)*sin(b*x+a),x)","\int x^{m + 3} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 3)*sin(a + b*x), x)","F",0
78,0,0,0,0.000000," ","integrate(x**(2+m)*sin(b*x+a),x)","\int x^{m + 2} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 2)*sin(a + b*x), x)","F",0
79,0,0,0,0.000000," ","integrate(x**(1+m)*sin(b*x+a),x)","\int x^{m + 1} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 1)*sin(a + b*x), x)","F",0
80,0,0,0,0.000000," ","integrate(x**m*sin(b*x+a),x)","\int x^{m} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**m*sin(a + b*x), x)","F",0
81,0,0,0,0.000000," ","integrate(x**(-1+m)*sin(b*x+a),x)","\int x^{m - 1} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 1)*sin(a + b*x), x)","F",0
82,0,0,0,0.000000," ","integrate(x**(-2+m)*sin(b*x+a),x)","\int x^{m - 2} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 2)*sin(a + b*x), x)","F",0
83,0,0,0,0.000000," ","integrate(x**(-3+m)*sin(b*x+a),x)","\int x^{m - 3} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 3)*sin(a + b*x), x)","F",0
84,0,0,0,0.000000," ","integrate(x**(3+m)*sin(b*x+a)**2,x)","\int x^{m + 3} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 3)*sin(a + b*x)**2, x)","F",0
85,0,0,0,0.000000," ","integrate(x**(2+m)*sin(b*x+a)**2,x)","\int x^{m + 2} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 2)*sin(a + b*x)**2, x)","F",0
86,0,0,0,0.000000," ","integrate(x**(1+m)*sin(b*x+a)**2,x)","\int x^{m + 1} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 1)*sin(a + b*x)**2, x)","F",0
87,0,0,0,0.000000," ","integrate(x**m*sin(b*x+a)**2,x)","\int x^{m} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**m*sin(a + b*x)**2, x)","F",0
88,0,0,0,0.000000," ","integrate(x**(-1+m)*sin(b*x+a)**2,x)","\int x^{m - 1} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 1)*sin(a + b*x)**2, x)","F",0
89,0,0,0,0.000000," ","integrate(x**(-2+m)*sin(b*x+a)**2,x)","\int x^{m - 2} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 2)*sin(a + b*x)**2, x)","F",0
90,0,0,0,0.000000," ","integrate(x**(-3+m)*sin(b*x+a)**2,x)","\int x^{m - 3} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 3)*sin(a + b*x)**2, x)","F",0
91,0,0,0,0.000000," ","integrate(x/csc(f*x+e)**(3/2)-1/3*x*csc(f*x+e)**(1/2),x)","- \frac{\int \left(- \frac{3 x}{\csc^{\frac{3}{2}}{\left(e + f x \right)}}\right)\, dx + \int x \sqrt{\csc{\left(e + f x \right)}}\, dx}{3}"," ",0,"-(Integral(-3*x/csc(e + f*x)**(3/2), x) + Integral(x*sqrt(csc(e + f*x)), x))/3","F",0
92,0,0,0,0.000000," ","integrate(x**2/csc(f*x+e)**(3/2)-1/3*x**2*csc(f*x+e)**(1/2),x)","- \frac{\int \left(- \frac{3 x^{2}}{\csc^{\frac{3}{2}}{\left(e + f x \right)}}\right)\, dx + \int x^{2} \sqrt{\csc{\left(e + f x \right)}}\, dx}{3}"," ",0,"-(Integral(-3*x**2/csc(e + f*x)**(3/2), x) + Integral(x**2*sqrt(csc(e + f*x)), x))/3","F",0
93,0,0,0,0.000000," ","integrate(x/csc(f*x+e)**(5/2)-3/5*x/csc(f*x+e)**(1/2),x)","- \frac{\int \left(- \frac{5 x}{\csc^{\frac{5}{2}}{\left(e + f x \right)}}\right)\, dx + \int \frac{3 x}{\sqrt{\csc{\left(e + f x \right)}}}\, dx}{5}"," ",0,"-(Integral(-5*x/csc(e + f*x)**(5/2), x) + Integral(3*x/sqrt(csc(e + f*x)), x))/5","F",0
94,0,0,0,0.000000," ","integrate(x/csc(f*x+e)**(7/2)-5/21*x*csc(f*x+e)**(1/2),x)","- \frac{\int \left(- \frac{21 x}{\csc^{\frac{7}{2}}{\left(e + f x \right)}}\right)\, dx + \int 5 x \sqrt{\csc{\left(e + f x \right)}}\, dx}{21}"," ",0,"-(Integral(-21*x/csc(e + f*x)**(7/2), x) + Integral(5*x*sqrt(csc(e + f*x)), x))/21","F",0
95,1,264,0,1.787432," ","integrate((d*x+c)**3*(a+a*sin(f*x+e)),x)","\begin{cases} a c^{3} x - \frac{a c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 a c^{2} d x^{2}}{2} - \frac{3 a c^{2} d x \cos{\left(e + f x \right)}}{f} + \frac{3 a c^{2} d \sin{\left(e + f x \right)}}{f^{2}} + a c d^{2} x^{3} - \frac{3 a c d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{6 a c d^{2} x \sin{\left(e + f x \right)}}{f^{2}} + \frac{6 a c d^{2} \cos{\left(e + f x \right)}}{f^{3}} + \frac{a d^{3} x^{4}}{4} - \frac{a d^{3} x^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 a d^{3} x^{2} \sin{\left(e + f x \right)}}{f^{2}} + \frac{6 a d^{3} x \cos{\left(e + f x \right)}}{f^{3}} - \frac{6 a d^{3} \sin{\left(e + f x \right)}}{f^{4}} & \text{for}\: f \neq 0 \\\left(a \sin{\left(e \right)} + a\right) \left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*x - a*c**3*cos(e + f*x)/f + 3*a*c**2*d*x**2/2 - 3*a*c**2*d*x*cos(e + f*x)/f + 3*a*c**2*d*sin(e + f*x)/f**2 + a*c*d**2*x**3 - 3*a*c*d**2*x**2*cos(e + f*x)/f + 6*a*c*d**2*x*sin(e + f*x)/f**2 + 6*a*c*d**2*cos(e + f*x)/f**3 + a*d**3*x**4/4 - a*d**3*x**3*cos(e + f*x)/f + 3*a*d**3*x**2*sin(e + f*x)/f**2 + 6*a*d**3*x*cos(e + f*x)/f**3 - 6*a*d**3*sin(e + f*x)/f**4, Ne(f, 0)), ((a*sin(e) + a)*(c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4), True))","A",0
96,1,151,0,0.805484," ","integrate((d*x+c)**2*(a+a*sin(f*x+e)),x)","\begin{cases} a c^{2} x - \frac{a c^{2} \cos{\left(e + f x \right)}}{f} + a c d x^{2} - \frac{2 a c d x \cos{\left(e + f x \right)}}{f} + \frac{2 a c d \sin{\left(e + f x \right)}}{f^{2}} + \frac{a d^{2} x^{3}}{3} - \frac{a d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{2 a d^{2} x \sin{\left(e + f x \right)}}{f^{2}} + \frac{2 a d^{2} \cos{\left(e + f x \right)}}{f^{3}} & \text{for}\: f \neq 0 \\\left(a \sin{\left(e \right)} + a\right) \left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*x - a*c**2*cos(e + f*x)/f + a*c*d*x**2 - 2*a*c*d*x*cos(e + f*x)/f + 2*a*c*d*sin(e + f*x)/f**2 + a*d**2*x**3/3 - a*d**2*x**2*cos(e + f*x)/f + 2*a*d**2*x*sin(e + f*x)/f**2 + 2*a*d**2*cos(e + f*x)/f**3, Ne(f, 0)), ((a*sin(e) + a)*(c**2*x + c*d*x**2 + d**2*x**3/3), True))","A",0
97,1,68,0,0.314936," ","integrate((d*x+c)*(a+a*sin(f*x+e)),x)","\begin{cases} a c x - \frac{a c \cos{\left(e + f x \right)}}{f} + \frac{a d x^{2}}{2} - \frac{a d x \cos{\left(e + f x \right)}}{f} + \frac{a d \sin{\left(e + f x \right)}}{f^{2}} & \text{for}\: f \neq 0 \\\left(a \sin{\left(e \right)} + a\right) \left(c x + \frac{d x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x - a*c*cos(e + f*x)/f + a*d*x**2/2 - a*d*x*cos(e + f*x)/f + a*d*sin(e + f*x)/f**2, Ne(f, 0)), ((a*sin(e) + a)*(c*x + d*x**2/2), True))","A",0
98,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(d*x+c),x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{c + d x}\, dx + \int \frac{1}{c + d x}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/(c + d*x), x) + Integral(1/(c + d*x), x))","F",0
99,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(d*x+c)**2,x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{1}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(1/(c**2 + 2*c*d*x + d**2*x**2), x))","F",0
100,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(d*x+c)**3,x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{1}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(1/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))","F",0
101,1,779,0,4.619185," ","integrate((d*x+c)**3*(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{a^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{3} x - \frac{a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} c^{2} d x^{2} \sin^{2}{\left(e + f x \right)}}{4} + \frac{3 a^{2} c^{2} d x^{2} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a^{2} c^{2} d x^{2}}{2} - \frac{3 a^{2} c^{2} d x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{6 a^{2} c^{2} d x \cos{\left(e + f x \right)}}{f} + \frac{6 a^{2} c^{2} d \sin{\left(e + f x \right)}}{f^{2}} - \frac{3 a^{2} c^{2} d \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{a^{2} c d^{2} x^{3} \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c d^{2} x^{3} \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c d^{2} x^{3} - \frac{3 a^{2} c d^{2} x^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{6 a^{2} c d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{12 a^{2} c d^{2} x \sin{\left(e + f x \right)}}{f^{2}} - \frac{3 a^{2} c d^{2} x \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{3 a^{2} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f^{3}} + \frac{12 a^{2} c d^{2} \cos{\left(e + f x \right)}}{f^{3}} + \frac{a^{2} d^{3} x^{4} \sin^{2}{\left(e + f x \right)}}{8} + \frac{a^{2} d^{3} x^{4} \cos^{2}{\left(e + f x \right)}}{8} + \frac{a^{2} d^{3} x^{4}}{4} - \frac{a^{2} d^{3} x^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} d^{3} x^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} d^{3} x^{2} \sin^{2}{\left(e + f x \right)}}{8 f^{2}} + \frac{6 a^{2} d^{3} x^{2} \sin{\left(e + f x \right)}}{f^{2}} - \frac{3 a^{2} d^{3} x^{2} \cos^{2}{\left(e + f x \right)}}{8 f^{2}} + \frac{3 a^{2} d^{3} x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f^{3}} + \frac{12 a^{2} d^{3} x \cos{\left(e + f x \right)}}{f^{3}} - \frac{12 a^{2} d^{3} \sin{\left(e + f x \right)}}{f^{4}} + \frac{3 a^{2} d^{3} \cos^{2}{\left(e + f x \right)}}{8 f^{4}} & \text{for}\: f \neq 0 \\\left(a \sin{\left(e \right)} + a\right)^{2} \left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*x*sin(e + f*x)**2/2 + a**2*c**3*x*cos(e + f*x)**2/2 + a**2*c**3*x - a**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c**3*cos(e + f*x)/f + 3*a**2*c**2*d*x**2*sin(e + f*x)**2/4 + 3*a**2*c**2*d*x**2*cos(e + f*x)**2/4 + 3*a**2*c**2*d*x**2/2 - 3*a**2*c**2*d*x*sin(e + f*x)*cos(e + f*x)/(2*f) - 6*a**2*c**2*d*x*cos(e + f*x)/f + 6*a**2*c**2*d*sin(e + f*x)/f**2 - 3*a**2*c**2*d*cos(e + f*x)**2/(4*f**2) + a**2*c*d**2*x**3*sin(e + f*x)**2/2 + a**2*c*d**2*x**3*cos(e + f*x)**2/2 + a**2*c*d**2*x**3 - 3*a**2*c*d**2*x**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 6*a**2*c*d**2*x**2*cos(e + f*x)/f + 3*a**2*c*d**2*x*sin(e + f*x)**2/(4*f**2) + 12*a**2*c*d**2*x*sin(e + f*x)/f**2 - 3*a**2*c*d**2*x*cos(e + f*x)**2/(4*f**2) + 3*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)/(4*f**3) + 12*a**2*c*d**2*cos(e + f*x)/f**3 + a**2*d**3*x**4*sin(e + f*x)**2/8 + a**2*d**3*x**4*cos(e + f*x)**2/8 + a**2*d**3*x**4/4 - a**2*d**3*x**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*d**3*x**3*cos(e + f*x)/f + 3*a**2*d**3*x**2*sin(e + f*x)**2/(8*f**2) + 6*a**2*d**3*x**2*sin(e + f*x)/f**2 - 3*a**2*d**3*x**2*cos(e + f*x)**2/(8*f**2) + 3*a**2*d**3*x*sin(e + f*x)*cos(e + f*x)/(4*f**3) + 12*a**2*d**3*x*cos(e + f*x)/f**3 - 12*a**2*d**3*sin(e + f*x)/f**4 + 3*a**2*d**3*cos(e + f*x)**2/(8*f**4), Ne(f, 0)), ((a*sin(e) + a)**2*(c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4), True))","A",0
102,1,456,0,2.118336," ","integrate((d*x+c)**2*(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{a^{2} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{2} x - \frac{a^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c^{2} \cos{\left(e + f x \right)}}{f} + \frac{a^{2} c d x^{2} \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c d x^{2} \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c d x^{2} - \frac{a^{2} c d x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a^{2} c d x \cos{\left(e + f x \right)}}{f} + \frac{4 a^{2} c d \sin{\left(e + f x \right)}}{f^{2}} - \frac{a^{2} c d \cos^{2}{\left(e + f x \right)}}{2 f^{2}} + \frac{a^{2} d^{2} x^{3} \sin^{2}{\left(e + f x \right)}}{6} + \frac{a^{2} d^{2} x^{3} \cos^{2}{\left(e + f x \right)}}{6} + \frac{a^{2} d^{2} x^{3}}{3} - \frac{a^{2} d^{2} x^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{a^{2} d^{2} x \sin^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{4 a^{2} d^{2} x \sin{\left(e + f x \right)}}{f^{2}} - \frac{a^{2} d^{2} x \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{a^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f^{3}} + \frac{4 a^{2} d^{2} \cos{\left(e + f x \right)}}{f^{3}} & \text{for}\: f \neq 0 \\\left(a \sin{\left(e \right)} + a\right)^{2} \left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*x*sin(e + f*x)**2/2 + a**2*c**2*x*cos(e + f*x)**2/2 + a**2*c**2*x - a**2*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c**2*cos(e + f*x)/f + a**2*c*d*x**2*sin(e + f*x)**2/2 + a**2*c*d*x**2*cos(e + f*x)**2/2 + a**2*c*d*x**2 - a**2*c*d*x*sin(e + f*x)*cos(e + f*x)/f - 4*a**2*c*d*x*cos(e + f*x)/f + 4*a**2*c*d*sin(e + f*x)/f**2 - a**2*c*d*cos(e + f*x)**2/(2*f**2) + a**2*d**2*x**3*sin(e + f*x)**2/6 + a**2*d**2*x**3*cos(e + f*x)**2/6 + a**2*d**2*x**3/3 - a**2*d**2*x**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*d**2*x**2*cos(e + f*x)/f + a**2*d**2*x*sin(e + f*x)**2/(4*f**2) + 4*a**2*d**2*x*sin(e + f*x)/f**2 - a**2*d**2*x*cos(e + f*x)**2/(4*f**2) + a**2*d**2*sin(e + f*x)*cos(e + f*x)/(4*f**3) + 4*a**2*d**2*cos(e + f*x)/f**3, Ne(f, 0)), ((a*sin(e) + a)**2*(c**2*x + c*d*x**2 + d**2*x**3/3), True))","A",0
103,1,219,0,0.816922," ","integrate((d*x+c)*(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c x - \frac{a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c \cos{\left(e + f x \right)}}{f} + \frac{a^{2} d x^{2} \sin^{2}{\left(e + f x \right)}}{4} + \frac{a^{2} d x^{2} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a^{2} d x^{2}}{2} - \frac{a^{2} d x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} d x \cos{\left(e + f x \right)}}{f} + \frac{2 a^{2} d \sin{\left(e + f x \right)}}{f^{2}} - \frac{a^{2} d \cos^{2}{\left(e + f x \right)}}{4 f^{2}} & \text{for}\: f \neq 0 \\\left(a \sin{\left(e \right)} + a\right)^{2} \left(c x + \frac{d x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x*sin(e + f*x)**2/2 + a**2*c*x*cos(e + f*x)**2/2 + a**2*c*x - a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c*cos(e + f*x)/f + a**2*d*x**2*sin(e + f*x)**2/4 + a**2*d*x**2*cos(e + f*x)**2/4 + a**2*d*x**2/2 - a**2*d*x*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*d*x*cos(e + f*x)/f + 2*a**2*d*sin(e + f*x)/f**2 - a**2*d*cos(e + f*x)**2/(4*f**2), Ne(f, 0)), ((a*sin(e) + a)**2*(c*x + d*x**2/2), True))","A",0
104,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(d*x+c),x)","a^{2} \left(\int \frac{2 \sin{\left(e + f x \right)}}{c + d x}\, dx + \int \frac{\sin^{2}{\left(e + f x \right)}}{c + d x}\, dx + \int \frac{1}{c + d x}\, dx\right)"," ",0,"a**2*(Integral(2*sin(e + f*x)/(c + d*x), x) + Integral(sin(e + f*x)**2/(c + d*x), x) + Integral(1/(c + d*x), x))","F",0
105,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(d*x+c)**2,x)","a^{2} \left(\int \frac{2 \sin{\left(e + f x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{\sin^{2}{\left(e + f x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{1}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx\right)"," ",0,"a**2*(Integral(2*sin(e + f*x)/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(sin(e + f*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(1/(c**2 + 2*c*d*x + d**2*x**2), x))","F",0
106,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(d*x+c)**3,x)","a^{2} \left(\int \frac{2 \sin{\left(e + f x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{\sin^{2}{\left(e + f x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{1}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx\right)"," ",0,"a**2*(Integral(2*sin(e + f*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(sin(e + f*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(1/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))","F",0
107,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+a*sin(f*x+e)),x)","\frac{\int \frac{c^{3}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{3} x^{3}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c d^{2} x^{2}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c^{2} d x}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(c**3/(sin(e + f*x) + 1), x) + Integral(d**3*x**3/(sin(e + f*x) + 1), x) + Integral(3*c*d**2*x**2/(sin(e + f*x) + 1), x) + Integral(3*c**2*d*x/(sin(e + f*x) + 1), x))/a","F",0
108,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+a*sin(f*x+e)),x)","\frac{\int \frac{c^{2}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{2} x^{2}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{2 c d x}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(c**2/(sin(e + f*x) + 1), x) + Integral(d**2*x**2/(sin(e + f*x) + 1), x) + Integral(2*c*d*x/(sin(e + f*x) + 1), x))/a","F",0
109,1,272,0,1.120752," ","integrate((d*x+c)/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{2 c f}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} + \frac{d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} - \frac{d f x}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} + \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} + \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f^{2}} & \text{for}\: f \neq 0 \\\frac{c x + \frac{d x^{2}}{2}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*c*f/(a*f**2*tan(e/2 + f*x/2) + a*f**2) + d*f*x*tan(e/2 + f*x/2)/(a*f**2*tan(e/2 + f*x/2) + a*f**2) - d*f*x/(a*f**2*tan(e/2 + f*x/2) + a*f**2) + 2*d*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)/(a*f**2*tan(e/2 + f*x/2) + a*f**2) + 2*d*log(tan(e/2 + f*x/2) + 1)/(a*f**2*tan(e/2 + f*x/2) + a*f**2) - d*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)/(a*f**2*tan(e/2 + f*x/2) + a*f**2) - d*log(tan(e/2 + f*x/2)**2 + 1)/(a*f**2*tan(e/2 + f*x/2) + a*f**2), Ne(f, 0)), ((c*x + d*x**2/2)/(a*sin(e) + a), True))","A",0
110,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{1}{c \sin{\left(e + f x \right)} + c + d x \sin{\left(e + f x \right)} + d x}\, dx}{a}"," ",0,"Integral(1/(c*sin(e + f*x) + c + d*x*sin(e + f*x) + d*x), x)/a","F",0
111,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a+a*sin(f*x+e)),x)","\frac{\int \frac{1}{c^{2} \sin{\left(e + f x \right)} + c^{2} + 2 c d x \sin{\left(e + f x \right)} + 2 c d x + d^{2} x^{2} \sin{\left(e + f x \right)} + d^{2} x^{2}}\, dx}{a}"," ",0,"Integral(1/(c**2*sin(e + f*x) + c**2 + 2*c*d*x*sin(e + f*x) + 2*c*d*x + d**2*x**2*sin(e + f*x) + d**2*x**2), x)/a","F",0
112,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{c^{3}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{3} x^{3}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c d^{2} x^{2}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c^{2} d x}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(c**3/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(d**3*x**3/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(3*c*d**2*x**2/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(3*c**2*d*x/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x))/a**2","F",0
113,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{c^{2}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{2} x^{2}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{2 c d x}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(c**2/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(d**2*x**2/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(2*c*d*x/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x))/a**2","F",0
114,1,1336,0,2.311716," ","integrate((d*x+c)/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{4 c f}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{2 d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{2 d f x}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{6 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{6 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{3 d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{3 d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{2 d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} + \frac{2 d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f^{2}} & \text{for}\: f \neq 0 \\\frac{c x + \frac{d x^{2}}{2}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*c*f*tan(e/2 + f*x/2)**2/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - 6*c*f*tan(e/2 + f*x/2)/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - 4*c*f/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 2*d*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - 2*d*f*x/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 2*d*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)**3/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 6*d*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)**2/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 6*d*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 2*d*log(tan(e/2 + f*x/2) + 1)/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - d*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)**3/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - 3*d*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)**2/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - 3*d*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) - d*log(tan(e/2 + f*x/2)**2 + 1)/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 2*d*tan(e/2 + f*x/2)**2/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2) + 2*d*tan(e/2 + f*x/2)/(3*a**2*f**2*tan(e/2 + f*x/2)**3 + 9*a**2*f**2*tan(e/2 + f*x/2)**2 + 9*a**2*f**2*tan(e/2 + f*x/2) + 3*a**2*f**2), Ne(f, 0)), ((c*x + d*x**2/2)/(a*sin(e) + a)**2, True))","A",0
115,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{1}{c \sin^{2}{\left(e + f x \right)} + 2 c \sin{\left(e + f x \right)} + c + d x \sin^{2}{\left(e + f x \right)} + 2 d x \sin{\left(e + f x \right)} + d x}\, dx}{a^{2}}"," ",0,"Integral(1/(c*sin(e + f*x)**2 + 2*c*sin(e + f*x) + c + d*x*sin(e + f*x)**2 + 2*d*x*sin(e + f*x) + d*x), x)/a**2","F",0
116,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{1}{c^{2} \sin^{2}{\left(e + f x \right)} + 2 c^{2} \sin{\left(e + f x \right)} + c^{2} + 2 c d x \sin^{2}{\left(e + f x \right)} + 4 c d x \sin{\left(e + f x \right)} + 2 c d x + d^{2} x^{2} \sin^{2}{\left(e + f x \right)} + 2 d^{2} x^{2} \sin{\left(e + f x \right)} + d^{2} x^{2}}\, dx}{a^{2}}"," ",0,"Integral(1/(c**2*sin(e + f*x)**2 + 2*c**2*sin(e + f*x) + c**2 + 2*c*d*x*sin(e + f*x)**2 + 4*c*d*x*sin(e + f*x) + 2*c*d*x + d**2*x**2*sin(e + f*x)**2 + 2*d**2*x**2*sin(e + f*x) + d**2*x**2), x)/a**2","F",0
117,0,0,0,0.000000," ","integrate((d*x+c)**3/(a-a*sin(f*x+e)),x)","- \frac{\int \frac{c^{3}}{\sin{\left(e + f x \right)} - 1}\, dx + \int \frac{d^{3} x^{3}}{\sin{\left(e + f x \right)} - 1}\, dx + \int \frac{3 c d^{2} x^{2}}{\sin{\left(e + f x \right)} - 1}\, dx + \int \frac{3 c^{2} d x}{\sin{\left(e + f x \right)} - 1}\, dx}{a}"," ",0,"-(Integral(c**3/(sin(e + f*x) - 1), x) + Integral(d**3*x**3/(sin(e + f*x) - 1), x) + Integral(3*c*d**2*x**2/(sin(e + f*x) - 1), x) + Integral(3*c**2*d*x/(sin(e + f*x) - 1), x))/a","F",0
118,0,0,0,0.000000," ","integrate((d*x+c)**2/(a-a*sin(f*x+e)),x)","- \frac{\int \frac{c^{2}}{\sin{\left(e + f x \right)} - 1}\, dx + \int \frac{d^{2} x^{2}}{\sin{\left(e + f x \right)} - 1}\, dx + \int \frac{2 c d x}{\sin{\left(e + f x \right)} - 1}\, dx}{a}"," ",0,"-(Integral(c**2/(sin(e + f*x) - 1), x) + Integral(d**2*x**2/(sin(e + f*x) - 1), x) + Integral(2*c*d*x/(sin(e + f*x) - 1), x))/a","F",0
119,1,272,0,1.118725," ","integrate((d*x+c)/(a-a*sin(f*x+e)),x)","\begin{cases} - \frac{2 c f}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} - \frac{d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} - \frac{d f x}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} + \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1 \right)} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} - \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1 \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} + \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a f^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a f^{2}} & \text{for}\: f \neq 0 \\\frac{c x + \frac{d x^{2}}{2}}{- a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*c*f/(a*f**2*tan(e/2 + f*x/2) - a*f**2) - d*f*x*tan(e/2 + f*x/2)/(a*f**2*tan(e/2 + f*x/2) - a*f**2) - d*f*x/(a*f**2*tan(e/2 + f*x/2) - a*f**2) + 2*d*log(tan(e/2 + f*x/2) - 1)*tan(e/2 + f*x/2)/(a*f**2*tan(e/2 + f*x/2) - a*f**2) - 2*d*log(tan(e/2 + f*x/2) - 1)/(a*f**2*tan(e/2 + f*x/2) - a*f**2) - d*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)/(a*f**2*tan(e/2 + f*x/2) - a*f**2) + d*log(tan(e/2 + f*x/2)**2 + 1)/(a*f**2*tan(e/2 + f*x/2) - a*f**2), Ne(f, 0)), ((c*x + d*x**2/2)/(-a*sin(e) + a), True))","A",0
120,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a-a*sin(f*x+e)),x)","- \frac{\int \frac{1}{c \sin{\left(e + f x \right)} - c + d x \sin{\left(e + f x \right)} - d x}\, dx}{a}"," ",0,"-Integral(1/(c*sin(e + f*x) - c + d*x*sin(e + f*x) - d*x), x)/a","F",0
121,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a-a*sin(f*x+e)),x)","- \frac{\int \frac{1}{c^{2} \sin{\left(e + f x \right)} - c^{2} + 2 c d x \sin{\left(e + f x \right)} - 2 c d x + d^{2} x^{2} \sin{\left(e + f x \right)} - d^{2} x^{2}}\, dx}{a}"," ",0,"-Integral(1/(c**2*sin(e + f*x) - c**2 + 2*c*d*x*sin(e + f*x) - 2*c*d*x + d**2*x**2*sin(e + f*x) - d**2*x**2), x)/a","F",0
122,0,0,0,0.000000," ","integrate(x**3*(a+a*sin(d*x+c))**(1/2),x)","\int x^{3} \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}\, dx"," ",0,"Integral(x**3*sqrt(a*(sin(c + d*x) + 1)), x)","F",0
123,0,0,0,0.000000," ","integrate(x**2*(a+a*sin(d*x+c))**(1/2),x)","\int x^{2} \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}\, dx"," ",0,"Integral(x**2*sqrt(a*(sin(c + d*x) + 1)), x)","F",0
124,0,0,0,0.000000," ","integrate(x*(a+a*sin(d*x+c))**(1/2),x)","\int x \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}\, dx"," ",0,"Integral(x*sqrt(a*(sin(c + d*x) + 1)), x)","F",0
125,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/x,x)","\int \frac{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}{x}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))/x, x)","F",0
126,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/x**2,x)","\int \frac{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))/x**2, x)","F",0
127,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/x**3,x)","\int \frac{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))/x**3, x)","F",0
128,0,0,0,0.000000," ","integrate(x**3*(a+a*sin(f*x+e))**(3/2),x)","\int x^{3} \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
129,0,0,0,0.000000," ","integrate(x**2*(a+a*sin(f*x+e))**(3/2),x)","\int x^{2} \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
130,0,0,0,0.000000," ","integrate(x*(a+a*sin(f*x+e))**(3/2),x)","\int x \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/x,x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/x, x)","F",0
132,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/x**2,x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/x**2, x)","F",0
133,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/x**3,x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/x**3, x)","F",0
134,0,0,0,0.000000," ","integrate(x**3/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{x^{3}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(x**3/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
135,0,0,0,0.000000," ","integrate(x**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(x**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
136,0,0,0,0.000000," ","integrate(x/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{x}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(x/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
137,0,0,0,0.000000," ","integrate(1/x/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{x \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(a*(sin(c + d*x) + 1))), x)","F",0
138,0,0,0,0.000000," ","integrate(1/x**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a*(sin(c + d*x) + 1))), x)","F",0
139,0,0,0,0.000000," ","integrate(x**3/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{x^{3}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
140,0,0,0,0.000000," ","integrate(x**2/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{x^{2}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
141,0,0,0,0.000000," ","integrate(x/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{x}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
142,0,0,0,0.000000," ","integrate(1/x/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{1}{x \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a*(sin(e + f*x) + 1))**(3/2)), x)","F",0
143,0,0,0,0.000000," ","integrate(1/x**2/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{1}{x^{2} \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a*(sin(e + f*x) + 1))**(3/2)), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/3)/x,x)","\int \frac{\sqrt[3]{a \left(\sin{\left(c + d x \right)} + 1\right)}}{x}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(1/3)/x, x)","F",0
145,-1,0,0,0.000000," ","integrate((d*x+c)**m*(a+a*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate((d*x+c)**m*(a+a*sin(f*x+e))**3,x)","a^{3} \left(\int 3 \left(c + d x\right)^{m} \sin{\left(e + f x \right)}\, dx + \int 3 \left(c + d x\right)^{m} \sin^{2}{\left(e + f x \right)}\, dx + \int \left(c + d x\right)^{m} \sin^{3}{\left(e + f x \right)}\, dx + \int \left(c + d x\right)^{m}\, dx\right)"," ",0,"a**3*(Integral(3*(c + d*x)**m*sin(e + f*x), x) + Integral(3*(c + d*x)**m*sin(e + f*x)**2, x) + Integral((c + d*x)**m*sin(e + f*x)**3, x) + Integral((c + d*x)**m, x))","F",0
147,0,0,0,0.000000," ","integrate((d*x+c)**m*(a+a*sin(f*x+e))**2,x)","a^{2} \left(\int 2 \left(c + d x\right)^{m} \sin{\left(e + f x \right)}\, dx + \int \left(c + d x\right)^{m} \sin^{2}{\left(e + f x \right)}\, dx + \int \left(c + d x\right)^{m}\, dx\right)"," ",0,"a**2*(Integral(2*(c + d*x)**m*sin(e + f*x), x) + Integral((c + d*x)**m*sin(e + f*x)**2, x) + Integral((c + d*x)**m, x))","F",0
148,0,0,0,0.000000," ","integrate((d*x+c)**m*(a+a*sin(f*x+e)),x)","a \left(\int \left(c + d x\right)^{m} \sin{\left(e + f x \right)}\, dx + \int \left(c + d x\right)^{m}\, dx\right)"," ",0,"a*(Integral((c + d*x)**m*sin(e + f*x), x) + Integral((c + d*x)**m, x))","F",0
149,0,0,0,0.000000," ","integrate((d*x+c)**m/(a+a*sin(f*x+e)),x)","\frac{\int \frac{\left(c + d x\right)^{m}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral((c + d*x)**m/(sin(e + f*x) + 1), x)/a","F",0
150,0,0,0,0.000000," ","integrate((d*x+c)**m/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{\left(c + d x\right)^{m}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((c + d*x)**m/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x)/a**2","F",0
151,1,264,0,1.861765," ","integrate((d*x+c)**3*(a+b*sin(f*x+e)),x)","\begin{cases} a c^{3} x + \frac{3 a c^{2} d x^{2}}{2} + a c d^{2} x^{3} + \frac{a d^{3} x^{4}}{4} - \frac{b c^{3} \cos{\left(e + f x \right)}}{f} - \frac{3 b c^{2} d x \cos{\left(e + f x \right)}}{f} + \frac{3 b c^{2} d \sin{\left(e + f x \right)}}{f^{2}} - \frac{3 b c d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{6 b c d^{2} x \sin{\left(e + f x \right)}}{f^{2}} + \frac{6 b c d^{2} \cos{\left(e + f x \right)}}{f^{3}} - \frac{b d^{3} x^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 b d^{3} x^{2} \sin{\left(e + f x \right)}}{f^{2}} + \frac{6 b d^{3} x \cos{\left(e + f x \right)}}{f^{3}} - \frac{6 b d^{3} \sin{\left(e + f x \right)}}{f^{4}} & \text{for}\: f \neq 0 \\\left(a + b \sin{\left(e \right)}\right) \left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*x + 3*a*c**2*d*x**2/2 + a*c*d**2*x**3 + a*d**3*x**4/4 - b*c**3*cos(e + f*x)/f - 3*b*c**2*d*x*cos(e + f*x)/f + 3*b*c**2*d*sin(e + f*x)/f**2 - 3*b*c*d**2*x**2*cos(e + f*x)/f + 6*b*c*d**2*x*sin(e + f*x)/f**2 + 6*b*c*d**2*cos(e + f*x)/f**3 - b*d**3*x**3*cos(e + f*x)/f + 3*b*d**3*x**2*sin(e + f*x)/f**2 + 6*b*d**3*x*cos(e + f*x)/f**3 - 6*b*d**3*sin(e + f*x)/f**4, Ne(f, 0)), ((a + b*sin(e))*(c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4), True))","A",0
152,1,151,0,0.814111," ","integrate((d*x+c)**2*(a+b*sin(f*x+e)),x)","\begin{cases} a c^{2} x + a c d x^{2} + \frac{a d^{2} x^{3}}{3} - \frac{b c^{2} \cos{\left(e + f x \right)}}{f} - \frac{2 b c d x \cos{\left(e + f x \right)}}{f} + \frac{2 b c d \sin{\left(e + f x \right)}}{f^{2}} - \frac{b d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{2 b d^{2} x \sin{\left(e + f x \right)}}{f^{2}} + \frac{2 b d^{2} \cos{\left(e + f x \right)}}{f^{3}} & \text{for}\: f \neq 0 \\\left(a + b \sin{\left(e \right)}\right) \left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*x + a*c*d*x**2 + a*d**2*x**3/3 - b*c**2*cos(e + f*x)/f - 2*b*c*d*x*cos(e + f*x)/f + 2*b*c*d*sin(e + f*x)/f**2 - b*d**2*x**2*cos(e + f*x)/f + 2*b*d**2*x*sin(e + f*x)/f**2 + 2*b*d**2*cos(e + f*x)/f**3, Ne(f, 0)), ((a + b*sin(e))*(c**2*x + c*d*x**2 + d**2*x**3/3), True))","A",0
153,1,68,0,0.314619," ","integrate((d*x+c)*(a+b*sin(f*x+e)),x)","\begin{cases} a c x + \frac{a d x^{2}}{2} - \frac{b c \cos{\left(e + f x \right)}}{f} - \frac{b d x \cos{\left(e + f x \right)}}{f} + \frac{b d \sin{\left(e + f x \right)}}{f^{2}} & \text{for}\: f \neq 0 \\\left(a + b \sin{\left(e \right)}\right) \left(c x + \frac{d x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x + a*d*x**2/2 - b*c*cos(e + f*x)/f - b*d*x*cos(e + f*x)/f + b*d*sin(e + f*x)/f**2, Ne(f, 0)), ((a + b*sin(e))*(c*x + d*x**2/2), True))","A",0
154,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(d*x+c),x)","\int \frac{a + b \sin{\left(e + f x \right)}}{c + d x}\, dx"," ",0,"Integral((a + b*sin(e + f*x))/(c + d*x), x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(d*x+c)**2,x)","\int \frac{a + b \sin{\left(e + f x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))/(c + d*x)**2, x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(d*x+c)**3,x)","\int \frac{a + b \sin{\left(e + f x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))/(c + d*x)**3, x)","F",0
157,1,779,0,4.963372," ","integrate((d*x+c)**3*(a+b*sin(f*x+e))**2,x)","\begin{cases} a^{2} c^{3} x + \frac{3 a^{2} c^{2} d x^{2}}{2} + a^{2} c d^{2} x^{3} + \frac{a^{2} d^{3} x^{4}}{4} - \frac{2 a b c^{3} \cos{\left(e + f x \right)}}{f} - \frac{6 a b c^{2} d x \cos{\left(e + f x \right)}}{f} + \frac{6 a b c^{2} d \sin{\left(e + f x \right)}}{f^{2}} - \frac{6 a b c d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{12 a b c d^{2} x \sin{\left(e + f x \right)}}{f^{2}} + \frac{12 a b c d^{2} \cos{\left(e + f x \right)}}{f^{3}} - \frac{2 a b d^{3} x^{3} \cos{\left(e + f x \right)}}{f} + \frac{6 a b d^{3} x^{2} \sin{\left(e + f x \right)}}{f^{2}} + \frac{12 a b d^{3} x \cos{\left(e + f x \right)}}{f^{3}} - \frac{12 a b d^{3} \sin{\left(e + f x \right)}}{f^{4}} + \frac{b^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{3 b^{2} c^{2} d x^{2} \sin^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{2} c^{2} d x^{2} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 b^{2} c^{2} d x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 b^{2} c^{2} d \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{b^{2} c d^{2} x^{3} \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c d^{2} x^{3} \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 b^{2} c d^{2} x^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{3 b^{2} c d^{2} x \sin^{2}{\left(e + f x \right)}}{4 f^{2}} - \frac{3 b^{2} c d^{2} x \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{3 b^{2} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f^{3}} + \frac{b^{2} d^{3} x^{4} \sin^{2}{\left(e + f x \right)}}{8} + \frac{b^{2} d^{3} x^{4} \cos^{2}{\left(e + f x \right)}}{8} - \frac{b^{2} d^{3} x^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{3 b^{2} d^{3} x^{2} \sin^{2}{\left(e + f x \right)}}{8 f^{2}} - \frac{3 b^{2} d^{3} x^{2} \cos^{2}{\left(e + f x \right)}}{8 f^{2}} + \frac{3 b^{2} d^{3} x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f^{3}} + \frac{3 b^{2} d^{3} \cos^{2}{\left(e + f x \right)}}{8 f^{4}} & \text{for}\: f \neq 0 \\\left(a + b \sin{\left(e \right)}\right)^{2} \left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*x + 3*a**2*c**2*d*x**2/2 + a**2*c*d**2*x**3 + a**2*d**3*x**4/4 - 2*a*b*c**3*cos(e + f*x)/f - 6*a*b*c**2*d*x*cos(e + f*x)/f + 6*a*b*c**2*d*sin(e + f*x)/f**2 - 6*a*b*c*d**2*x**2*cos(e + f*x)/f + 12*a*b*c*d**2*x*sin(e + f*x)/f**2 + 12*a*b*c*d**2*cos(e + f*x)/f**3 - 2*a*b*d**3*x**3*cos(e + f*x)/f + 6*a*b*d**3*x**2*sin(e + f*x)/f**2 + 12*a*b*d**3*x*cos(e + f*x)/f**3 - 12*a*b*d**3*sin(e + f*x)/f**4 + b**2*c**3*x*sin(e + f*x)**2/2 + b**2*c**3*x*cos(e + f*x)**2/2 - b**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) + 3*b**2*c**2*d*x**2*sin(e + f*x)**2/4 + 3*b**2*c**2*d*x**2*cos(e + f*x)**2/4 - 3*b**2*c**2*d*x*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*b**2*c**2*d*cos(e + f*x)**2/(4*f**2) + b**2*c*d**2*x**3*sin(e + f*x)**2/2 + b**2*c*d**2*x**3*cos(e + f*x)**2/2 - 3*b**2*c*d**2*x**2*sin(e + f*x)*cos(e + f*x)/(2*f) + 3*b**2*c*d**2*x*sin(e + f*x)**2/(4*f**2) - 3*b**2*c*d**2*x*cos(e + f*x)**2/(4*f**2) + 3*b**2*c*d**2*sin(e + f*x)*cos(e + f*x)/(4*f**3) + b**2*d**3*x**4*sin(e + f*x)**2/8 + b**2*d**3*x**4*cos(e + f*x)**2/8 - b**2*d**3*x**3*sin(e + f*x)*cos(e + f*x)/(2*f) + 3*b**2*d**3*x**2*sin(e + f*x)**2/(8*f**2) - 3*b**2*d**3*x**2*cos(e + f*x)**2/(8*f**2) + 3*b**2*d**3*x*sin(e + f*x)*cos(e + f*x)/(4*f**3) + 3*b**2*d**3*cos(e + f*x)**2/(8*f**4), Ne(f, 0)), ((a + b*sin(e))**2*(c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4), True))","A",0
158,1,456,0,2.224607," ","integrate((d*x+c)**2*(a+b*sin(f*x+e))**2,x)","\begin{cases} a^{2} c^{2} x + a^{2} c d x^{2} + \frac{a^{2} d^{2} x^{3}}{3} - \frac{2 a b c^{2} \cos{\left(e + f x \right)}}{f} - \frac{4 a b c d x \cos{\left(e + f x \right)}}{f} + \frac{4 a b c d \sin{\left(e + f x \right)}}{f^{2}} - \frac{2 a b d^{2} x^{2} \cos{\left(e + f x \right)}}{f} + \frac{4 a b d^{2} x \sin{\left(e + f x \right)}}{f^{2}} + \frac{4 a b d^{2} \cos{\left(e + f x \right)}}{f^{3}} + \frac{b^{2} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{b^{2} c d x^{2} \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c d x^{2} \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c d x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{b^{2} c d \cos^{2}{\left(e + f x \right)}}{2 f^{2}} + \frac{b^{2} d^{2} x^{3} \sin^{2}{\left(e + f x \right)}}{6} + \frac{b^{2} d^{2} x^{3} \cos^{2}{\left(e + f x \right)}}{6} - \frac{b^{2} d^{2} x^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{b^{2} d^{2} x \sin^{2}{\left(e + f x \right)}}{4 f^{2}} - \frac{b^{2} d^{2} x \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{b^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f^{3}} & \text{for}\: f \neq 0 \\\left(a + b \sin{\left(e \right)}\right)^{2} \left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*x + a**2*c*d*x**2 + a**2*d**2*x**3/3 - 2*a*b*c**2*cos(e + f*x)/f - 4*a*b*c*d*x*cos(e + f*x)/f + 4*a*b*c*d*sin(e + f*x)/f**2 - 2*a*b*d**2*x**2*cos(e + f*x)/f + 4*a*b*d**2*x*sin(e + f*x)/f**2 + 4*a*b*d**2*cos(e + f*x)/f**3 + b**2*c**2*x*sin(e + f*x)**2/2 + b**2*c**2*x*cos(e + f*x)**2/2 - b**2*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) + b**2*c*d*x**2*sin(e + f*x)**2/2 + b**2*c*d*x**2*cos(e + f*x)**2/2 - b**2*c*d*x*sin(e + f*x)*cos(e + f*x)/f - b**2*c*d*cos(e + f*x)**2/(2*f**2) + b**2*d**2*x**3*sin(e + f*x)**2/6 + b**2*d**2*x**3*cos(e + f*x)**2/6 - b**2*d**2*x**2*sin(e + f*x)*cos(e + f*x)/(2*f) + b**2*d**2*x*sin(e + f*x)**2/(4*f**2) - b**2*d**2*x*cos(e + f*x)**2/(4*f**2) + b**2*d**2*sin(e + f*x)*cos(e + f*x)/(4*f**3), Ne(f, 0)), ((a + b*sin(e))**2*(c**2*x + c*d*x**2 + d**2*x**3/3), True))","A",0
159,1,219,0,0.861562," ","integrate((d*x+c)*(a+b*sin(f*x+e))**2,x)","\begin{cases} a^{2} c x + \frac{a^{2} d x^{2}}{2} - \frac{2 a b c \cos{\left(e + f x \right)}}{f} - \frac{2 a b d x \cos{\left(e + f x \right)}}{f} + \frac{2 a b d \sin{\left(e + f x \right)}}{f^{2}} + \frac{b^{2} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{b^{2} d x^{2} \sin^{2}{\left(e + f x \right)}}{4} + \frac{b^{2} d x^{2} \cos^{2}{\left(e + f x \right)}}{4} - \frac{b^{2} d x \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{b^{2} d \cos^{2}{\left(e + f x \right)}}{4 f^{2}} & \text{for}\: f \neq 0 \\\left(a + b \sin{\left(e \right)}\right)^{2} \left(c x + \frac{d x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x + a**2*d*x**2/2 - 2*a*b*c*cos(e + f*x)/f - 2*a*b*d*x*cos(e + f*x)/f + 2*a*b*d*sin(e + f*x)/f**2 + b**2*c*x*sin(e + f*x)**2/2 + b**2*c*x*cos(e + f*x)**2/2 - b**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + b**2*d*x**2*sin(e + f*x)**2/4 + b**2*d*x**2*cos(e + f*x)**2/4 - b**2*d*x*sin(e + f*x)*cos(e + f*x)/(2*f) - b**2*d*cos(e + f*x)**2/(4*f**2), Ne(f, 0)), ((a + b*sin(e))**2*(c*x + d*x**2/2), True))","A",0
160,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(d*x+c),x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}{c + d x}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2/(c + d*x), x)","F",0
161,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(d*x+c)**2,x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2/(c + d*x)**2, x)","F",0
162,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(d*x+c)**3,x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2/(c + d*x)**3, x)","F",0
163,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+b*sin(f*x+e)),x)","\int \frac{\left(c + d x\right)^{3}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*x)**3/(a + b*sin(e + f*x)), x)","F",0
164,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+b*sin(f*x+e)),x)","\int \frac{\left(c + d x\right)^{2}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*x)**2/(a + b*sin(e + f*x)), x)","F",0
165,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*sin(f*x+e)),x)","\int \frac{c + d x}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*x)/(a + b*sin(e + f*x)), x)","F",0
166,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*sin(f*x+e)),x)","\int \frac{1}{\left(a + b \sin{\left(e + f x \right)}\right) \left(c + d x\right)}\, dx"," ",0,"Integral(1/((a + b*sin(e + f*x))*(c + d*x)), x)","F",0
167,-1,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((d*x+c)**3/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate((d*x+c)**2/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate((d*x+c)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((d*x+c)**m*(a+b*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,0,0,0,0.000000," ","integrate((d*x+c)**m*(a+b*sin(f*x+e))**3,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{3} \left(c + d x\right)^{m}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3*(c + d*x)**m, x)","F",0
175,0,0,0,0.000000," ","integrate((d*x+c)**m*(a+b*sin(f*x+e))**2,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \left(c + d x\right)^{m}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*(c + d*x)**m, x)","F",0
176,0,0,0,0.000000," ","integrate((d*x+c)**m*(a+b*sin(f*x+e)),x)","\int \left(a + b \sin{\left(e + f x \right)}\right) \left(c + d x\right)^{m}\, dx"," ",0,"Integral((a + b*sin(e + f*x))*(c + d*x)**m, x)","F",0
177,0,0,0,0.000000," ","integrate((d*x+c)**m/(a+b*sin(f*x+e)),x)","\int \frac{\left(c + d x\right)^{m}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*x)**m/(a + b*sin(e + f*x)), x)","F",0
178,0,0,0,0.000000," ","integrate((d*x+c)**m/(a+b*sin(f*x+e))**2,x)","\int \frac{\left(c + d x\right)^{m}}{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((c + d*x)**m/(a + b*sin(e + f*x))**2, x)","F",0
179,0,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*sin(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*sin(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*sin(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*sin(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
180,0,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*sin(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*sin(c + d*x)/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*sin(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
181,1,456,0,2.003469," ","integrate((f*x+e)*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 d^{2} e x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{2 d^{2} e x}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{d^{2} f x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{d^{2} f x^{2}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 d e}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 d f x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{2 d f x}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{4 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{4 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{2 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{2 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} & \text{for}\: d \neq 0 \\\frac{\left(e x + \frac{f x^{2}}{2}\right) \sin{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*d**2*e*x*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 2*d**2*e*x/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + d**2*f*x**2*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + d**2*f*x**2/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*d*e/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*d*f*x*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 2*d*f*x/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 4*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 4*f*log(tan(c/2 + d*x/2) + 1)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 2*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 2*f*log(tan(c/2 + d*x/2)**2 + 1)/(2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2), Ne(d, 0)), ((e*x + f*x**2/2)*sin(c)/(a*sin(c) + a), True))","A",0
182,1,80,0,1.608222," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{d x}{a d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{2}{a d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*x*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2) + a*d) + d*x/(a*d*tan(c/2 + d*x/2) + a*d) + 2/(a*d*tan(c/2 + d*x/2) + a*d), Ne(d, 0)), (x*sin(c)/(a*sin(c) + a), True))","A",0
183,0,0,0,0.000000," ","integrate(sin(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(sin(c + d*x)/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
184,0,0,0,0.000000," ","integrate(sin(d*x+c)/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(sin(c + d*x)/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
185,0,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*sin(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*sin(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*sin(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*sin(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
186,0,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*sin(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*sin(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*sin(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
187,1,1867,0,3.943451," ","integrate((f*x+e)*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{2 d^{2} e x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 d^{2} e x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 d^{2} e x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 d^{2} e x}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{d^{2} f x^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{d^{2} f x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{d^{2} f x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{d^{2} f x^{2}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{4 d e \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{4 d e \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{8 d e}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 d f x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{4 d f x}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 f \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} & \text{for}\: d \neq 0 \\\frac{\left(e x + \frac{f x^{2}}{2}\right) \sin^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*d**2*e*x*tan(c/2 + d*x/2)**3/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*d**2*e*x*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*d**2*e*x*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*d**2*e*x/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - d**2*f*x**2*tan(c/2 + d*x/2)**3/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - d**2*f*x**2*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - d**2*f*x**2*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - d**2*f*x**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 4*d*e*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 4*d*e*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 8*d*e/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*d*f*x*tan(c/2 + d*x/2)**3/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 4*d*f*x/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**3/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*f*log(tan(c/2 + d*x/2) + 1)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**3/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) - 2*f*log(tan(c/2 + d*x/2)**2 + 1)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*f*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2) + 4*f*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**3 + 2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2*tan(c/2 + d*x/2) + 2*a*d**2), Ne(d, 0)), ((e*x + f*x**2/2)*sin(c)**2/(a*sin(c) + a), True))","A",0
188,1,422,0,3.048597," ","integrate(sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{d x}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{4}{a d \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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d*x*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d) - d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d) - d*x*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d) - d*x/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d) - 2*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d) - 2*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d) - 4/(a*d*tan(c/2 + d*x/2)**3 + a*d*tan(c/2 + d*x/2)**2 + a*d*tan(c/2 + d*x/2) + a*d), Ne(d, 0)), (x*sin(c)**2/(a*sin(c) + a), True))","A",0
189,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(sin(c + d*x)**2/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
190,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(sin(c + d*x)**2/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
191,0,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*sin(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*sin(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*sin(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*sin(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
192,0,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \sin^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*sin(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*sin(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*sin(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
193,1,4653,0,8.316509," ","integrate((f*x+e)*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{6 d^{2} e x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{6 d^{2} e x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{12 d^{2} e x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{12 d^{2} e x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{6 d^{2} e x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{6 d^{2} e x}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{3 d^{2} f x^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{3 d^{2} f x^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{6 d^{2} f x^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{6 d^{2} f x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{3 d^{2} f x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{3 d^{2} f x^{2}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{12 d e \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{12 d e \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{20 d e \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 d e \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{16 d e}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 d f x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 d f x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{4 d f x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 d f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{4 d f x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 d f x}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{16 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{16 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 f \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{4 f \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 f \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{4 f \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{4 f \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} & \text{for}\: d \neq 0 \\\frac{\left(e x + \frac{f x^{2}}{2}\right) \sin^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*d**2*e*x*tan(c/2 + d*x/2)**5/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 6*d**2*e*x*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 12*d**2*e*x*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 12*d**2*e*x*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 6*d**2*e*x*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 6*d**2*e*x/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 3*d**2*f*x**2*tan(c/2 + d*x/2)**5/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 3*d**2*f*x**2*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 6*d**2*f*x**2*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 6*d**2*f*x**2*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 3*d**2*f*x**2*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 3*d**2*f*x**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 12*d*e*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 12*d*e*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 20*d*e*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*d*e*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 16*d*e/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*d*f*x*tan(c/2 + d*x/2)**5/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*d*f*x*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 4*d*f*x*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*d*f*x*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 4*d*f*x*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 8*d*f*x/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**5/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 16*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 16*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*f*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*f*log(tan(c/2 + d*x/2) + 1)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**5/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 8*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 8*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*f*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) + 4*f*log(tan(c/2 + d*x/2)**2 + 1)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*f*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 4*f*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 4*f*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2) - 8*f*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**5 + 4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**3 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2*tan(c/2 + d*x/2) + 4*a*d**2), Ne(d, 0)), ((e*x + f*x**2/2)*sin(c)**3/(a*sin(c) + a), True))","A",0
194,1,1127,0,6.519156," ","integrate(sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 d x}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{10 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{8}{2 a d \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^{3}{\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 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c/2 + d*x/2)**5/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 3*d*x*tan(c/2 + d*x/2)**4/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 6*d*x*tan(c/2 + d*x/2)**3/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 6*d*x*tan(c/2 + d*x/2)**2/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 3*d*x*tan(c/2 + d*x/2)/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 3*d*x/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 6*tan(c/2 + d*x/2)**4/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 6*tan(c/2 + d*x/2)**3/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 10*tan(c/2 + d*x/2)**2/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 2*tan(c/2 + d*x/2)/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d) + 8/(2*a*d*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)**3 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d*tan(c/2 + d*x/2) + 2*a*d), Ne(d, 0)), (x*sin(c)**3/(a*sin(c) + a), True))","A",0
195,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(f*x+e)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,0,0,0,0.000000," ","integrate((f*x+e)**3*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*csc(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*csc(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*csc(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*csc(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
198,0,0,0,0.000000," ","integrate((f*x+e)**2*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*csc(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*csc(c + d*x)/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*csc(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
199,0,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*csc(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f*x*csc(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
200,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
201,0,0,0,0.000000," ","integrate(csc(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(csc(c + d*x)/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
202,0,0,0,0.000000," ","integrate(csc(d*x+c)/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(csc(c + d*x)/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
203,0,0,0,0.000000," ","integrate((f*x+e)**3*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*csc(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*csc(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*csc(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*csc(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
204,0,0,0,0.000000," ","integrate((f*x+e)**2*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*csc(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*csc(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*csc(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
205,0,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*csc(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f*x*csc(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
206,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
207,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{2}{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**2/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
208,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{2}{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**2/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
209,0,0,0,0.000000," ","integrate((f*x+e)**3*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*csc(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*csc(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*csc(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*csc(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
210,0,0,0,0.000000," ","integrate((f*x+e)**2*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*csc(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*csc(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*csc(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
211,0,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*csc(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f*x*csc(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
212,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**3/(sin(c + d*x) + 1), x)/a","F",0
213,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{3}{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**3/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
214,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{3}{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**3/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
215,0,0,0,0.000000," ","integrate((f*x+e)**m*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \sin^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*sin(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
216,0,0,0,0.000000," ","integrate((f*x+e)**m*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*sin(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
217,0,0,0,0.000000," ","integrate((f*x+e)**m/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m/(sin(c + d*x) + 1), x)/a","F",0
218,0,0,0,0.000000," ","integrate((f*x+e)**m*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*csc(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
219,0,0,0,0.000000," ","integrate((f*x+e)**m*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*csc(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
220,-1,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,0,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \sin{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*sin(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
222,0,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \sin{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*sin(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
223,1,335,0,61.340796," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{b d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b d \sqrt{b^{2}}} + \frac{2 b}{b^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b d \sqrt{b^{2}}} - \frac{d x \sqrt{b^{2}}}{b^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b d \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\\frac{b d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \sqrt{b^{2}}} + \frac{2 b}{b^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \sqrt{b^{2}}} + \frac{d x \sqrt{b^{2}}}{b^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{x}{b} & \text{for}\: a = 0 \\\frac{x \sin{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{\cos{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\- \frac{a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{b d \sqrt{- a^{2} + b^{2}}} + \frac{a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{b d \sqrt{- a^{2} + b^{2}}} + \frac{x}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (b*d*x*tan(c/2 + d*x/2)/(b**2*d*tan(c/2 + d*x/2) - b*d*sqrt(b**2)) + 2*b/(b**2*d*tan(c/2 + d*x/2) - b*d*sqrt(b**2)) - d*x*sqrt(b**2)/(b**2*d*tan(c/2 + d*x/2) - b*d*sqrt(b**2)), Eq(a, -sqrt(b**2))), (b*d*x*tan(c/2 + d*x/2)/(b**2*d*tan(c/2 + d*x/2) + b*d*sqrt(b**2)) + 2*b/(b**2*d*tan(c/2 + d*x/2) + b*d*sqrt(b**2)) + d*x*sqrt(b**2)/(b**2*d*tan(c/2 + d*x/2) + b*d*sqrt(b**2)), Eq(a, sqrt(b**2))), (x/b, Eq(a, 0)), (x*sin(c)/(a + b*sin(c)), Eq(d, 0)), (-cos(c + d*x)/(a*d), Eq(b, 0)), (-a*log(tan(c/2 + d*x/2) + b/a - sqrt(-a**2 + b**2)/a)/(b*d*sqrt(-a**2 + b**2)) + a*log(tan(c/2 + d*x/2) + b/a + sqrt(-a**2 + b**2)/a)/(b*d*sqrt(-a**2 + b**2)) + x/b, True))","A",0
224,-1,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,0,0,0,0.000000," ","integrate((f*x+e)**3*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
233,0,0,0,0.000000," ","integrate((f*x+e)**2*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
234,0,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
235,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
236,0,0,0,0.000000," ","integrate((f*x+e)**3*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
237,0,0,0,0.000000," ","integrate((f*x+e)**2*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
238,0,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
239,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
240,0,0,0,0.000000," ","integrate((f*x+e)**m*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \sin^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*sin(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
241,0,0,0,0.000000," ","integrate((f*x+e)**m*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \sin{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*sin(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
242,0,0,0,0.000000," ","integrate((f*x+e)**m/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m/(a + b*sin(c + d*x)), x)","F",0
243,0,0,0,0.000000," ","integrate((f*x+e)**m*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
244,0,0,0,0.000000," ","integrate((f*x+e)**m*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
245,-1,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((f*x+e)**2*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate((f*x+e)**3*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,0,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*cos(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*cos(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*cos(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*cos(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
252,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*cos(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*cos(c + d*x)/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*cos(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
253,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*cos(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f*x*cos(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
254,1,24,0,0.493731," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(c + d*x) + 1)/(a*d), Ne(d, 0)), (x*cos(c)/(a*sin(c) + a), True))","A",0
255,0,0,0,0.000000," ","integrate(cos(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(cos(c + d*x)/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
256,0,0,0,0.000000," ","integrate(cos(d*x+c)/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(cos(c + d*x)/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
257,1,984,0,10.036723," ","integrate((f*x+e)**3*cos(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{4 d^{4} e^{3} x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{4 d^{4} e^{3} x}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{6 d^{4} e^{2} f x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{6 d^{4} e^{2} f x^{2}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{4 d^{4} e f^{2} x^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{4 d^{4} e f^{2} x^{3}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{d^{4} f^{3} x^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{d^{4} f^{3} x^{4}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{8 d^{3} e^{3}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{12 d^{3} e^{2} f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{12 d^{3} e^{2} f x}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{12 d^{3} e f^{2} x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{12 d^{3} e f^{2} x^{2}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{4 d^{3} f^{3} x^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{4 d^{3} f^{3} x^{3}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{24 d^{2} e^{2} f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{48 d^{2} e f^{2} x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{24 d^{2} f^{3} x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{48 d e f^{2}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{24 d f^{3} x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} - \frac{24 d f^{3} x}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} + \frac{48 f^{3} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{4}} & \text{for}\: d \neq 0 \\\frac{\left(e^{3} x + \frac{3 e^{2} f x^{2}}{2} + e f^{2} x^{3} + \frac{f^{3} x^{4}}{4}\right) \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*d**4*e**3*x*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 4*d**4*e**3*x/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 6*d**4*e**2*f*x**2*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 6*d**4*e**2*f*x**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 4*d**4*e*f**2*x**3*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 4*d**4*e*f**2*x**3/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + d**4*f**3*x**4*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + d**4*f**3*x**4/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 8*d**3*e**3/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 12*d**3*e**2*f*x*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 12*d**3*e**2*f*x/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 12*d**3*e*f**2*x**2*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 12*d**3*e*f**2*x**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 4*d**3*f**3*x**3*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 4*d**3*f**3*x**3/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 24*d**2*e**2*f*tan(c/2 + d*x/2)/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 48*d**2*e*f**2*x*tan(c/2 + d*x/2)/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 24*d**2*f**3*x**2*tan(c/2 + d*x/2)/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 48*d*e*f**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 24*d*f**3*x*tan(c/2 + d*x/2)**2/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) - 24*d*f**3*x/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4) + 48*f**3*tan(c/2 + d*x/2)/(4*a*d**4*tan(c/2 + d*x/2)**2 + 4*a*d**4), Ne(d, 0)), ((e**3*x + 3*e**2*f*x**2/2 + e*f**2*x**3 + f**3*x**4/4)*cos(c)**2/(a*sin(c) + a), True))","A",0
258,1,605,0,6.549916," ","integrate((f*x+e)**2*cos(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 d^{3} e^{2} x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{3 d^{3} e^{2} x}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{3 d^{3} e f x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{3 d^{3} e f x^{2}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{d^{3} f^{2} x^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{d^{3} f^{2} x^{3}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{6 d^{2} e^{2}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} - \frac{6 d^{2} e f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{6 d^{2} e f x}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} - \frac{3 d^{2} f^{2} x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} + \frac{3 d^{2} f^{2} x^{2}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} - \frac{12 d e f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} - \frac{12 d f^{2} x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} - \frac{12 f^{2}}{3 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d^{3}} & \text{for}\: d \neq 0 \\\frac{\left(e^{2} x + e f x^{2} + \frac{f^{2} x^{3}}{3}\right) \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d**3*e**2*x*tan(c/2 + d*x/2)**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + 3*d**3*e**2*x/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + 3*d**3*e*f*x**2*tan(c/2 + d*x/2)**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + 3*d**3*e*f*x**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + d**3*f**2*x**3*tan(c/2 + d*x/2)**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + d**3*f**2*x**3/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + 6*d**2*e**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) - 6*d**2*e*f*x*tan(c/2 + d*x/2)**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + 6*d**2*e*f*x/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) - 3*d**2*f**2*x**2*tan(c/2 + d*x/2)**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) + 3*d**2*f**2*x**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) - 12*d*e*f*tan(c/2 + d*x/2)/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) - 12*d*f**2*x*tan(c/2 + d*x/2)/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3) - 12*f**2/(3*a*d**3*tan(c/2 + d*x/2)**2 + 3*a*d**3), Ne(d, 0)), ((e**2*x + e*f*x**2 + f**2*x**3/3)*cos(c)**2/(a*sin(c) + a), True))","A",0
259,1,326,0,4.155363," ","integrate((f*x+e)*cos(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 d^{2} e x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{2 d^{2} e x}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{d^{2} f x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{d^{2} f x^{2}}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{4 d e}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{2 d f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} + \frac{2 d f x}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} - \frac{4 f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d^{2}} & \text{for}\: d \neq 0 \\\frac{\left(e x + \frac{f x^{2}}{2}\right) \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*d**2*e*x*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) + 2*d**2*e*x/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) + d**2*f*x**2*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) + d**2*f*x**2/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) + 4*d*e/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) - 2*d*f*x*tan(c/2 + d*x/2)**2/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) + 2*d*f*x/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2) - 4*f*tan(c/2 + d*x/2)/(2*a*d**2*tan(c/2 + d*x/2)**2 + 2*a*d**2), Ne(d, 0)), ((e*x + f*x**2/2)*cos(c)**2/(a*sin(c) + a), True))","A",0
260,1,88,0,2.765063," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{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{d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{2}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 + a*d) + d*x/(a*d*tan(c/2 + d*x/2)**2 + a*d) + 2/(a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*cos(c)**2/(a*sin(c) + a), True))","A",0
261,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
262,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
263,1,2725,0,18.777184," ","integrate((f*x+e)**3*cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 d^{3} e^{3} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{16 d^{3} e^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{16 d^{3} e^{3} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{6 d^{3} e^{2} f x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{3} e^{2} f x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{36 d^{3} e^{2} f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{3} e^{2} f x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{6 d^{3} e^{2} f x}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{6 d^{3} e f^{2} x^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{3} e f^{2} x^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{36 d^{3} e f^{2} x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{3} e f^{2} x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{6 d^{3} e f^{2} x^{2}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{2 d^{3} f^{3} x^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{16 d^{3} f^{3} x^{3} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{12 d^{3} f^{3} x^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{16 d^{3} f^{3} x^{3} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{2 d^{3} f^{3} x^{3}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{12 d^{2} e^{2} f \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{2} e^{2} f \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{12 d^{2} e^{2} f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{2} e^{2} f}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{48 d^{2} e f^{2} x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{24 d^{2} e f^{2} x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{24 d^{2} e f^{2} x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{48 d^{2} e f^{2} x}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{24 d^{2} f^{3} x^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{12 d^{2} f^{3} x^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{12 d^{2} f^{3} x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{24 d^{2} f^{3} x^{2}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{96 d e f^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{24 d e f^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{96 d e f^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{3 d f^{3} x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{96 d f^{3} x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{18 d f^{3} x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{96 d f^{3} x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{3 d f^{3} x}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{6 f^{3} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{96 f^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} + \frac{6 f^{3} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} - \frac{96 f^{3}}{8 a d^{4} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d^{4} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{4}} & \text{for}\: d \neq 0 \\\frac{\left(e^{3} x + \frac{3 e^{2} f x^{2}}{2} + e f^{2} x^{3} + \frac{f^{3} x^{4}}{4}\right) \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*d**3*e**3*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 16*d**3*e**3*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 16*d**3*e**3*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 6*d**3*e**2*f*x*tan(c/2 + d*x/2)**4/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**3*e**2*f*x*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 36*d**3*e**2*f*x*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**3*e**2*f*x*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 6*d**3*e**2*f*x/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 6*d**3*e*f**2*x**2*tan(c/2 + d*x/2)**4/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**3*e*f**2*x**2*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 36*d**3*e*f**2*x**2*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**3*e*f**2*x**2*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 6*d**3*e*f**2*x**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 2*d**3*f**3*x**3*tan(c/2 + d*x/2)**4/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 16*d**3*f**3*x**3*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 12*d**3*f**3*x**3*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 16*d**3*f**3*x**3*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 2*d**3*f**3*x**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 12*d**2*e**2*f*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**2*e**2*f*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 12*d**2*e**2*f*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**2*e**2*f/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 48*d**2*e*f**2*x*tan(c/2 + d*x/2)**4/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 24*d**2*e*f**2*x*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 24*d**2*e*f**2*x*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 48*d**2*e*f**2*x/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 24*d**2*f**3*x**2*tan(c/2 + d*x/2)**4/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 12*d**2*f**3*x**2*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 12*d**2*f**3*x**2*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 24*d**2*f**3*x**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 96*d*e*f**2*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 24*d*e*f**2*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 96*d*e*f**2*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 3*d*f**3*x*tan(c/2 + d*x/2)**4/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 96*d*f**3*x*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 18*d*f**3*x*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 96*d*f**3*x*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 3*d*f**3*x/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 6*f**3*tan(c/2 + d*x/2)**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 96*f**3*tan(c/2 + d*x/2)**2/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) + 6*f**3*tan(c/2 + d*x/2)/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4) - 96*f**3/(8*a*d**4*tan(c/2 + d*x/2)**4 + 16*a*d**4*tan(c/2 + d*x/2)**2 + 8*a*d**4), Ne(d, 0)), ((e**3*x + 3*e**2*f*x**2/2 + e*f**2*x**3 + f**3*x**4/4)*cos(c)**3/(a*sin(c) + a), True))","A",0
264,1,1528,0,12.348539," ","integrate((f*x+e)**2*cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 d^{2} e^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{8 d^{2} e^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{8 d^{2} e^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{2 d^{2} e f x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{16 d^{2} e f x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{12 d^{2} e f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{16 d^{2} e f x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{2 d^{2} e f x}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{d^{2} f^{2} x^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{8 d^{2} f^{2} x^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{6 d^{2} f^{2} x^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{8 d^{2} f^{2} x^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{d^{2} f^{2} x^{2}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{4 d e f \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{16 d e f \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{4 d e f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{16 d e f}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{8 d f^{2} x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{4 d f^{2} x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{4 d f^{2} x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{8 d f^{2} x}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{16 f^{2} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} + \frac{4 f^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} - \frac{16 f^{2} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{3} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{3} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{3}} & \text{for}\: d \neq 0 \\\frac{\left(e^{2} x + e f x^{2} + \frac{f^{2} x^{3}}{3}\right) \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*d**2*e**2*tan(c/2 + d*x/2)**3/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 8*d**2*e**2*tan(c/2 + d*x/2)**2/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 8*d**2*e**2*tan(c/2 + d*x/2)/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 2*d**2*e*f*x*tan(c/2 + d*x/2)**4/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 16*d**2*e*f*x*tan(c/2 + d*x/2)**3/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 12*d**2*e*f*x*tan(c/2 + d*x/2)**2/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 16*d**2*e*f*x*tan(c/2 + d*x/2)/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 2*d**2*e*f*x/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + d**2*f**2*x**2*tan(c/2 + d*x/2)**4/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 8*d**2*f**2*x**2*tan(c/2 + d*x/2)**3/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 6*d**2*f**2*x**2*tan(c/2 + d*x/2)**2/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 8*d**2*f**2*x**2*tan(c/2 + d*x/2)/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + d**2*f**2*x**2/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 4*d*e*f*tan(c/2 + d*x/2)**3/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 16*d*e*f*tan(c/2 + d*x/2)**2/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 4*d*e*f*tan(c/2 + d*x/2)/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 16*d*e*f/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 8*d*f**2*x*tan(c/2 + d*x/2)**4/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 4*d*f**2*x*tan(c/2 + d*x/2)**3/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 4*d*f**2*x*tan(c/2 + d*x/2)/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 8*d*f**2*x/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 16*f**2*tan(c/2 + d*x/2)**3/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) + 4*f**2*tan(c/2 + d*x/2)**2/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3) - 16*f**2*tan(c/2 + d*x/2)/(4*a*d**3*tan(c/2 + d*x/2)**4 + 8*a*d**3*tan(c/2 + d*x/2)**2 + 4*a*d**3), Ne(d, 0)), ((e**2*x + e*f*x**2 + f**2*x**3/3)*cos(c)**3/(a*sin(c) + a), True))","A",0
265,1,724,0,7.986296," ","integrate((f*x+e)*cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 d e \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{8 d e \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 d e \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{d f x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 d f x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{6 d f x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 d f x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{d f x}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{2 f \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 f \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} - \frac{2 f \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} + \frac{8 f}{4 a d^{2} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a d^{2} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d^{2}} & \text{for}\: d \neq 0 \\\frac{\left(e x + \frac{f x^{2}}{2}\right) \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*d*e*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) - 8*d*e*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + 8*d*e*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + d*f*x*tan(c/2 + d*x/2)**4/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + 8*d*f*x*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) - 6*d*f*x*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + 8*d*f*x*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + d*f*x/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + 2*f*tan(c/2 + d*x/2)**3/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + 8*f*tan(c/2 + d*x/2)**2/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) - 2*f*tan(c/2 + d*x/2)/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2) + 8*f/(4*a*d**2*tan(c/2 + d*x/2)**4 + 8*a*d**2*tan(c/2 + d*x/2)**2 + 4*a*d**2), Ne(d, 0)), ((e*x + f*x**2/2)*cos(c)**3/(a*sin(c) + a), True))","A",0
266,1,158,0,5.375195," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d) - 2*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d) + 2*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*cos(c)**3/(a*sin(c) + a), True))","A",0
267,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(f*x+e)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,0,0,0,0.000000," ","integrate((f*x+e)**3*sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*sec(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
270,0,0,0,0.000000," ","integrate((f*x+e)**2*sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*sec(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
271,0,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(f*x*sec(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
272,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
273,0,0,0,0.000000," ","integrate(sec(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(sec(c + d*x)/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
274,0,0,0,0.000000," ","integrate(sec(d*x+c)/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
275,0,0,0,0.000000," ","integrate((f*x+e)**3*sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*sec(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*sec(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*sec(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*sec(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
276,0,0,0,0.000000," ","integrate((f*x+e)**2*sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*sec(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*sec(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*sec(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
277,0,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*sec(c + d*x)**2/(sin(c + d*x) + 1), x) + Integral(f*x*sec(c + d*x)**2/(sin(c + d*x) + 1), x))/a","F",0
278,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
279,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**2/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
280,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**2/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
281,0,0,0,0.000000," ","integrate((f*x+e)**3*sec(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{3} \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{3} x^{3} \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e f^{2} x^{2} \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{3 e^{2} f x \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**3*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f**3*x**3*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(3*e*f**2*x**2*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(3*e**2*f*x*sec(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
282,0,0,0,0.000000," ","integrate((f*x+e)**2*sec(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e^{2} \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f^{2} x^{2} \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{2 e f x \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e**2*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f**2*x**2*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(2*e*f*x*sec(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
283,0,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{e \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{f x \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(e*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(f*x*sec(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
284,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**3/(sin(c + d*x) + 1), x)/a","F",0
285,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(f*x+e)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{e \sin{\left(c + d x \right)} + e + f x \sin{\left(c + d x \right)} + f x}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**3/(e*sin(c + d*x) + e + f*x*sin(c + d*x) + f*x), x)/a","F",0
286,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(f*x+e)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{e^{2} \sin{\left(c + d x \right)} + e^{2} + 2 e f x \sin{\left(c + d x \right)} + 2 e f x + f^{2} x^{2} \sin{\left(c + d x \right)} + f^{2} x^{2}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**3/(e**2*sin(c + d*x) + e**2 + 2*e*f*x*sin(c + d*x) + 2*e*f*x + f**2*x**2*sin(c + d*x) + f**2*x**2), x)/a","F",0
287,0,0,0,0.000000," ","integrate((f*x+e)**m*cos(d*x+c)**4/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \cos^{4}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*cos(c + d*x)**4/(sin(c + d*x) + 1), x)/a","F",0
288,-1,0,0,0.000000," ","integrate((f*x+e)**m*cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,0,0,0,0.000000," ","integrate((f*x+e)**m*cos(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \cos^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*cos(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
290,0,0,0,0.000000," ","integrate((f*x+e)**m*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*cos(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
291,0,0,0,0.000000," ","integrate((f*x+e)**m/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m/(sin(c + d*x) + 1), x)/a","F",0
292,0,0,0,0.000000," ","integrate((f*x+e)**m*sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*sec(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
293,0,0,0,0.000000," ","integrate((f*x+e)**m*sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e + f x\right)^{m} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e + f*x)**m*sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
294,-1,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
296,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
297,1,41,0,0.624285," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \cos{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a, Eq(b, 0) & Eq(d, 0)), (x*cos(c)/(a + b*sin(c)), Eq(d, 0)), (sin(c + d*x)/(a*d), Eq(b, 0)), (log(a/b + sin(c + d*x))/(b*d), True))","A",0
298,-1,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,0,0,0,0.000000," ","integrate((f*x+e)**3*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
307,0,0,0,0.000000," ","integrate((f*x+e)**2*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
308,0,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
309,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
310,0,0,0,0.000000," ","integrate((f*x+e)**3*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
311,0,0,0,0.000000," ","integrate((f*x+e)**2*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
312,0,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
313,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
314,0,0,0,0.000000," ","integrate((f*x+e)**m*cos(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \cos^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*cos(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
315,0,0,0,0.000000," ","integrate((f*x+e)**m*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \cos{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*cos(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
316,0,0,0,0.000000," ","integrate((f*x+e)**m/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m/(a + b*sin(c + d*x)), x)","F",0
317,0,0,0,0.000000," ","integrate((f*x+e)**m*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
318,0,0,0,0.000000," ","integrate((f*x+e)**m*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{m} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**m*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
319,-1,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,0,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \cos{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*cos(c + d*x)*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
326,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
327,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
328,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
329,0,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)**2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \cos^{2}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*cos(c + d*x)**2*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
330,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)**2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos^{2}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)**2*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
331,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)**2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos^{2}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)**2*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
332,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
333,0,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \cos^{3}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*cos(c + d*x)**3*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
334,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos^{3}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)**3*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
335,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos^{3}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)**3*cot(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
336,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,0,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \cos{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*cos(c + d*x)*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
338,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
339,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
340,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
341,0,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{3} \cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**3*cos(c + d*x)**2*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
342,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)**2*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
343,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)**2*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
344,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
345,-1,0,0,0.000000," ","integrate((f*x+e)**3*cos(d*x+c)**3*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
346,0,0,0,0.000000," ","integrate((f*x+e)**2*cos(d*x+c)**3*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right)^{2} \cos^{3}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)**2*cos(c + d*x)**3*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
347,0,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)**3*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\left(e + f x\right) \cos^{3}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e + f*x)*cos(c + d*x)**3*cot(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
348,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
