1,1,311,0,2.547454," ","integrate((d*x+c)**4*cos(b*x+a),x)","\begin{cases} \frac{c^{4} \sin{\left(a + b x \right)}}{b} + \frac{4 c^{3} d x \sin{\left(a + b x \right)}}{b} + \frac{6 c^{2} d^{2} x^{2} \sin{\left(a + b x \right)}}{b} + \frac{4 c d^{3} x^{3} \sin{\left(a + b x \right)}}{b} + \frac{d^{4} x^{4} \sin{\left(a + b x \right)}}{b} + \frac{4 c^{3} d \cos{\left(a + b x \right)}}{b^{2}} + \frac{12 c^{2} d^{2} x \cos{\left(a + b x \right)}}{b^{2}} + \frac{12 c d^{3} x^{2} \cos{\left(a + b x \right)}}{b^{2}} + \frac{4 d^{4} x^{3} \cos{\left(a + b x \right)}}{b^{2}} - \frac{12 c^{2} d^{2} \sin{\left(a + b x \right)}}{b^{3}} - \frac{24 c d^{3} x \sin{\left(a + b x \right)}}{b^{3}} - \frac{12 d^{4} x^{2} \sin{\left(a + b x \right)}}{b^{3}} - \frac{24 c d^{3} \cos{\left(a + b x \right)}}{b^{4}} - \frac{24 d^{4} x \cos{\left(a + b x \right)}}{b^{4}} + \frac{24 d^{4} \sin{\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) \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*sin(a + b*x)/b + 4*c**3*d*x*sin(a + b*x)/b + 6*c**2*d**2*x**2*sin(a + b*x)/b + 4*c*d**3*x**3*sin(a + b*x)/b + d**4*x**4*sin(a + b*x)/b + 4*c**3*d*cos(a + b*x)/b**2 + 12*c**2*d**2*x*cos(a + b*x)/b**2 + 12*c*d**3*x**2*cos(a + b*x)/b**2 + 4*d**4*x**3*cos(a + b*x)/b**2 - 12*c**2*d**2*sin(a + b*x)/b**3 - 24*c*d**3*x*sin(a + b*x)/b**3 - 12*d**4*x**2*sin(a + b*x)/b**3 - 24*c*d**3*cos(a + b*x)/b**4 - 24*d**4*x*cos(a + b*x)/b**4 + 24*d**4*sin(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)*cos(a), True))","A",0
2,1,202,0,1.189918," ","integrate((d*x+c)**3*cos(b*x+a),x)","\begin{cases} \frac{c^{3} \sin{\left(a + b x \right)}}{b} + \frac{3 c^{2} d x \sin{\left(a + b x \right)}}{b} + \frac{3 c d^{2} x^{2} \sin{\left(a + b x \right)}}{b} + \frac{d^{3} x^{3} \sin{\left(a + b x \right)}}{b} + \frac{3 c^{2} d \cos{\left(a + b x \right)}}{b^{2}} + \frac{6 c d^{2} x \cos{\left(a + b x \right)}}{b^{2}} + \frac{3 d^{3} x^{2} \cos{\left(a + b x \right)}}{b^{2}} - \frac{6 c d^{2} \sin{\left(a + b x \right)}}{b^{3}} - \frac{6 d^{3} x \sin{\left(a + b x \right)}}{b^{3}} - \frac{6 d^{3} \cos{\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) \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*sin(a + b*x)/b + 3*c**2*d*x*sin(a + b*x)/b + 3*c*d**2*x**2*sin(a + b*x)/b + d**3*x**3*sin(a + b*x)/b + 3*c**2*d*cos(a + b*x)/b**2 + 6*c*d**2*x*cos(a + b*x)/b**2 + 3*d**3*x**2*cos(a + b*x)/b**2 - 6*c*d**2*sin(a + b*x)/b**3 - 6*d**3*x*sin(a + b*x)/b**3 - 6*d**3*cos(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)*cos(a), True))","A",0
3,1,112,0,0.539707," ","integrate((d*x+c)**2*cos(b*x+a),x)","\begin{cases} \frac{c^{2} \sin{\left(a + b x \right)}}{b} + \frac{2 c d x \sin{\left(a + b x \right)}}{b} + \frac{d^{2} x^{2} \sin{\left(a + b x \right)}}{b} + \frac{2 c d \cos{\left(a + b x \right)}}{b^{2}} + \frac{2 d^{2} x \cos{\left(a + b x \right)}}{b^{2}} - \frac{2 d^{2} \sin{\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) \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*sin(a + b*x)/b + 2*c*d*x*sin(a + b*x)/b + d**2*x**2*sin(a + b*x)/b + 2*c*d*cos(a + b*x)/b**2 + 2*d**2*x*cos(a + b*x)/b**2 - 2*d**2*sin(a + b*x)/b**3, Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*cos(a), True))","A",0
4,1,46,0,0.204260," ","integrate((d*x+c)*cos(b*x+a),x)","\begin{cases} \frac{c \sin{\left(a + b x \right)}}{b} + \frac{d x \sin{\left(a + b x \right)}}{b} + \frac{d \cos{\left(a + b x \right)}}{b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*sin(a + b*x)/b + d*x*sin(a + b*x)/b + d*cos(a + b*x)/b**2, Ne(b, 0)), ((c*x + d*x**2/2)*cos(a), True))","A",0
5,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c),x)","\int \frac{\cos{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x), x)","F",0
6,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**2,x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**2, x)","F",0
7,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**3,x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**3, x)","F",0
8,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**4,x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**4, x)","F",0
9,1,660,0,4.597630," ","integrate((d*x+c)**4*cos(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 \sin^{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} \sin^{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) \cos^{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*sin(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*sin(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)*cos(a)**2, True))","A",0
10,1,456,0,2.547249," ","integrate((d*x+c)**3*cos(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 \sin^{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} \sin^{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) \cos^{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*sin(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*sin(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)*cos(a)**2, True))","A",0
11,1,264,0,1.181416," ","integrate((d*x+c)**2*cos(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 \sin^{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) \cos^{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*sin(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)*cos(a)**2, True))","A",0
12,1,126,0,0.498769," ","integrate((d*x+c)*cos(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 \sin^{2}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \cos^{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*sin(a + b*x)**2/(4*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*cos(a)**2, True))","A",0
13,0,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c),x)","\int \frac{\cos^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)**2/(c + d*x), x)","F",0
14,0,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)**2/(c + d*x)**2, x)","F",0
15,0,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**3,x)","\int \frac{\cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(cos(a + b*x)**2/(c + d*x)**3, x)","F",0
16,1,772,0,7.881562," ","integrate((d*x+c)**4*cos(b*x+a)**3,x)","\begin{cases} \frac{2 c^{4} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{c^{4} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{8 c^{3} d x \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{4 c^{3} d x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{4 c^{2} d^{2} x^{2} \sin^{3}{\left(a + b x \right)}}{b} + \frac{6 c^{2} d^{2} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{8 c d^{3} x^{3} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{4 c d^{3} x^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 d^{4} x^{4} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d^{4} x^{4} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{8 c^{3} d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{28 c^{3} d \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{8 c^{2} d^{2} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{28 c^{2} d^{2} x \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{8 c d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{28 c d^{3} x^{2} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{8 d^{4} x^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{28 d^{4} x^{3} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} - \frac{80 c^{2} d^{2} \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{28 c^{2} d^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{160 c d^{3} x \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{56 c d^{3} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{80 d^{4} x^{2} \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{28 d^{4} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{160 c d^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{4}} - \frac{488 c d^{3} \cos^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{160 d^{4} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{4}} - \frac{488 d^{4} x \cos^{3}{\left(a + b x \right)}}{27 b^{4}} + \frac{1456 d^{4} \sin^{3}{\left(a + b x \right)}}{81 b^{5}} + \frac{488 d^{4} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{27 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) \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**4*sin(a + b*x)**3/(3*b) + c**4*sin(a + b*x)*cos(a + b*x)**2/b + 8*c**3*d*x*sin(a + b*x)**3/(3*b) + 4*c**3*d*x*sin(a + b*x)*cos(a + b*x)**2/b + 4*c**2*d**2*x**2*sin(a + b*x)**3/b + 6*c**2*d**2*x**2*sin(a + b*x)*cos(a + b*x)**2/b + 8*c*d**3*x**3*sin(a + b*x)**3/(3*b) + 4*c*d**3*x**3*sin(a + b*x)*cos(a + b*x)**2/b + 2*d**4*x**4*sin(a + b*x)**3/(3*b) + d**4*x**4*sin(a + b*x)*cos(a + b*x)**2/b + 8*c**3*d*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 28*c**3*d*cos(a + b*x)**3/(9*b**2) + 8*c**2*d**2*x*sin(a + b*x)**2*cos(a + b*x)/b**2 + 28*c**2*d**2*x*cos(a + b*x)**3/(3*b**2) + 8*c*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)/b**2 + 28*c*d**3*x**2*cos(a + b*x)**3/(3*b**2) + 8*d**4*x**3*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 28*d**4*x**3*cos(a + b*x)**3/(9*b**2) - 80*c**2*d**2*sin(a + b*x)**3/(9*b**3) - 28*c**2*d**2*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 160*c*d**3*x*sin(a + b*x)**3/(9*b**3) - 56*c*d**3*x*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 80*d**4*x**2*sin(a + b*x)**3/(9*b**3) - 28*d**4*x**2*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 160*c*d**3*sin(a + b*x)**2*cos(a + b*x)/(9*b**4) - 488*c*d**3*cos(a + b*x)**3/(27*b**4) - 160*d**4*x*sin(a + b*x)**2*cos(a + b*x)/(9*b**4) - 488*d**4*x*cos(a + b*x)**3/(27*b**4) + 1456*d**4*sin(a + b*x)**3/(81*b**5) + 488*d**4*sin(a + b*x)*cos(a + b*x)**2/(27*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)*cos(a)**3, True))","A",0
17,1,495,0,4.187271," ","integrate((d*x+c)**3*cos(b*x+a)**3,x)","\begin{cases} \frac{2 c^{3} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{c^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 c^{2} d x \sin^{3}{\left(a + b x \right)}}{b} + \frac{3 c^{2} d x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 c d^{2} x^{2} \sin^{3}{\left(a + b x \right)}}{b} + \frac{3 c d^{2} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 d^{3} x^{3} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d^{3} x^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 c^{2} d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{7 c^{2} d \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 c d^{2} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{14 c d^{2} x \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{7 d^{3} x^{2} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} - \frac{40 c d^{2} \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{14 c d^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{40 d^{3} x \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{14 d^{3} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{40 d^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{4}} - \frac{122 d^{3} \cos^{3}{\left(a + b x \right)}}{27 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) \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**3*sin(a + b*x)**3/(3*b) + c**3*sin(a + b*x)*cos(a + b*x)**2/b + 2*c**2*d*x*sin(a + b*x)**3/b + 3*c**2*d*x*sin(a + b*x)*cos(a + b*x)**2/b + 2*c*d**2*x**2*sin(a + b*x)**3/b + 3*c*d**2*x**2*sin(a + b*x)*cos(a + b*x)**2/b + 2*d**3*x**3*sin(a + b*x)**3/(3*b) + d**3*x**3*sin(a + b*x)*cos(a + b*x)**2/b + 2*c**2*d*sin(a + b*x)**2*cos(a + b*x)/b**2 + 7*c**2*d*cos(a + b*x)**3/(3*b**2) + 4*c*d**2*x*sin(a + b*x)**2*cos(a + b*x)/b**2 + 14*c*d**2*x*cos(a + b*x)**3/(3*b**2) + 2*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)/b**2 + 7*d**3*x**2*cos(a + b*x)**3/(3*b**2) - 40*c*d**2*sin(a + b*x)**3/(9*b**3) - 14*c*d**2*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 40*d**3*x*sin(a + b*x)**3/(9*b**3) - 14*d**3*x*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 40*d**3*sin(a + b*x)**2*cos(a + b*x)/(9*b**4) - 122*d**3*cos(a + b*x)**3/(27*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)*cos(a)**3, True))","A",0
18,1,284,0,2.224258," ","integrate((d*x+c)**2*cos(b*x+a)**3,x)","\begin{cases} \frac{2 c^{2} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{c^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{4 c d x \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{2 c d x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 d^{2} x^{2} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d^{2} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{4 c d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{14 c d \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{4 d^{2} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{14 d^{2} x \cos^{3}{\left(a + b x \right)}}{9 b^{2}} - \frac{40 d^{2} \sin^{3}{\left(a + b x \right)}}{27 b^{3}} - \frac{14 d^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{3}} & \text{for}\: b \neq 0 \\\left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**2*sin(a + b*x)**3/(3*b) + c**2*sin(a + b*x)*cos(a + b*x)**2/b + 4*c*d*x*sin(a + b*x)**3/(3*b) + 2*c*d*x*sin(a + b*x)*cos(a + b*x)**2/b + 2*d**2*x**2*sin(a + b*x)**3/(3*b) + d**2*x**2*sin(a + b*x)*cos(a + b*x)**2/b + 4*c*d*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 14*c*d*cos(a + b*x)**3/(9*b**2) + 4*d**2*x*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 14*d**2*x*cos(a + b*x)**3/(9*b**2) - 40*d**2*sin(a + b*x)**3/(27*b**3) - 14*d**2*sin(a + b*x)*cos(a + b*x)**2/(9*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*cos(a)**3, True))","A",0
19,1,126,0,0.916201," ","integrate((d*x+c)*cos(b*x+a)**3,x)","\begin{cases} \frac{2 c \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{c \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 d x \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{7 d \cos^{3}{\left(a + b x \right)}}{9 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c*sin(a + b*x)**3/(3*b) + c*sin(a + b*x)*cos(a + b*x)**2/b + 2*d*x*sin(a + b*x)**3/(3*b) + d*x*sin(a + b*x)*cos(a + b*x)**2/b + 2*d*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 7*d*cos(a + b*x)**3/(9*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*cos(a)**3, True))","A",0
20,0,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c),x)","\int \frac{\cos^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)**3/(c + d*x), x)","F",0
21,0,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)**3/(c + d*x)**2, x)","F",0
22,0,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c)**3,x)","\int \frac{\cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(cos(a + b*x)**3/(c + d*x)**3, x)","F",0
23,1,253,0,5.669834," ","integrate(x**3*cos(b*x+a)**4,x)","\begin{cases} \frac{3 x^{4} \sin^{4}{\left(a + b x \right)}}{32} + \frac{3 x^{4} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{3 x^{4} \cos^{4}{\left(a + b x \right)}}{32} + \frac{3 x^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} + \frac{5 x^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{45 x^{2} \sin^{4}{\left(a + b x \right)}}{128 b^{2}} - \frac{9 x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{64 b^{2}} + \frac{51 x^{2} \cos^{4}{\left(a + b x \right)}}{128 b^{2}} - \frac{45 x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{3}} - \frac{51 x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{3}} + \frac{45 \sin^{4}{\left(a + b x \right)}}{256 b^{4}} - \frac{51 \cos^{4}{\left(a + b x \right)}}{256 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \cos^{4}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x**4*sin(a + b*x)**4/32 + 3*x**4*sin(a + b*x)**2*cos(a + b*x)**2/16 + 3*x**4*cos(a + b*x)**4/32 + 3*x**3*sin(a + b*x)**3*cos(a + b*x)/(8*b) + 5*x**3*sin(a + b*x)*cos(a + b*x)**3/(8*b) - 45*x**2*sin(a + b*x)**4/(128*b**2) - 9*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(64*b**2) + 51*x**2*cos(a + b*x)**4/(128*b**2) - 45*x*sin(a + b*x)**3*cos(a + b*x)/(64*b**3) - 51*x*sin(a + b*x)*cos(a + b*x)**3/(64*b**3) + 45*sin(a + b*x)**4/(256*b**4) - 51*cos(a + b*x)**4/(256*b**4), Ne(b, 0)), (x**4*cos(a)**4/4, True))","A",0
24,1,209,0,3.217182," ","integrate(x**2*cos(b*x+a)**4,x)","\begin{cases} \frac{x^{3} \sin^{4}{\left(a + b x \right)}}{8} + \frac{x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{x^{3} \cos^{4}{\left(a + b x \right)}}{8} + \frac{3 x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} + \frac{5 x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{15 x \sin^{4}{\left(a + b x \right)}}{64 b^{2}} - \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32 b^{2}} + \frac{17 x \cos^{4}{\left(a + b x \right)}}{64 b^{2}} - \frac{15 \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{3}} - \frac{17 \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \cos^{4}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*sin(a + b*x)**4/8 + x**3*sin(a + b*x)**2*cos(a + b*x)**2/4 + x**3*cos(a + b*x)**4/8 + 3*x**2*sin(a + b*x)**3*cos(a + b*x)/(8*b) + 5*x**2*sin(a + b*x)*cos(a + b*x)**3/(8*b) - 15*x*sin(a + b*x)**4/(64*b**2) - 3*x*sin(a + b*x)**2*cos(a + b*x)**2/(32*b**2) + 17*x*cos(a + b*x)**4/(64*b**2) - 15*sin(a + b*x)**3*cos(a + b*x)/(64*b**3) - 17*sin(a + b*x)*cos(a + b*x)**3/(64*b**3), Ne(b, 0)), (x**3*cos(a)**4/3, True))","A",0
25,1,138,0,1.811322," ","integrate(x*cos(b*x+a)**4,x)","\begin{cases} \frac{3 x^{2} \sin^{4}{\left(a + b x \right)}}{16} + \frac{3 x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8} + \frac{3 x^{2} \cos^{4}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} + \frac{5 x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{3 \sin^{4}{\left(a + b x \right)}}{32 b^{2}} + \frac{5 \cos^{4}{\left(a + b x \right)}}{32 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \cos^{4}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x**2*sin(a + b*x)**4/16 + 3*x**2*sin(a + b*x)**2*cos(a + b*x)**2/8 + 3*x**2*cos(a + b*x)**4/16 + 3*x*sin(a + b*x)**3*cos(a + b*x)/(8*b) + 5*x*sin(a + b*x)*cos(a + b*x)**3/(8*b) - 3*sin(a + b*x)**4/(32*b**2) + 5*cos(a + b*x)**4/(32*b**2), Ne(b, 0)), (x**2*cos(a)**4/2, True))","A",0
26,1,60,0,2.460364," ","integrate(cos(b*x+a)**4/x,x)","\frac{3 \log{\left(x \right)}}{8} - \frac{\sin{\left(2 a \right)} \operatorname{Si}{\left(2 b x \right)}}{2} - \frac{\sin{\left(4 a \right)} \operatorname{Si}{\left(4 b x \right)}}{8} + \frac{\cos{\left(2 a \right)} \operatorname{Ci}{\left(2 b x \right)}}{2} + \frac{\cos{\left(4 a \right)} \operatorname{Ci}{\left(4 b x \right)}}{8}"," ",0,"3*log(x)/8 - sin(2*a)*Si(2*b*x)/2 - sin(4*a)*Si(4*b*x)/8 + cos(2*a)*Ci(2*b*x)/2 + cos(4*a)*Ci(4*b*x)/8","A",0
27,0,0,0,0.000000," ","integrate(cos(b*x+a)**4/x**2,x)","\int \frac{\cos^{4}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(cos(a + b*x)**4/x**2, x)","F",0
28,0,0,0,0.000000," ","integrate(cos(b*x+a)**4/x**3,x)","\int \frac{\cos^{4}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(cos(a + b*x)**4/x**3, x)","F",0
29,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a),x)","\int \left(c + d x\right)^{3} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*sec(a + b*x), x)","F",0
30,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a),x)","\int \left(c + d x\right)^{2} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sec(a + b*x), x)","F",0
31,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a),x)","\int \left(c + d x\right) \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sec(a + b*x), x)","F",0
32,0,0,0,0.000000," ","integrate(sec(b*x+a)/(d*x+c),x)","\int \frac{\sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sec(a + b*x)/(c + d*x), x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*sec(a + b*x)**2, x)","F",0
34,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sec(a + b*x)**2, x)","F",0
35,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)**2,x)","\int \left(c + d x\right) \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sec(a + b*x)**2, x)","F",0
36,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/(d*x+c),x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sec(a + b*x)**2/(c + d*x), x)","F",0
37,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)**3,x)","\int \left(c + d x\right)^{3} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*sec(a + b*x)**3, x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sec(a + b*x)**3, x)","F",0
39,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)**3,x)","\int \left(c + d x\right) \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sec(a + b*x)**3, x)","F",0
40,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/(d*x+c),x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sec(a + b*x)**2/(c + d*x), x)","F",0
41,0,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a),x)","\int \left(c + d x\right)^{\frac{5}{2}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(5/2)*cos(a + b*x), x)","F",0
42,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a),x)","\int \left(c + d x\right)^{\frac{3}{2}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*cos(a + b*x), x)","F",0
43,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a),x)","\int \sqrt{c + d x} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*cos(a + b*x), x)","F",0
44,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(1/2),x)","\int \frac{\cos{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(cos(a + b*x)/sqrt(c + d*x), x)","F",0
45,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(3/2),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(3/2), x)","F",0
46,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(5/2),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(5/2), x)","F",0
47,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(7/2),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(7/2), x)","F",0
48,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2,x)","\int \left(c + d x\right)^{\frac{3}{2}} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*cos(a + b*x)**2, x)","F",0
50,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2,x)","\int \sqrt{c + d x} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*cos(a + b*x)**2, x)","F",0
51,0,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**(1/2),x)","\int \frac{\cos^{2}{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(cos(a + b*x)**2/sqrt(c + d*x), x)","F",0
52,0,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**(3/2),x)","\int \frac{\cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)**2/(c + d*x)**(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**(5/2),x)","\int \frac{\cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)**2/(c + d*x)**(5/2), x)","F",0
54,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3,x)","\int \left(c + d x\right)^{\frac{3}{2}} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*cos(a + b*x)**3, x)","F",0
58,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3,x)","\int \sqrt{c + d x} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*cos(a + b*x)**3, x)","F",0
59,0,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c)**(1/2),x)","\int \frac{\cos^{3}{\left(a + b x \right)}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(cos(a + b*x)**3/sqrt(c + d*x), x)","F",0
60,0,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c)**(3/2),x)","\int \frac{\cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)**3/(c + d*x)**(3/2), x)","F",0
61,0,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c)**(5/2),x)","\int \frac{\cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(a + b*x)**3/(c + d*x)**(5/2), x)","F",0
62,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,1,83,0,4.775744," ","integrate(x**(3/2)*cos(x),x)","\frac{5 x^{\frac{3}{2}} \sin{\left(x \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{15 \sqrt{x} \cos{\left(x \right)} \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)} - \frac{15 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{16 \Gamma\left(\frac{9}{4}\right)}"," ",0,"5*x**(3/2)*sin(x)*gamma(5/4)/(4*gamma(9/4)) + 15*sqrt(x)*cos(x)*gamma(5/4)/(8*gamma(9/4)) - 15*sqrt(2)*sqrt(pi)*fresnelc(sqrt(2)*sqrt(x)/sqrt(pi))*gamma(5/4)/(16*gamma(9/4))","A",0
64,1,61,0,0.853264," ","integrate(x**(1/2)*cos(x),x)","\frac{3 \sqrt{x} \sin{\left(x \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)} - \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}"," ",0,"3*sqrt(x)*sin(x)*gamma(3/4)/(4*gamma(7/4)) - 3*sqrt(2)*sqrt(pi)*fresnels(sqrt(2)*sqrt(x)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))","A",0
65,1,37,0,0.719583," ","integrate(cos(x)/x**(1/2),x)","\frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(2)*sqrt(pi)*fresnelc(sqrt(2)*sqrt(x)/sqrt(pi))*gamma(1/4)/(4*gamma(5/4))","A",0
66,1,61,0,1.597053," ","integrate(cos(x)/x**(3/2),x)","\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} + \frac{\cos{\left(x \right)} \Gamma\left(- \frac{1}{4}\right)}{2 \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(2)*sqrt(pi)*fresnels(sqrt(2)*sqrt(x)/sqrt(pi))*gamma(-1/4)/(2*gamma(3/4)) + cos(x)*gamma(-1/4)/(2*sqrt(x)*gamma(3/4))","A",0
67,0,0,0,0.000000," ","integrate((d*x+c)**(4/3)*cos(b*x+a),x)","\int \left(c + d x\right)^{\frac{4}{3}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(4/3)*cos(a + b*x), x)","F",0
68,0,0,0,0.000000," ","integrate((d*x+c)**(2/3)*cos(b*x+a),x)","\int \left(c + d x\right)^{\frac{2}{3}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(2/3)*cos(a + b*x), x)","F",0
69,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)*cos(b*x+a),x)","\int \sqrt[3]{c + d x} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(1/3)*cos(a + b*x), x)","F",0
70,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(1/3),x)","\int \frac{\cos{\left(a + b x \right)}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(1/3), x)","F",0
71,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(2/3),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(2/3), x)","F",0
72,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(4/3),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(4/3), x)","F",0
73,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(5/3),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(5/3), x)","F",0
74,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)**(7/3),x)","\int \frac{\cos{\left(a + b x \right)}}{\left(c + d x\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x)**(7/3), x)","F",0
75,0,0,0,0.000000," ","integrate(x*cos(b*x+a)**(1/2),x)","\int x \sqrt{\cos{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sqrt(cos(a + b*x)), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(b*x+a)**(1/2),x)","\int \sqrt{\cos{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(cos(a + b*x)), x)","F",0
77,0,0,0,0.000000," ","integrate(cos(b*x+a)**(1/2)/x,x)","\int \frac{\sqrt{\cos{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(sqrt(cos(a + b*x))/x, x)","F",0
78,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,0.000000," ","integrate(cos(b*x+a)**(3/2),x)","\int \cos^{\frac{3}{2}}{\left(a + b x \right)}\, dx"," ",0,"Integral(cos(a + b*x)**(3/2), x)","F",0
80,0,0,0,0.000000," ","integrate(cos(b*x+a)**(3/2)/x,x)","\int \frac{\cos^{\frac{3}{2}}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(cos(a + b*x)**(3/2)/x, x)","F",0
81,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)**(3/2)-1/3*x/cos(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,0,0,0,0.000000," ","integrate(cos(x)**(3/2)/x**3,x)","\int \frac{\cos^{\frac{3}{2}}{\left(x \right)}}{x^{3}}\, dx"," ",0,"Integral(cos(x)**(3/2)/x**3, x)","F",0
83,0,0,0,0.000000," ","integrate(x/cos(b*x+a)**(1/2),x)","\int \frac{x}{\sqrt{\cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x/sqrt(cos(a + b*x)), x)","F",0
84,0,0,0,0.000000," ","integrate(1/cos(b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(cos(a + b*x)), x)","F",0
85,0,0,0,0.000000," ","integrate(1/x/cos(b*x+a)**(1/2),x)","\int \frac{1}{x \sqrt{\cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/(x*sqrt(cos(a + b*x))), x)","F",0
86,0,0,0,0.000000," ","integrate(x/cos(b*x+a)**(3/2),x)","\int \frac{x}{\cos^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/cos(a + b*x)**(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate(1/cos(b*x+a)**(3/2),x)","\int \frac{1}{\cos^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(cos(a + b*x)**(-3/2), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x/cos(b*x+a)**(3/2),x)","\int \frac{1}{x \cos^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*cos(a + b*x)**(3/2)), x)","F",0
89,0,0,0,0.000000," ","integrate(x/cos(b*x+a)**(3/2)+x*cos(b*x+a)**(1/2),x)","\int \frac{x \left(\cos^{2}{\left(a + b x \right)} + 1\right)}{\cos^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*(cos(a + b*x)**2 + 1)/cos(a + b*x)**(3/2), x)","F",0
90,0,0,0,0.000000," ","integrate(x/cos(x)**(3/2)+x*cos(x)**(1/2),x)","\int \frac{x \left(\cos^{2}{\left(x \right)} + 1\right)}{\cos^{\frac{3}{2}}{\left(x \right)}}\, dx"," ",0,"Integral(x*(cos(x)**2 + 1)/cos(x)**(3/2), x)","F",0
91,0,0,0,0.000000," ","integrate(x/cos(x)**(5/2)-1/3*x/cos(x)**(1/2),x)","- \frac{\int \left(- \frac{3 x}{\cos^{\frac{5}{2}}{\left(x \right)}}\right)\, dx + \int \frac{x}{\sqrt{\cos{\left(x \right)}}}\, dx}{3}"," ",0,"-(Integral(-3*x/cos(x)**(5/2), x) + Integral(x/sqrt(cos(x)), x))/3","F",0
92,-1,0,0,0.000000," ","integrate(x/cos(x)**(7/2)+3/5*x*cos(x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,0,0,0,0.000000," ","integrate(x**2/cos(x)**(3/2)+x**2*cos(x)**(1/2),x)","\int \frac{x^{2} \left(\cos^{2}{\left(x \right)} + 1\right)}{\cos^{\frac{3}{2}}{\left(x \right)}}\, dx"," ",0,"Integral(x**2*(cos(x)**2 + 1)/cos(x)**(3/2), x)","F",0
94,0,0,0,0.000000," ","integrate(x/sec(x)**(3/2)-1/3*x*sec(x)**(1/2),x)","- \frac{\int \left(- \frac{3 x}{\sec^{\frac{3}{2}}{\left(x \right)}}\right)\, dx + \int x \sqrt{\sec{\left(x \right)}}\, dx}{3}"," ",0,"-(Integral(-3*x/sec(x)**(3/2), x) + Integral(x*sqrt(sec(x)), x))/3","F",0
95,0,0,0,0.000000," ","integrate(x/sec(x)**(5/2)-3/5*x/sec(x)**(1/2),x)","- \frac{\int \left(- \frac{5 x}{\sec^{\frac{5}{2}}{\left(x \right)}}\right)\, dx + \int \frac{3 x}{\sqrt{\sec{\left(x \right)}}}\, dx}{5}"," ",0,"-(Integral(-5*x/sec(x)**(5/2), x) + Integral(3*x/sqrt(sec(x)), x))/5","F",0
96,0,0,0,0.000000," ","integrate(x/sec(x)**(7/2)-5/21*x*sec(x)**(1/2),x)","- \frac{\int \left(- \frac{21 x}{\sec^{\frac{7}{2}}{\left(x \right)}}\right)\, dx + \int 5 x \sqrt{\sec{\left(x \right)}}\, dx}{21}"," ",0,"-(Integral(-21*x/sec(x)**(7/2), x) + Integral(5*x*sqrt(sec(x)), x))/21","F",0
97,0,0,0,0.000000," ","integrate(x**2/sec(x)**(3/2)-1/3*x**2*sec(x)**(1/2),x)","- \frac{\int \left(- \frac{3 x^{2}}{\sec^{\frac{3}{2}}{\left(x \right)}}\right)\, dx + \int x^{2} \sqrt{\sec{\left(x \right)}}\, dx}{3}"," ",0,"-(Integral(-3*x**2/sec(x)**(3/2), x) + Integral(x**2*sqrt(sec(x)), x))/3","F",0
98,0,0,0,0.000000," ","integrate((d*x+c)**m*(b*cos(f*x+e))**n,x)","\int \left(b \cos{\left(e + f x \right)}\right)^{n} \left(c + d x\right)^{m}\, dx"," ",0,"Integral((b*cos(e + f*x))**n*(c + d*x)**m, x)","F",0
99,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**3,x)","\int \left(c + d x\right)^{m} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)**3, x)","F",0
100,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)**2, x)","F",0
101,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a),x)","\int \left(c + d x\right)^{m} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x), x)","F",0
102,0,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a),x)","\int \left(c + d x\right)^{m} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sec(a + b*x), x)","F",0
103,0,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sec(a + b*x)**2, x)","F",0
104,0,0,0,0.000000," ","integrate(x**(3+m)*cos(b*x+a),x)","\int x^{m + 3} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 3)*cos(a + b*x), x)","F",0
105,0,0,0,0.000000," ","integrate(x**(2+m)*cos(b*x+a),x)","\int x^{m + 2} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 2)*cos(a + b*x), x)","F",0
106,0,0,0,0.000000," ","integrate(x**(1+m)*cos(b*x+a),x)","\int x^{m + 1} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 1)*cos(a + b*x), x)","F",0
107,0,0,0,0.000000," ","integrate(x**m*cos(b*x+a),x)","\int x^{m} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**m*cos(a + b*x), x)","F",0
108,0,0,0,0.000000," ","integrate(x**(-1+m)*cos(b*x+a),x)","\int x^{m - 1} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 1)*cos(a + b*x), x)","F",0
109,0,0,0,0.000000," ","integrate(x**(-2+m)*cos(b*x+a),x)","\int x^{m - 2} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 2)*cos(a + b*x), x)","F",0
110,0,0,0,0.000000," ","integrate(x**(-3+m)*cos(b*x+a),x)","\int x^{m - 3} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 3)*cos(a + b*x), x)","F",0
111,0,0,0,0.000000," ","integrate(x**(3+m)*cos(b*x+a)**2,x)","\int x^{m + 3} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 3)*cos(a + b*x)**2, x)","F",0
112,0,0,0,0.000000," ","integrate(x**(2+m)*cos(b*x+a)**2,x)","\int x^{m + 2} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 2)*cos(a + b*x)**2, x)","F",0
113,0,0,0,0.000000," ","integrate(x**(1+m)*cos(b*x+a)**2,x)","\int x^{m + 1} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m + 1)*cos(a + b*x)**2, x)","F",0
114,0,0,0,0.000000," ","integrate(x**m*cos(b*x+a)**2,x)","\int x^{m} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**m*cos(a + b*x)**2, x)","F",0
115,0,0,0,0.000000," ","integrate(x**(-1+m)*cos(b*x+a)**2,x)","\int x^{m - 1} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 1)*cos(a + b*x)**2, x)","F",0
116,0,0,0,0.000000," ","integrate(x**(-2+m)*cos(b*x+a)**2,x)","\int x^{m - 2} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 2)*cos(a + b*x)**2, x)","F",0
117,0,0,0,0.000000," ","integrate(x**(-3+m)*cos(b*x+a)**2,x)","\int x^{m - 3} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**(m - 3)*cos(a + b*x)**2, x)","F",0
118,1,264,0,1.381814," ","integrate((d*x+c)**3*(a+a*cos(f*x+e)),x)","\begin{cases} a c^{3} x + \frac{a c^{3} \sin{\left(e + f x \right)}}{f} + \frac{3 a c^{2} d x^{2}}{2} + \frac{3 a c^{2} d x \sin{\left(e + f x \right)}}{f} + \frac{3 a c^{2} d \cos{\left(e + f x \right)}}{f^{2}} + a c d^{2} x^{3} + \frac{3 a c d^{2} x^{2} \sin{\left(e + f x \right)}}{f} + \frac{6 a c d^{2} x \cos{\left(e + f x \right)}}{f^{2}} - \frac{6 a c d^{2} \sin{\left(e + f x \right)}}{f^{3}} + \frac{a d^{3} x^{4}}{4} + \frac{a d^{3} x^{3} \sin{\left(e + f x \right)}}{f} + \frac{3 a d^{3} x^{2} \cos{\left(e + f x \right)}}{f^{2}} - \frac{6 a d^{3} x \sin{\left(e + f x \right)}}{f^{3}} - \frac{6 a d^{3} \cos{\left(e + f x \right)}}{f^{4}} & \text{for}\: f \neq 0 \\\left(a \cos{\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*sin(e + f*x)/f + 3*a*c**2*d*x**2/2 + 3*a*c**2*d*x*sin(e + f*x)/f + 3*a*c**2*d*cos(e + f*x)/f**2 + a*c*d**2*x**3 + 3*a*c*d**2*x**2*sin(e + f*x)/f + 6*a*c*d**2*x*cos(e + f*x)/f**2 - 6*a*c*d**2*sin(e + f*x)/f**3 + a*d**3*x**4/4 + a*d**3*x**3*sin(e + f*x)/f + 3*a*d**3*x**2*cos(e + f*x)/f**2 - 6*a*d**3*x*sin(e + f*x)/f**3 - 6*a*d**3*cos(e + f*x)/f**4, Ne(f, 0)), ((a*cos(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
119,1,151,0,0.612984," ","integrate((d*x+c)**2*(a+a*cos(f*x+e)),x)","\begin{cases} a c^{2} x + \frac{a c^{2} \sin{\left(e + f x \right)}}{f} + a c d x^{2} + \frac{2 a c d x \sin{\left(e + f x \right)}}{f} + \frac{2 a c d \cos{\left(e + f x \right)}}{f^{2}} + \frac{a d^{2} x^{3}}{3} + \frac{a d^{2} x^{2} \sin{\left(e + f x \right)}}{f} + \frac{2 a d^{2} x \cos{\left(e + f x \right)}}{f^{2}} - \frac{2 a d^{2} \sin{\left(e + f x \right)}}{f^{3}} & \text{for}\: f \neq 0 \\\left(a \cos{\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*sin(e + f*x)/f + a*c*d*x**2 + 2*a*c*d*x*sin(e + f*x)/f + 2*a*c*d*cos(e + f*x)/f**2 + a*d**2*x**3/3 + a*d**2*x**2*sin(e + f*x)/f + 2*a*d**2*x*cos(e + f*x)/f**2 - 2*a*d**2*sin(e + f*x)/f**3, Ne(f, 0)), ((a*cos(e) + a)*(c**2*x + c*d*x**2 + d**2*x**3/3), True))","A",0
120,1,68,0,0.254048," ","integrate((d*x+c)*(a+a*cos(f*x+e)),x)","\begin{cases} a c x + \frac{a c \sin{\left(e + f x \right)}}{f} + \frac{a d x^{2}}{2} + \frac{a d x \sin{\left(e + f x \right)}}{f} + \frac{a d \cos{\left(e + f x \right)}}{f^{2}} & \text{for}\: f \neq 0 \\\left(a \cos{\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*sin(e + f*x)/f + a*d*x**2/2 + a*d*x*sin(e + f*x)/f + a*d*cos(e + f*x)/f**2, Ne(f, 0)), ((a*cos(e) + a)*(c*x + d*x**2/2), True))","A",0
121,0,0,0,0.000000," ","integrate((a+a*cos(f*x+e))/(d*x+c),x)","a \left(\int \frac{\cos{\left(e + f x \right)}}{c + d x}\, dx + \int \frac{1}{c + d x}\, dx\right)"," ",0,"a*(Integral(cos(e + f*x)/(c + d*x), x) + Integral(1/(c + d*x), x))","F",0
122,0,0,0,0.000000," ","integrate((a+a*cos(f*x+e))/(d*x+c)**2,x)","a \left(\int \frac{\cos{\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(cos(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
123,1,779,0,3.453205," ","integrate((d*x+c)**3*(a+a*cos(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} \sin{\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 \sin{\left(e + f x \right)}}{f} - \frac{3 a^{2} c^{2} d \sin^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{6 a^{2} c^{2} d \cos{\left(e + f x \right)}}{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} \sin{\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{3 a^{2} c d^{2} x \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{12 a^{2} c d^{2} x \cos{\left(e + f x \right)}}{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} \sin{\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} \sin{\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{3 a^{2} d^{3} x^{2} \cos^{2}{\left(e + f x \right)}}{8 f^{2}} + \frac{6 a^{2} d^{3} x^{2} \cos{\left(e + f x \right)}}{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 \sin{\left(e + f x \right)}}{f^{3}} + \frac{3 a^{2} d^{3} \sin^{2}{\left(e + f x \right)}}{8 f^{4}} - \frac{12 a^{2} d^{3} \cos{\left(e + f x \right)}}{f^{4}} & \text{for}\: f \neq 0 \\\left(a \cos{\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*sin(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*sin(e + f*x)/f - 3*a**2*c**2*d*sin(e + f*x)**2/(4*f**2) + 6*a**2*c**2*d*cos(e + f*x)/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*sin(e + f*x)/f - 3*a**2*c*d**2*x*sin(e + f*x)**2/(4*f**2) + 3*a**2*c*d**2*x*cos(e + f*x)**2/(4*f**2) + 12*a**2*c*d**2*x*cos(e + f*x)/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*sin(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*sin(e + f*x)/f - 3*a**2*d**3*x**2*sin(e + f*x)**2/(8*f**2) + 3*a**2*d**3*x**2*cos(e + f*x)**2/(8*f**2) + 6*a**2*d**3*x**2*cos(e + f*x)/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*sin(e + f*x)/f**3 + 3*a**2*d**3*sin(e + f*x)**2/(8*f**4) - 12*a**2*d**3*cos(e + f*x)/f**4, Ne(f, 0)), ((a*cos(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
124,1,456,0,1.591904," ","integrate((d*x+c)**2*(a+a*cos(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} \sin{\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 \sin{\left(e + f x \right)}}{f} - \frac{a^{2} c d \sin^{2}{\left(e + f x \right)}}{2 f^{2}} + \frac{4 a^{2} c d \cos{\left(e + f x \right)}}{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} \sin{\left(e + f x \right)}}{f} - \frac{a^{2} d^{2} x \sin^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{a^{2} d^{2} x \cos^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{4 a^{2} d^{2} x \cos{\left(e + f x \right)}}{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} \sin{\left(e + f x \right)}}{f^{3}} & \text{for}\: f \neq 0 \\\left(a \cos{\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*sin(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*sin(e + f*x)/f - a**2*c*d*sin(e + f*x)**2/(2*f**2) + 4*a**2*c*d*cos(e + f*x)/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*sin(e + f*x)/f - a**2*d**2*x*sin(e + f*x)**2/(4*f**2) + a**2*d**2*x*cos(e + f*x)**2/(4*f**2) + 4*a**2*d**2*x*cos(e + f*x)/f**2 - a**2*d**2*sin(e + f*x)*cos(e + f*x)/(4*f**3) - 4*a**2*d**2*sin(e + f*x)/f**3, Ne(f, 0)), ((a*cos(e) + a)**2*(c**2*x + c*d*x**2 + d**2*x**3/3), True))","A",0
125,1,219,0,0.628050," ","integrate((d*x+c)*(a+a*cos(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 \sin{\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 \sin{\left(e + f x \right)}}{f} - \frac{a^{2} d \sin^{2}{\left(e + f x \right)}}{4 f^{2}} + \frac{2 a^{2} d \cos{\left(e + f x \right)}}{f^{2}} & \text{for}\: f \neq 0 \\\left(a \cos{\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*sin(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*sin(e + f*x)/f - a**2*d*sin(e + f*x)**2/(4*f**2) + 2*a**2*d*cos(e + f*x)/f**2, Ne(f, 0)), ((a*cos(e) + a)**2*(c*x + d*x**2/2), True))","A",0
126,0,0,0,0.000000," ","integrate((a+a*cos(f*x+e))**2/(d*x+c),x)","a^{2} \left(\int \frac{2 \cos{\left(e + f x \right)}}{c + d x}\, dx + \int \frac{\cos^{2}{\left(e + f x \right)}}{c + d x}\, dx + \int \frac{1}{c + d x}\, dx\right)"," ",0,"a**2*(Integral(2*cos(e + f*x)/(c + d*x), x) + Integral(cos(e + f*x)**2/(c + d*x), x) + Integral(1/(c + d*x), x))","F",0
127,0,0,0,0.000000," ","integrate((a+a*cos(f*x+e))**2/(d*x+c)**2,x)","a^{2} \left(\int \frac{2 \cos{\left(e + f x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{\cos^{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*cos(e + f*x)/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(cos(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
128,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+a*cos(f*x+e)),x)","\frac{\int \frac{c^{3}}{\cos{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{3} x^{3}}{\cos{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c d^{2} x^{2}}{\cos{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c^{2} d x}{\cos{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(c**3/(cos(e + f*x) + 1), x) + Integral(d**3*x**3/(cos(e + f*x) + 1), x) + Integral(3*c*d**2*x**2/(cos(e + f*x) + 1), x) + Integral(3*c**2*d*x/(cos(e + f*x) + 1), x))/a","F",0
129,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+a*cos(f*x+e)),x)","\frac{\int \frac{c^{2}}{\cos{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{2} x^{2}}{\cos{\left(e + f x \right)} + 1}\, dx + \int \frac{2 c d x}{\cos{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(c**2/(cos(e + f*x) + 1), x) + Integral(d**2*x**2/(cos(e + f*x) + 1), x) + Integral(2*c*d*x/(cos(e + f*x) + 1), x))/a","F",0
130,1,70,0,0.647527," ","integrate((d*x+c)/(a+a*cos(f*x+e)),x)","\begin{cases} \frac{c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f} + \frac{d x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a f^{2}} & \text{for}\: f \neq 0 \\\frac{c x + \frac{d x^{2}}{2}}{a \cos{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*tan(e/2 + f*x/2)/(a*f) + d*x*tan(e/2 + f*x/2)/(a*f) - d*log(tan(e/2 + f*x/2)**2 + 1)/(a*f**2), Ne(f, 0)), ((c*x + d*x**2/2)/(a*cos(e) + a), True))","A",0
131,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e)),x)","\frac{\int \frac{1}{c \cos{\left(e + f x \right)} + c + d x \cos{\left(e + f x \right)} + d x}\, dx}{a}"," ",0,"Integral(1/(c*cos(e + f*x) + c + d*x*cos(e + f*x) + d*x), x)/a","F",0
132,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a+a*cos(f*x+e)),x)","\frac{\int \frac{1}{c^{2} \cos{\left(e + f x \right)} + c^{2} + 2 c d x \cos{\left(e + f x \right)} + 2 c d x + d^{2} x^{2} \cos{\left(e + f x \right)} + d^{2} x^{2}}\, dx}{a}"," ",0,"Integral(1/(c**2*cos(e + f*x) + c**2 + 2*c*d*x*cos(e + f*x) + 2*c*d*x + d**2*x**2*cos(e + f*x) + d**2*x**2), x)/a","F",0
133,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+a*cos(f*x+e))**2,x)","\frac{\int \frac{c^{3}}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{3} x^{3}}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c d^{2} x^{2}}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx + \int \frac{3 c^{2} d x}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(c**3/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x) + Integral(d**3*x**3/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x) + Integral(3*c*d**2*x**2/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x) + Integral(3*c**2*d*x/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x))/a**2","F",0
134,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+a*cos(f*x+e))**2,x)","\frac{\int \frac{c^{2}}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{2} x^{2}}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx + \int \frac{2 c d x}{\cos^{2}{\left(e + f x \right)} + 2 \cos{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(c**2/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x) + Integral(d**2*x**2/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x) + Integral(2*c*d*x/(cos(e + f*x)**2 + 2*cos(e + f*x) + 1), x))/a**2","F",0
135,1,146,0,1.091447," ","integrate((d*x+c)/(a+a*cos(f*x+e))**2,x)","\begin{cases} \frac{c \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f} + \frac{c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a^{2} f} + \frac{d x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f} + \frac{d x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a^{2} f} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{3 a^{2} f^{2}} - \frac{d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f^{2}} & \text{for}\: f \neq 0 \\\frac{c x + \frac{d x^{2}}{2}}{\left(a \cos{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*tan(e/2 + f*x/2)**3/(6*a**2*f) + c*tan(e/2 + f*x/2)/(2*a**2*f) + d*x*tan(e/2 + f*x/2)**3/(6*a**2*f) + d*x*tan(e/2 + f*x/2)/(2*a**2*f) - d*log(tan(e/2 + f*x/2)**2 + 1)/(3*a**2*f**2) - d*tan(e/2 + f*x/2)**2/(6*a**2*f**2), Ne(f, 0)), ((c*x + d*x**2/2)/(a*cos(e) + a)**2, True))","A",0
136,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e))**2,x)","\frac{\int \frac{1}{c \cos^{2}{\left(e + f x \right)} + 2 c \cos{\left(e + f x \right)} + c + d x \cos^{2}{\left(e + f x \right)} + 2 d x \cos{\left(e + f x \right)} + d x}\, dx}{a^{2}}"," ",0,"Integral(1/(c*cos(e + f*x)**2 + 2*c*cos(e + f*x) + c + d*x*cos(e + f*x)**2 + 2*d*x*cos(e + f*x) + d*x), x)/a**2","F",0
137,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a+a*cos(f*x+e))**2,x)","\frac{\int \frac{1}{c^{2} \cos^{2}{\left(e + f x \right)} + 2 c^{2} \cos{\left(e + f x \right)} + c^{2} + 2 c d x \cos^{2}{\left(e + f x \right)} + 4 c d x \cos{\left(e + f x \right)} + 2 c d x + d^{2} x^{2} \cos^{2}{\left(e + f x \right)} + 2 d^{2} x^{2} \cos{\left(e + f x \right)} + d^{2} x^{2}}\, dx}{a^{2}}"," ",0,"Integral(1/(c**2*cos(e + f*x)**2 + 2*c**2*cos(e + f*x) + c**2 + 2*c*d*x*cos(e + f*x)**2 + 4*c*d*x*cos(e + f*x) + 2*c*d*x + d**2*x**2*cos(e + f*x)**2 + 2*d**2*x**2*cos(e + f*x) + d**2*x**2), x)/a**2","F",0
138,0,0,0,0.000000," ","integrate((d*x+c)**3/(a-a*cos(f*x+e)),x)","- \frac{\int \frac{c^{3}}{\cos{\left(e + f x \right)} - 1}\, dx + \int \frac{d^{3} x^{3}}{\cos{\left(e + f x \right)} - 1}\, dx + \int \frac{3 c d^{2} x^{2}}{\cos{\left(e + f x \right)} - 1}\, dx + \int \frac{3 c^{2} d x}{\cos{\left(e + f x \right)} - 1}\, dx}{a}"," ",0,"-(Integral(c**3/(cos(e + f*x) - 1), x) + Integral(d**3*x**3/(cos(e + f*x) - 1), x) + Integral(3*c*d**2*x**2/(cos(e + f*x) - 1), x) + Integral(3*c**2*d*x/(cos(e + f*x) - 1), x))/a","F",0
139,0,0,0,0.000000," ","integrate((d*x+c)**2/(a-a*cos(f*x+e)),x)","- \frac{\int \frac{c^{2}}{\cos{\left(e + f x \right)} - 1}\, dx + \int \frac{d^{2} x^{2}}{\cos{\left(e + f x \right)} - 1}\, dx + \int \frac{2 c d x}{\cos{\left(e + f x \right)} - 1}\, dx}{a}"," ",0,"-(Integral(c**2/(cos(e + f*x) - 1), x) + Integral(d**2*x**2/(cos(e + f*x) - 1), x) + Integral(2*c*d*x/(cos(e + f*x) - 1), x))/a","F",0
140,1,90,0,0.770573," ","integrate((d*x+c)/(a-a*cos(f*x+e)),x)","\begin{cases} - \frac{c}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}} - \frac{d x}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}} - \frac{d \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a f^{2}} + \frac{2 d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} \right)}}{a f^{2}} & \text{for}\: f \neq 0 \\\frac{c x + \frac{d x^{2}}{2}}{- a \cos{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c/(a*f*tan(e/2 + f*x/2)) - d*x/(a*f*tan(e/2 + f*x/2)) - d*log(tan(e/2 + f*x/2)**2 + 1)/(a*f**2) + 2*d*log(tan(e/2 + f*x/2))/(a*f**2), Ne(f, 0)), ((c*x + d*x**2/2)/(-a*cos(e) + a), True))","A",0
141,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a-a*cos(f*x+e)),x)","- \frac{\int \frac{1}{c \cos{\left(e + f x \right)} - c + d x \cos{\left(e + f x \right)} - d x}\, dx}{a}"," ",0,"-Integral(1/(c*cos(e + f*x) - c + d*x*cos(e + f*x) - d*x), x)/a","F",0
142,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(a-a*cos(f*x+e)),x)","- \frac{\int \frac{1}{c^{2} \cos{\left(e + f x \right)} - c^{2} + 2 c d x \cos{\left(e + f x \right)} - 2 c d x + d^{2} x^{2} \cos{\left(e + f x \right)} - d^{2} x^{2}}\, dx}{a}"," ",0,"-Integral(1/(c**2*cos(e + f*x) - c**2 + 2*c*d*x*cos(e + f*x) - 2*c*d*x + d**2*x**2*cos(e + f*x) - d**2*x**2), x)/a","F",0
143,0,0,0,0.000000," ","integrate(x**3*(a+a*cos(d*x+c))**(1/2),x)","\int x^{3} \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}\, dx"," ",0,"Integral(x**3*sqrt(a*(cos(c + d*x) + 1)), x)","F",0
144,0,0,0,0.000000," ","integrate(x**2*(a+a*cos(d*x+c))**(1/2),x)","\int x^{2} \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}\, dx"," ",0,"Integral(x**2*sqrt(a*(cos(c + d*x) + 1)), x)","F",0
145,0,0,0,0.000000," ","integrate(x*(a+a*cos(d*x+c))**(1/2),x)","\int x \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}\, dx"," ",0,"Integral(x*sqrt(a*(cos(c + d*x) + 1)), x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \cos{\left(c + d x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*cos(c + d*x) + a), x)","F",0
147,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/x,x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{x}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/x, x)","F",0
148,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/x**2,x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/x**2, x)","F",0
149,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/x**3,x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/x**3, x)","F",0
150,0,0,0,0.000000," ","integrate(x**3*(a+a*cos(x))**(1/2),x)","\int x^{3} \sqrt{a \left(\cos{\left(x \right)} + 1\right)}\, dx"," ",0,"Integral(x**3*sqrt(a*(cos(x) + 1)), x)","F",0
151,0,0,0,0.000000," ","integrate(x**2*(a+a*cos(x))**(1/2),x)","\int x^{2} \sqrt{a \left(\cos{\left(x \right)} + 1\right)}\, dx"," ",0,"Integral(x**2*sqrt(a*(cos(x) + 1)), x)","F",0
152,0,0,0,0.000000," ","integrate(x*(a+a*cos(x))**(1/2),x)","\int x \sqrt{a \left(\cos{\left(x \right)} + 1\right)}\, dx"," ",0,"Integral(x*sqrt(a*(cos(x) + 1)), x)","F",0
153,0,0,0,0.000000," ","integrate((a+a*cos(x))**(1/2),x)","\int \sqrt{a \cos{\left(x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*cos(x) + a), x)","F",0
154,0,0,0,0.000000," ","integrate((a+a*cos(x))**(1/2)/x,x)","\int \frac{\sqrt{a \left(\cos{\left(x \right)} + 1\right)}}{x}\, dx"," ",0,"Integral(sqrt(a*(cos(x) + 1))/x, x)","F",0
155,0,0,0,0.000000," ","integrate((a+a*cos(x))**(1/2)/x**2,x)","\int \frac{\sqrt{a \left(\cos{\left(x \right)} + 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a*(cos(x) + 1))/x**2, x)","F",0
156,0,0,0,0.000000," ","integrate((a+a*cos(x))**(1/2)/x**3,x)","\int \frac{\sqrt{a \left(\cos{\left(x \right)} + 1\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a*(cos(x) + 1))/x**3, x)","F",0
157,0,0,0,0.000000," ","integrate(x**3*(a-a*cos(x))**(1/2),x)","\int x^{3} \sqrt{- a \left(\cos{\left(x \right)} - 1\right)}\, dx"," ",0,"Integral(x**3*sqrt(-a*(cos(x) - 1)), x)","F",0
158,0,0,0,0.000000," ","integrate(x**2*(a-a*cos(x))**(1/2),x)","\int x^{2} \sqrt{- a \left(\cos{\left(x \right)} - 1\right)}\, dx"," ",0,"Integral(x**2*sqrt(-a*(cos(x) - 1)), x)","F",0
159,0,0,0,0.000000," ","integrate(x*(a-a*cos(x))**(1/2),x)","\int x \sqrt{- a \left(\cos{\left(x \right)} - 1\right)}\, dx"," ",0,"Integral(x*sqrt(-a*(cos(x) - 1)), x)","F",0
160,0,0,0,0.000000," ","integrate((a-a*cos(x))**(1/2),x)","\int \sqrt{- a \cos{\left(x \right)} + a}\, dx"," ",0,"Integral(sqrt(-a*cos(x) + a), x)","F",0
161,0,0,0,0.000000," ","integrate((a-a*cos(x))**(1/2)/x,x)","\int \frac{\sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}{x}\, dx"," ",0,"Integral(sqrt(-a*(cos(x) - 1))/x, x)","F",0
162,0,0,0,0.000000," ","integrate((a-a*cos(x))**(1/2)/x**2,x)","\int \frac{\sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(-a*(cos(x) - 1))/x**2, x)","F",0
163,0,0,0,0.000000," ","integrate((a-a*cos(x))**(1/2)/x**3,x)","\int \frac{\sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(-a*(cos(x) - 1))/x**3, x)","F",0
164,0,0,0,0.000000," ","integrate(x**3*(a+a*cos(x))**(3/2),x)","\int x^{3} \left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a*(cos(x) + 1))**(3/2), x)","F",0
165,0,0,0,0.000000," ","integrate(x**2*(a+a*cos(x))**(3/2),x)","\int x^{2} \left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a*(cos(x) + 1))**(3/2), x)","F",0
166,0,0,0,0.000000," ","integrate(x*(a+a*cos(x))**(3/2),x)","\int x \left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a*(cos(x) + 1))**(3/2), x)","F",0
167,0,0,0,0.000000," ","integrate((a+a*cos(x))**(3/2)/x,x)","\int \frac{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a*(cos(x) + 1))**(3/2)/x, x)","F",0
168,0,0,0,0.000000," ","integrate((a+a*cos(x))**(3/2)/x**2,x)","\int \frac{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a*(cos(x) + 1))**(3/2)/x**2, x)","F",0
169,0,0,0,0.000000," ","integrate((a+a*cos(x))**(3/2)/x**3,x)","\int \frac{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a*(cos(x) + 1))**(3/2)/x**3, x)","F",0
170,0,0,0,0.000000," ","integrate(x**3/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{x^{3}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(x**3/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
171,0,0,0,0.000000," ","integrate(x**2/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(x**2/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
172,0,0,0,0.000000," ","integrate(x/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{x}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(x/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
173,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \cos{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(a*cos(c + d*x) + a), x)","F",0
174,0,0,0,0.000000," ","integrate(1/x/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{x \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(a*(cos(c + d*x) + 1))), x)","F",0
175,0,0,0,0.000000," ","integrate(x**3/(a-a*cos(x))**(1/2),x)","\int \frac{x^{3}}{\sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}\, dx"," ",0,"Integral(x**3/sqrt(-a*(cos(x) - 1)), x)","F",0
176,0,0,0,0.000000," ","integrate(x**2/(a-a*cos(x))**(1/2),x)","\int \frac{x^{2}}{\sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}\, dx"," ",0,"Integral(x**2/sqrt(-a*(cos(x) - 1)), x)","F",0
177,0,0,0,0.000000," ","integrate(x/(a-a*cos(x))**(1/2),x)","\int \frac{x}{\sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}\, dx"," ",0,"Integral(x/sqrt(-a*(cos(x) - 1)), x)","F",0
178,0,0,0,0.000000," ","integrate(1/(a-a*cos(x))**(1/2),x)","\int \frac{1}{\sqrt{- a \cos{\left(x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(-a*cos(x) + a), x)","F",0
179,0,0,0,0.000000," ","integrate(1/x/(a-a*cos(x))**(1/2),x)","\int \frac{1}{x \sqrt{- a \left(\cos{\left(x \right)} - 1\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-a*(cos(x) - 1))), x)","F",0
180,0,0,0,0.000000," ","integrate(x**3/(a+a*cos(x))**(3/2),x)","\int \frac{x^{3}}{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(a*(cos(x) + 1))**(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate(x**2/(a+a*cos(x))**(3/2),x)","\int \frac{x^{2}}{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(a*(cos(x) + 1))**(3/2), x)","F",0
182,0,0,0,0.000000," ","integrate(x/(a+a*cos(x))**(3/2),x)","\int \frac{x}{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a*(cos(x) + 1))**(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate(1/x/(a+a*cos(x))**(3/2),x)","\int \frac{1}{x \left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a*(cos(x) + 1))**(3/2)), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/3)/x,x)","\int \frac{\sqrt[3]{a \left(\cos{\left(c + d x \right)} + 1\right)}}{x}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(1/3)/x, x)","F",0
185,0,0,0,0.000000," ","integrate(x**3/(a+b*cos(x)),x)","\int \frac{x^{3}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(x**3/(a + b*cos(x)), x)","F",0
186,0,0,0,0.000000," ","integrate(x**2/(a+b*cos(d*x+c)),x)","\int \frac{x^{2}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(x**2/(a + b*cos(c + d*x)), x)","F",0
187,0,0,0,0.000000," ","integrate(x/(a+b*cos(d*x+c)),x)","\int \frac{x}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(x/(a + b*cos(c + d*x)), x)","F",0
188,0,0,0,0.000000," ","integrate(1/x/(a+b*cos(x)),x)","\int \frac{1}{x \left(a + b \cos{\left(x \right)}\right)}\, dx"," ",0,"Integral(1/(x*(a + b*cos(x))), x)","F",0
189,-1,0,0,0.000000," ","integrate((f*x+e)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
