1,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*sin(b*x+a),x)","\int \left(c + d x\right)^{m} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)*cos(a + b*x), x)","F",0
2,1,502,0,4.251570," ","integrate((d*x+c)**4*cos(b*x+a)*sin(b*x+a),x)","\begin{cases} - \frac{c^{4} \cos^{2}{\left(a + b x \right)}}{2 b} + \frac{c^{3} d x \sin^{2}{\left(a + b x \right)}}{b} - \frac{c^{3} d x \cos^{2}{\left(a + b x \right)}}{b} + \frac{3 c^{2} d^{2} x^{2} \sin^{2}{\left(a + b x \right)}}{2 b} - \frac{3 c^{2} d^{2} x^{2} \cos^{2}{\left(a + b x \right)}}{2 b} + \frac{c d^{3} x^{3} \sin^{2}{\left(a + b x \right)}}{b} - \frac{c d^{3} x^{3} \cos^{2}{\left(a + b x \right)}}{b} + \frac{d^{4} x^{4} \sin^{2}{\left(a + b x \right)}}{4 b} - \frac{d^{4} x^{4} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{c^{3} d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{3 c^{2} d^{2} x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{3 c d^{3} x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{d^{4} x^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{3 c^{2} d^{2} \cos^{2}{\left(a + b x \right)}}{2 b^{3}} - \frac{3 c d^{3} x \sin^{2}{\left(a + b x \right)}}{2 b^{3}} + \frac{3 c d^{3} x \cos^{2}{\left(a + b x \right)}}{2 b^{3}} - \frac{3 d^{4} x^{2} \sin^{2}{\left(a + b x \right)}}{4 b^{3}} + \frac{3 d^{4} x^{2} \cos^{2}{\left(a + b x \right)}}{4 b^{3}} - \frac{3 c d^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{4}} - \frac{3 d^{4} x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{4}} - \frac{3 d^{4} \cos^{2}{\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{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**4*cos(a + b*x)**2/(2*b) + c**3*d*x*sin(a + b*x)**2/b - c**3*d*x*cos(a + b*x)**2/b + 3*c**2*d**2*x**2*sin(a + b*x)**2/(2*b) - 3*c**2*d**2*x**2*cos(a + b*x)**2/(2*b) + c*d**3*x**3*sin(a + b*x)**2/b - c*d**3*x**3*cos(a + b*x)**2/b + d**4*x**4*sin(a + b*x)**2/(4*b) - d**4*x**4*cos(a + b*x)**2/(4*b) + c**3*d*sin(a + b*x)*cos(a + b*x)/b**2 + 3*c**2*d**2*x*sin(a + b*x)*cos(a + b*x)/b**2 + 3*c*d**3*x**2*sin(a + b*x)*cos(a + b*x)/b**2 + d**4*x**3*sin(a + b*x)*cos(a + b*x)/b**2 + 3*c**2*d**2*cos(a + b*x)**2/(2*b**3) - 3*c*d**3*x*sin(a + b*x)**2/(2*b**3) + 3*c*d**3*x*cos(a + b*x)**2/(2*b**3) - 3*d**4*x**2*sin(a + b*x)**2/(4*b**3) + 3*d**4*x**2*cos(a + b*x)**2/(4*b**3) - 3*c*d**3*sin(a + b*x)*cos(a + b*x)/(2*b**4) - 3*d**4*x*sin(a + b*x)*cos(a + b*x)/(2*b**4) - 3*d**4*cos(a + b*x)**2/(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)*cos(a), True))","A",0
3,1,342,0,2.385181," ","integrate((d*x+c)**3*cos(b*x+a)*sin(b*x+a),x)","\begin{cases} - \frac{c^{3} \cos^{2}{\left(a + b x \right)}}{2 b} + \frac{3 c^{2} d x \sin^{2}{\left(a + b x \right)}}{4 b} - \frac{3 c^{2} d x \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{3 c d^{2} x^{2} \sin^{2}{\left(a + b x \right)}}{4 b} - \frac{3 c d^{2} x^{2} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{d^{3} x^{3} \sin^{2}{\left(a + b x \right)}}{4 b} - \frac{d^{3} x^{3} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{3 c^{2} d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{2}} + \frac{3 c d^{2} x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{2}} + \frac{3 d^{3} x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{2}} + \frac{3 c d^{2} \cos^{2}{\left(a + b x \right)}}{4 b^{3}} - \frac{3 d^{3} x \sin^{2}{\left(a + b x \right)}}{8 b^{3}} + \frac{3 d^{3} x \cos^{2}{\left(a + b x \right)}}{8 b^{3}} - \frac{3 d^{3} \sin{\left(a + b x \right)} \cos{\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{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**3*cos(a + b*x)**2/(2*b) + 3*c**2*d*x*sin(a + b*x)**2/(4*b) - 3*c**2*d*x*cos(a + b*x)**2/(4*b) + 3*c*d**2*x**2*sin(a + b*x)**2/(4*b) - 3*c*d**2*x**2*cos(a + b*x)**2/(4*b) + d**3*x**3*sin(a + b*x)**2/(4*b) - d**3*x**3*cos(a + b*x)**2/(4*b) + 3*c**2*d*sin(a + b*x)*cos(a + b*x)/(4*b**2) + 3*c*d**2*x*sin(a + b*x)*cos(a + b*x)/(2*b**2) + 3*d**3*x**2*sin(a + b*x)*cos(a + b*x)/(4*b**2) + 3*c*d**2*cos(a + b*x)**2/(4*b**3) - 3*d**3*x*sin(a + b*x)**2/(8*b**3) + 3*d**3*x*cos(a + b*x)**2/(8*b**3) - 3*d**3*sin(a + b*x)*cos(a + b*x)/(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)*cos(a), True))","A",0
4,1,175,0,1.050078," ","integrate((d*x+c)**2*cos(b*x+a)*sin(b*x+a),x)","\begin{cases} - \frac{c^{2} \cos^{2}{\left(a + b x \right)}}{2 b} + \frac{c d x \sin^{2}{\left(a + b x \right)}}{2 b} - \frac{c d x \cos^{2}{\left(a + b x \right)}}{2 b} + \frac{d^{2} x^{2} \sin^{2}{\left(a + b x \right)}}{4 b} - \frac{d^{2} x^{2} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{c d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{2}} + \frac{d^{2} x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{2}} + \frac{d^{2} \cos^{2}{\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{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**2*cos(a + b*x)**2/(2*b) + c*d*x*sin(a + b*x)**2/(2*b) - c*d*x*cos(a + b*x)**2/(2*b) + d**2*x**2*sin(a + b*x)**2/(4*b) - d**2*x**2*cos(a + b*x)**2/(4*b) + c*d*sin(a + b*x)*cos(a + b*x)/(2*b**2) + d**2*x*sin(a + b*x)*cos(a + b*x)/(2*b**2) + d**2*cos(a + b*x)**2/(4*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)*cos(a), True))","A",0
5,1,80,0,0.472654," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a),x)","\begin{cases} - \frac{c \cos^{2}{\left(a + b x \right)}}{2 b} + \frac{d x \sin^{2}{\left(a + b x \right)}}{4 b} - \frac{d x \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*cos(a + b*x)**2/(2*b) + d*x*sin(a + b*x)**2/(4*b) - d*x*cos(a + b*x)**2/(4*b) + d*sin(a + b*x)*cos(a + b*x)/(4*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)*cos(a), True))","A",0
6,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c),x)","\int \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)/(c + d*x), x)","F",0
7,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)**2,x)","\int \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)/(c + d*x)**2, x)","F",0
8,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)**3,x)","\int \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)/(c + d*x)**3, x)","F",0
9,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)**4,x)","\int \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)/(c + d*x)**4, x)","F",0
10,1,5,0,0.859160," ","integrate(cos(x)*sin(x)/x,x)","\frac{\operatorname{Si}{\left(2 x \right)}}{2}"," ",0,"Si(2*x)/2","A",0
11,1,22,0,1.572395," ","integrate(cos(x)*sin(x)/x**2,x)","- \log{\left(x \right)} + \frac{\log{\left(x^{2} \right)}}{2} + \operatorname{Ci}{\left(2 x \right)} - \frac{\sin{\left(2 x \right)}}{2 x}"," ",0,"-log(x) + log(x**2)/2 + Ci(2*x) - sin(2*x)/(2*x)","A",0
12,1,24,0,1.161368," ","integrate(cos(x)*sin(x)/x**3,x)","- \operatorname{Si}{\left(2 x \right)} - \frac{\cos{\left(2 x \right)}}{2 x} - \frac{\sin{\left(2 x \right)}}{4 x^{2}}"," ",0,"-Si(2*x) - cos(2*x)/(2*x) - sin(2*x)/(4*x**2)","A",0
13,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)**2*cos(a + b*x), x)","F",0
14,1,646,0,7.476419," ","integrate((d*x+c)**4*cos(b*x+a)*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{4} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{4 c^{3} d x \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{2 c^{2} d^{2} x^{2} \sin^{3}{\left(a + b x \right)}}{b} + \frac{4 c d^{3} x^{3} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d^{4} x^{4} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{4 c^{3} d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{8 c^{3} d \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{4 c^{2} d^{2} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{8 c^{2} d^{2} x \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 c d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{8 c d^{3} x^{2} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 d^{4} x^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{8 d^{4} x^{3} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} - \frac{28 c^{2} d^{2} \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{8 c^{2} d^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{56 c d^{3} x \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{16 c d^{3} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{28 d^{4} x^{2} \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{8 d^{4} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{56 c d^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{4}} - \frac{160 c d^{3} \cos^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{56 d^{4} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{4}} - \frac{160 d^{4} x \cos^{3}{\left(a + b x \right)}}{27 b^{4}} + \frac{488 d^{4} \sin^{3}{\left(a + b x \right)}}{81 b^{5}} + \frac{160 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) \sin^{2}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*sin(a + b*x)**3/(3*b) + 4*c**3*d*x*sin(a + b*x)**3/(3*b) + 2*c**2*d**2*x**2*sin(a + b*x)**3/b + 4*c*d**3*x**3*sin(a + b*x)**3/(3*b) + d**4*x**4*sin(a + b*x)**3/(3*b) + 4*c**3*d*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 8*c**3*d*cos(a + b*x)**3/(9*b**2) + 4*c**2*d**2*x*sin(a + b*x)**2*cos(a + b*x)/b**2 + 8*c**2*d**2*x*cos(a + b*x)**3/(3*b**2) + 4*c*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)/b**2 + 8*c*d**3*x**2*cos(a + b*x)**3/(3*b**2) + 4*d**4*x**3*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 8*d**4*x**3*cos(a + b*x)**3/(9*b**2) - 28*c**2*d**2*sin(a + b*x)**3/(9*b**3) - 8*c**2*d**2*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 56*c*d**3*x*sin(a + b*x)**3/(9*b**3) - 16*c*d**3*x*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 28*d**4*x**2*sin(a + b*x)**3/(9*b**3) - 8*d**4*x**2*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 56*c*d**3*sin(a + b*x)**2*cos(a + b*x)/(9*b**4) - 160*c*d**3*cos(a + b*x)**3/(27*b**4) - 56*d**4*x*sin(a + b*x)**2*cos(a + b*x)/(9*b**4) - 160*d**4*x*cos(a + b*x)**3/(27*b**4) + 488*d**4*sin(a + b*x)**3/(81*b**5) + 160*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)*sin(a)**2*cos(a), True))","A",0
15,1,391,0,4.010495," ","integrate((d*x+c)**3*cos(b*x+a)*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{3} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{c^{2} d x \sin^{3}{\left(a + b x \right)}}{b} + \frac{c d^{2} x^{2} \sin^{3}{\left(a + b x \right)}}{b} + \frac{d^{3} x^{3} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{c^{2} d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{2 c^{2} d \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 c d^{2} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{4 c d^{2} x \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b^{2}} + \frac{2 d^{3} x^{2} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} - \frac{14 c d^{2} \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{4 c d^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{14 d^{3} x \sin^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{4 d^{3} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{14 d^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{4}} - \frac{40 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) \sin^{2}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*sin(a + b*x)**3/(3*b) + c**2*d*x*sin(a + b*x)**3/b + c*d**2*x**2*sin(a + b*x)**3/b + d**3*x**3*sin(a + b*x)**3/(3*b) + c**2*d*sin(a + b*x)**2*cos(a + b*x)/b**2 + 2*c**2*d*cos(a + b*x)**3/(3*b**2) + 2*c*d**2*x*sin(a + b*x)**2*cos(a + b*x)/b**2 + 4*c*d**2*x*cos(a + b*x)**3/(3*b**2) + d**3*x**2*sin(a + b*x)**2*cos(a + b*x)/b**2 + 2*d**3*x**2*cos(a + b*x)**3/(3*b**2) - 14*c*d**2*sin(a + b*x)**3/(9*b**3) - 4*c*d**2*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 14*d**3*x*sin(a + b*x)**3/(9*b**3) - 4*d**3*x*sin(a + b*x)*cos(a + b*x)**2/(3*b**3) - 14*d**3*sin(a + b*x)**2*cos(a + b*x)/(9*b**4) - 40*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)*sin(a)**2*cos(a), True))","A",0
16,1,216,0,2.093714," ","integrate((d*x+c)**2*cos(b*x+a)*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{2} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{2 c d x \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d^{2} x^{2} \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{2 c d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{4 c d \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{2 d^{2} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{4 d^{2} x \cos^{3}{\left(a + b x \right)}}{9 b^{2}} - \frac{14 d^{2} \sin^{3}{\left(a + b x \right)}}{27 b^{3}} - \frac{4 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) \sin^{2}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*sin(a + b*x)**3/(3*b) + 2*c*d*x*sin(a + b*x)**3/(3*b) + d**2*x**2*sin(a + b*x)**3/(3*b) + 2*c*d*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 4*c*d*cos(a + b*x)**3/(9*b**2) + 2*d**2*x*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 4*d**2*x*cos(a + b*x)**3/(9*b**2) - 14*d**2*sin(a + b*x)**3/(27*b**3) - 4*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)*sin(a)**2*cos(a), True))","A",0
17,1,85,0,0.871542," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a)**2,x)","\begin{cases} \frac{c \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d x \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{d \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{2}} + \frac{2 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) \sin^{2}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*sin(a + b*x)**3/(3*b) + d*x*sin(a + b*x)**3/(3*b) + d*sin(a + b*x)**2*cos(a + b*x)/(3*b**2) + 2*d*cos(a + b*x)**3/(9*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**2*cos(a), True))","A",0
18,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**2/(d*x+c),x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)/(c + d*x), x)","F",0
19,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)/(c + d*x)**2, x)","F",0
20,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**2/(d*x+c)**3,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)/(c + d*x)**3, x)","F",0
21,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**2/(d*x+c)**4,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)/(c + d*x)**4, x)","F",0
22,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*sin(b*x+a)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
23,1,935,0,13.311449," ","integrate((d*x+c)**4*cos(b*x+a)*sin(b*x+a)**3,x)","\begin{cases} \frac{c^{4} \sin^{4}{\left(a + b x \right)}}{4 b} + \frac{5 c^{3} d x \sin^{4}{\left(a + b x \right)}}{8 b} - \frac{3 c^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} - \frac{3 c^{3} d x \cos^{4}{\left(a + b x \right)}}{8 b} + \frac{15 c^{2} d^{2} x^{2} \sin^{4}{\left(a + b x \right)}}{16 b} - \frac{9 c^{2} d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{9 c^{2} d^{2} x^{2} \cos^{4}{\left(a + b x \right)}}{16 b} + \frac{5 c d^{3} x^{3} \sin^{4}{\left(a + b x \right)}}{8 b} - \frac{3 c d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} - \frac{3 c d^{3} x^{3} \cos^{4}{\left(a + b x \right)}}{8 b} + \frac{5 d^{4} x^{4} \sin^{4}{\left(a + b x \right)}}{32 b} - \frac{3 d^{4} x^{4} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{3 d^{4} x^{4} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{5 c^{3} d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{3 c^{3} d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} + \frac{15 c^{2} d^{2} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{9 c^{2} d^{2} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} + \frac{15 c d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{9 c d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} + \frac{5 d^{4} x^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{3 d^{4} x^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} - \frac{15 c^{2} d^{2} \sin^{4}{\left(a + b x \right)}}{32 b^{3}} + \frac{9 c^{2} d^{2} \cos^{4}{\left(a + b x \right)}}{32 b^{3}} - \frac{51 c d^{3} x \sin^{4}{\left(a + b x \right)}}{64 b^{3}} + \frac{9 c d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32 b^{3}} + \frac{45 c d^{3} x \cos^{4}{\left(a + b x \right)}}{64 b^{3}} - \frac{51 d^{4} x^{2} \sin^{4}{\left(a + b x \right)}}{128 b^{3}} + \frac{9 d^{4} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{64 b^{3}} + \frac{45 d^{4} x^{2} \cos^{4}{\left(a + b x \right)}}{128 b^{3}} - \frac{51 c d^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{4}} - \frac{45 c d^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{4}} - \frac{51 d^{4} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{4}} - \frac{45 d^{4} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{4}} + \frac{51 d^{4} \sin^{4}{\left(a + b x \right)}}{256 b^{5}} - \frac{45 d^{4} \cos^{4}{\left(a + b x \right)}}{256 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)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*sin(a + b*x)**4/(4*b) + 5*c**3*d*x*sin(a + b*x)**4/(8*b) - 3*c**3*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(4*b) - 3*c**3*d*x*cos(a + b*x)**4/(8*b) + 15*c**2*d**2*x**2*sin(a + b*x)**4/(16*b) - 9*c**2*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(8*b) - 9*c**2*d**2*x**2*cos(a + b*x)**4/(16*b) + 5*c*d**3*x**3*sin(a + b*x)**4/(8*b) - 3*c*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**2/(4*b) - 3*c*d**3*x**3*cos(a + b*x)**4/(8*b) + 5*d**4*x**4*sin(a + b*x)**4/(32*b) - 3*d**4*x**4*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 3*d**4*x**4*cos(a + b*x)**4/(32*b) + 5*c**3*d*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 3*c**3*d*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) + 15*c**2*d**2*x*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 9*c**2*d**2*x*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) + 15*c*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 9*c*d**3*x**2*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) + 5*d**4*x**3*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 3*d**4*x**3*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) - 15*c**2*d**2*sin(a + b*x)**4/(32*b**3) + 9*c**2*d**2*cos(a + b*x)**4/(32*b**3) - 51*c*d**3*x*sin(a + b*x)**4/(64*b**3) + 9*c*d**3*x*sin(a + b*x)**2*cos(a + b*x)**2/(32*b**3) + 45*c*d**3*x*cos(a + b*x)**4/(64*b**3) - 51*d**4*x**2*sin(a + b*x)**4/(128*b**3) + 9*d**4*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(64*b**3) + 45*d**4*x**2*cos(a + b*x)**4/(128*b**3) - 51*c*d**3*sin(a + b*x)**3*cos(a + b*x)/(64*b**4) - 45*c*d**3*sin(a + b*x)*cos(a + b*x)**3/(64*b**4) - 51*d**4*x*sin(a + b*x)**3*cos(a + b*x)/(64*b**4) - 45*d**4*x*sin(a + b*x)*cos(a + b*x)**3/(64*b**4) + 51*d**4*sin(a + b*x)**4/(256*b**5) - 45*d**4*cos(a + b*x)**4/(256*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*cos(a), True))","A",0
24,1,602,0,7.281491," ","integrate((d*x+c)**3*cos(b*x+a)*sin(b*x+a)**3,x)","\begin{cases} \frac{c^{3} \sin^{4}{\left(a + b x \right)}}{4 b} + \frac{15 c^{2} d x \sin^{4}{\left(a + b x \right)}}{32 b} - \frac{9 c^{2} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{9 c^{2} d x \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{15 c d^{2} x^{2} \sin^{4}{\left(a + b x \right)}}{32 b} - \frac{9 c d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{9 c d^{2} x^{2} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{5 d^{3} x^{3} \sin^{4}{\left(a + b x \right)}}{32 b} - \frac{3 d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{3 d^{3} x^{3} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{15 c^{2} d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{2}} + \frac{9 c^{2} d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{2}} + \frac{15 c d^{2} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{2}} + \frac{9 c d^{2} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{2}} + \frac{15 d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{2}} + \frac{9 d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{2}} - \frac{15 c d^{2} \sin^{4}{\left(a + b x \right)}}{64 b^{3}} + \frac{9 c d^{2} \cos^{4}{\left(a + b x \right)}}{64 b^{3}} - \frac{51 d^{3} x \sin^{4}{\left(a + b x \right)}}{256 b^{3}} + \frac{9 d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{128 b^{3}} + \frac{45 d^{3} x \cos^{4}{\left(a + b x \right)}}{256 b^{3}} - \frac{51 d^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{256 b^{4}} - \frac{45 d^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{256 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)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*sin(a + b*x)**4/(4*b) + 15*c**2*d*x*sin(a + b*x)**4/(32*b) - 9*c**2*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 9*c**2*d*x*cos(a + b*x)**4/(32*b) + 15*c*d**2*x**2*sin(a + b*x)**4/(32*b) - 9*c*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 9*c*d**2*x**2*cos(a + b*x)**4/(32*b) + 5*d**3*x**3*sin(a + b*x)**4/(32*b) - 3*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 3*d**3*x**3*cos(a + b*x)**4/(32*b) + 15*c**2*d*sin(a + b*x)**3*cos(a + b*x)/(32*b**2) + 9*c**2*d*sin(a + b*x)*cos(a + b*x)**3/(32*b**2) + 15*c*d**2*x*sin(a + b*x)**3*cos(a + b*x)/(16*b**2) + 9*c*d**2*x*sin(a + b*x)*cos(a + b*x)**3/(16*b**2) + 15*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)/(32*b**2) + 9*d**3*x**2*sin(a + b*x)*cos(a + b*x)**3/(32*b**2) - 15*c*d**2*sin(a + b*x)**4/(64*b**3) + 9*c*d**2*cos(a + b*x)**4/(64*b**3) - 51*d**3*x*sin(a + b*x)**4/(256*b**3) + 9*d**3*x*sin(a + b*x)**2*cos(a + b*x)**2/(128*b**3) + 45*d**3*x*cos(a + b*x)**4/(256*b**3) - 51*d**3*sin(a + b*x)**3*cos(a + b*x)/(256*b**4) - 45*d**3*sin(a + b*x)*cos(a + b*x)**3/(256*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*cos(a), True))","A",0
25,1,320,0,3.624893," ","integrate((d*x+c)**2*cos(b*x+a)*sin(b*x+a)**3,x)","\begin{cases} \frac{c^{2} \sin^{4}{\left(a + b x \right)}}{4 b} + \frac{5 c d x \sin^{4}{\left(a + b x \right)}}{16 b} - \frac{3 c d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{3 c d x \cos^{4}{\left(a + b x \right)}}{16 b} + \frac{5 d^{2} x^{2} \sin^{4}{\left(a + b x \right)}}{32 b} - \frac{3 d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{3 d^{2} x^{2} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{5 c d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{2}} + \frac{3 c d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{2}} + \frac{5 d^{2} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{2}} + \frac{3 d^{2} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{2}} - \frac{5 d^{2} \sin^{4}{\left(a + b x \right)}}{64 b^{3}} + \frac{3 d^{2} \cos^{4}{\left(a + b x \right)}}{64 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)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*sin(a + b*x)**4/(4*b) + 5*c*d*x*sin(a + b*x)**4/(16*b) - 3*c*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(8*b) - 3*c*d*x*cos(a + b*x)**4/(16*b) + 5*d**2*x**2*sin(a + b*x)**4/(32*b) - 3*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 3*d**2*x**2*cos(a + b*x)**4/(32*b) + 5*c*d*sin(a + b*x)**3*cos(a + b*x)/(16*b**2) + 3*c*d*sin(a + b*x)*cos(a + b*x)**3/(16*b**2) + 5*d**2*x*sin(a + b*x)**3*cos(a + b*x)/(16*b**2) + 3*d**2*x*sin(a + b*x)*cos(a + b*x)**3/(16*b**2) - 5*d**2*sin(a + b*x)**4/(64*b**3) + 3*d**2*cos(a + b*x)**4/(64*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**3*cos(a), True))","A",0
26,1,138,0,1.832467," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a)**3,x)","\begin{cases} \frac{c \sin^{4}{\left(a + b x \right)}}{4 b} + \frac{5 d x \sin^{4}{\left(a + b x \right)}}{32 b} - \frac{3 d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{3 d x \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{5 d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{2}} + \frac{3 d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{3}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*sin(a + b*x)**4/(4*b) + 5*d*x*sin(a + b*x)**4/(32*b) - 3*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 3*d*x*cos(a + b*x)**4/(32*b) + 5*d*sin(a + b*x)**3*cos(a + b*x)/(32*b**2) + 3*d*sin(a + b*x)*cos(a + b*x)**3/(32*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**3*cos(a), True))","A",0
27,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**3/(d*x+c),x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)/(c + d*x), x)","F",0
28,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)/(c + d*x)**2, x)","F",0
29,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**3/(d*x+c)**3,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)/(c + d*x)**3, x)","F",0
30,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(b*x+a)**3/(d*x+c)**4,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)/(c + d*x)**4, x)","F",0
31,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*csc(b*x+a),x)","\int \left(c + d x\right)^{m} \cos{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)*csc(a + b*x), x)","F",0
32,0,0,0,0.000000," ","integrate((d*x+c)**4*cos(b*x+a)*csc(b*x+a),x)","\int \left(c + d x\right)^{4} \cos{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cos(a + b*x)*csc(a + b*x), x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)**3*cos(b*x+a)*csc(b*x+a),x)","\int \left(c + d x\right)^{3} \cos{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cos(a + b*x)*csc(a + b*x), x)","F",0
34,0,0,0,0.000000," ","integrate((d*x+c)**2*cos(b*x+a)*csc(b*x+a),x)","\int \left(c + d x\right)^{2} \cos{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cos(a + b*x)*csc(a + b*x), x)","F",0
35,0,0,0,0.000000," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a),x)","\int \left(c + d x\right) \cos{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cos(a + b*x)*csc(a + b*x), x)","F",0
36,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)/(d*x+c),x)","\int \frac{\cos{\left(a + b x \right)} \csc{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)*csc(a + b*x)/(c + d*x), x)","F",0
37,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)/(d*x+c)**2,x)","\int \frac{\cos{\left(a + b x \right)} \csc{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)*csc(a + b*x)/(c + d*x)**2, x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)*csc(a + b*x)**2, x)","F",0
39,0,0,0,0.000000," ","integrate((d*x+c)**4*cos(b*x+a)*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{4} \cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cos(a + b*x)*csc(a + b*x)**2, x)","F",0
40,0,0,0,0.000000," ","integrate((d*x+c)**3*cos(b*x+a)*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cos(a + b*x)*csc(a + b*x)**2, x)","F",0
41,0,0,0,0.000000," ","integrate((d*x+c)**2*cos(b*x+a)*csc(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cos(a + b*x)*csc(a + b*x)**2, x)","F",0
42,0,0,0,0.000000," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a)**2,x)","\int \left(c + d x\right) \cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cos(a + b*x)*csc(a + b*x)**2, x)","F",0
43,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)**2/(d*x+c),x)","\int \frac{\cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)*csc(a + b*x)**2/(c + d*x), x)","F",0
44,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\cos{\left(a + b x \right)} \csc^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)*csc(a + b*x)**2/(c + d*x)**2, x)","F",0
45,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*csc(b*x+a)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
46,-1,0,0,0.000000," ","integrate((d*x+c)**4*cos(b*x+a)*csc(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,0,0,0,0.000000," ","integrate((d*x+c)**3*cos(b*x+a)*csc(b*x+a)**3,x)","\int \left(c + d x\right)^{3} \cos{\left(a + b x \right)} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cos(a + b*x)*csc(a + b*x)**3, x)","F",0
48,0,0,0,0.000000," ","integrate((d*x+c)**2*cos(b*x+a)*csc(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \cos{\left(a + b x \right)} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cos(a + b*x)*csc(a + b*x)**3, x)","F",0
49,0,0,0,0.000000," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a)**3,x)","\int \left(c + d x\right) \cos{\left(a + b x \right)} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cos(a + b*x)*csc(a + b*x)**3, x)","F",0
50,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)**3/(d*x+c),x)","\int \frac{\cos{\left(a + b x \right)} \csc^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)*csc(a + b*x)**3/(c + d*x), x)","F",0
51,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\cos{\left(a + b x \right)} \csc^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)*csc(a + b*x)**3/(c + d*x)**2, x)","F",0
52,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,1,665,0,41.478889," ","integrate((d*x+c)**(3/2)*cos(b*x+a)*sin(b*x+a),x)","- \frac{5 \sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{1}{4}\right)}{32 d \Gamma\left(\frac{9}{4}\right)} + \frac{\sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} - \frac{21 \sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{3}{4}\right)}{32 d \Gamma\left(\frac{11}{4}\right)} + \frac{\sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} - \frac{15 \sqrt{\pi} d \sqrt{\frac{d}{b}} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{1}{4}\right)}{512 b^{2} \Gamma\left(\frac{9}{4}\right)} - \frac{63 \sqrt{\pi} d \sqrt{\frac{d}{b}} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{3}{4}\right)}{512 b^{2} \Gamma\left(\frac{11}{4}\right)} + \frac{5 \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{3}{2}} \sin{\left(2 a - \frac{2 b c}{d} \right)} \sin{\left(\frac{2 b c}{d} + 2 b x \right)} \Gamma\left(\frac{1}{4}\right)}{64 \sqrt{b} \sqrt{d} \Gamma\left(\frac{9}{4}\right)} - \frac{21 \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{3}{2}} \cos{\left(2 a - \frac{2 b c}{d} \right)} \cos{\left(\frac{2 b c}{d} + 2 b x \right)} \Gamma\left(\frac{3}{4}\right)}{64 \sqrt{b} \sqrt{d} \Gamma\left(\frac{11}{4}\right)} + \frac{15 \sqrt{d} \sqrt{\frac{d}{b}} \sqrt{c + d x} \sin{\left(2 a - \frac{2 b c}{d} \right)} \cos{\left(\frac{2 b c}{d} + 2 b x \right)} \Gamma\left(\frac{1}{4}\right)}{256 b^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{63 \sqrt{d} \sqrt{\frac{d}{b}} \sqrt{c + d x} \sin{\left(\frac{2 b c}{d} + 2 b x \right)} \cos{\left(2 a - \frac{2 b c}{d} \right)} \Gamma\left(\frac{3}{4}\right)}{256 b^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"-5*sqrt(pi)*sqrt(d/b)*(c + d*x)**2*sin(2*a - 2*b*c/d)*fresnelc(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(1/4)/(32*d*gamma(9/4)) + sqrt(pi)*sqrt(d/b)*(c + d*x)**2*sin(2*a - 2*b*c/d)*fresnelc(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) - 21*sqrt(pi)*sqrt(d/b)*(c + d*x)**2*cos(2*a - 2*b*c/d)*fresnels(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(3/4)/(32*d*gamma(11/4)) + sqrt(pi)*sqrt(d/b)*(c + d*x)**2*cos(2*a - 2*b*c/d)*fresnels(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) - 15*sqrt(pi)*d*sqrt(d/b)*sin(2*a - 2*b*c/d)*fresnelc(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(1/4)/(512*b**2*gamma(9/4)) - 63*sqrt(pi)*d*sqrt(d/b)*cos(2*a - 2*b*c/d)*fresnels(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(3/4)/(512*b**2*gamma(11/4)) + 5*sqrt(d/b)*(c + d*x)**(3/2)*sin(2*a - 2*b*c/d)*sin(2*b*c/d + 2*b*x)*gamma(1/4)/(64*sqrt(b)*sqrt(d)*gamma(9/4)) - 21*sqrt(d/b)*(c + d*x)**(3/2)*cos(2*a - 2*b*c/d)*cos(2*b*c/d + 2*b*x)*gamma(3/4)/(64*sqrt(b)*sqrt(d)*gamma(11/4)) + 15*sqrt(d)*sqrt(d/b)*sqrt(c + d*x)*sin(2*a - 2*b*c/d)*cos(2*b*c/d + 2*b*x)*gamma(1/4)/(256*b**(3/2)*gamma(9/4)) + 63*sqrt(d)*sqrt(d/b)*sqrt(c + d*x)*sin(2*b*c/d + 2*b*x)*cos(2*a - 2*b*c/d)*gamma(3/4)/(256*b**(3/2)*gamma(11/4))","B",0
54,1,389,0,6.139070," ","integrate((d*x+c)**(1/2)*cos(b*x+a)*sin(b*x+a),x)","- \frac{b^{\frac{3}{2}} \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{5}{2}} \cos{\left(2 a - \frac{2 b c}{d} \right)} \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{b^{2} \left(c + d x\right)^{2}}{d^{2}}} \right)}}{4 d^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} - \frac{\sqrt{b} \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{3}{2}} \sin{\left(2 a - \frac{2 b c}{d} \right)} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{b^{2} \left(c + d x\right)^{2}}{d^{2}}} \right)}}{8 d^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{\pi} c \sqrt{\frac{d}{b}} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} + \frac{\sqrt{\pi} c \sqrt{\frac{d}{b}} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} + \frac{\sqrt{\pi} x \sqrt{\frac{d}{b}} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2} + \frac{\sqrt{\pi} x \sqrt{\frac{d}{b}} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2}"," ",0,"-b**(3/2)*sqrt(d/b)*(c + d*x)**(5/2)*cos(2*a - 2*b*c/d)*gamma(3/4)*gamma(5/4)*hyper((3/4, 5/4), (3/2, 7/4, 9/4), -b**2*(c + d*x)**2/d**2)/(4*d**(5/2)*gamma(7/4)*gamma(9/4)) - sqrt(b)*sqrt(d/b)*(c + d*x)**(3/2)*sin(2*a - 2*b*c/d)*gamma(1/4)*gamma(3/4)*hyper((1/4, 3/4), (1/2, 5/4, 7/4), -b**2*(c + d*x)**2/d**2)/(8*d**(3/2)*gamma(5/4)*gamma(7/4)) + sqrt(pi)*c*sqrt(d/b)*sin(2*a - 2*b*c/d)*fresnelc(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) + sqrt(pi)*c*sqrt(d/b)*cos(2*a - 2*b*c/d)*fresnels(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) + sqrt(pi)*x*sqrt(d/b)*sin(2*a - 2*b*c/d)*fresnelc(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/2 + sqrt(pi)*x*sqrt(d/b)*cos(2*a - 2*b*c/d)*fresnels(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/2","B",0
55,1,389,0,6.212840," ","integrate((d*x+c)**(1/2)*cos(b*x+a)*sin(b*x+a),x)","- \frac{b^{\frac{3}{2}} \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{5}{2}} \cos{\left(2 a - \frac{2 b c}{d} \right)} \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{b^{2} \left(c + d x\right)^{2}}{d^{2}}} \right)}}{4 d^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} - \frac{\sqrt{b} \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{3}{2}} \sin{\left(2 a - \frac{2 b c}{d} \right)} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{b^{2} \left(c + d x\right)^{2}}{d^{2}}} \right)}}{8 d^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{\pi} c \sqrt{\frac{d}{b}} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} + \frac{\sqrt{\pi} c \sqrt{\frac{d}{b}} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} + \frac{\sqrt{\pi} x \sqrt{\frac{d}{b}} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2} + \frac{\sqrt{\pi} x \sqrt{\frac{d}{b}} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2}"," ",0,"-b**(3/2)*sqrt(d/b)*(c + d*x)**(5/2)*cos(2*a - 2*b*c/d)*gamma(3/4)*gamma(5/4)*hyper((3/4, 5/4), (3/2, 7/4, 9/4), -b**2*(c + d*x)**2/d**2)/(4*d**(5/2)*gamma(7/4)*gamma(9/4)) - sqrt(b)*sqrt(d/b)*(c + d*x)**(3/2)*sin(2*a - 2*b*c/d)*gamma(1/4)*gamma(3/4)*hyper((1/4, 3/4), (1/2, 5/4, 7/4), -b**2*(c + d*x)**2/d**2)/(8*d**(3/2)*gamma(5/4)*gamma(7/4)) + sqrt(pi)*c*sqrt(d/b)*sin(2*a - 2*b*c/d)*fresnelc(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) + sqrt(pi)*c*sqrt(d/b)*cos(2*a - 2*b*c/d)*fresnels(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) + sqrt(pi)*x*sqrt(d/b)*sin(2*a - 2*b*c/d)*fresnelc(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/2 + sqrt(pi)*x*sqrt(d/b)*cos(2*a - 2*b*c/d)*fresnels(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/2","B",0
56,1,665,0,42.222262," ","integrate((d*x+c)**(3/2)*cos(b*x+a)*sin(b*x+a),x)","- \frac{5 \sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{1}{4}\right)}{32 d \Gamma\left(\frac{9}{4}\right)} + \frac{\sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} - \frac{21 \sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{3}{4}\right)}{32 d \Gamma\left(\frac{11}{4}\right)} + \frac{\sqrt{\pi} \sqrt{\frac{d}{b}} \left(c + d x\right)^{2} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 b \sqrt{c + d x}}{\sqrt{\pi} d \sqrt{\frac{b}{d}}}\right)}{2 d} - \frac{15 \sqrt{\pi} d \sqrt{\frac{d}{b}} \sin{\left(2 a - \frac{2 b c}{d} \right)} C\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{1}{4}\right)}{512 b^{2} \Gamma\left(\frac{9}{4}\right)} - \frac{63 \sqrt{\pi} d \sqrt{\frac{d}{b}} \cos{\left(2 a - \frac{2 b c}{d} \right)} S\left(\frac{2 \sqrt{b} \sqrt{c + d x}}{\sqrt{\pi} \sqrt{d}}\right) \Gamma\left(\frac{3}{4}\right)}{512 b^{2} \Gamma\left(\frac{11}{4}\right)} + \frac{5 \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{3}{2}} \sin{\left(2 a - \frac{2 b c}{d} \right)} \sin{\left(\frac{2 b c}{d} + 2 b x \right)} \Gamma\left(\frac{1}{4}\right)}{64 \sqrt{b} \sqrt{d} \Gamma\left(\frac{9}{4}\right)} - \frac{21 \sqrt{\frac{d}{b}} \left(c + d x\right)^{\frac{3}{2}} \cos{\left(2 a - \frac{2 b c}{d} \right)} \cos{\left(\frac{2 b c}{d} + 2 b x \right)} \Gamma\left(\frac{3}{4}\right)}{64 \sqrt{b} \sqrt{d} \Gamma\left(\frac{11}{4}\right)} + \frac{15 \sqrt{d} \sqrt{\frac{d}{b}} \sqrt{c + d x} \sin{\left(2 a - \frac{2 b c}{d} \right)} \cos{\left(\frac{2 b c}{d} + 2 b x \right)} \Gamma\left(\frac{1}{4}\right)}{256 b^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{63 \sqrt{d} \sqrt{\frac{d}{b}} \sqrt{c + d x} \sin{\left(\frac{2 b c}{d} + 2 b x \right)} \cos{\left(2 a - \frac{2 b c}{d} \right)} \Gamma\left(\frac{3}{4}\right)}{256 b^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"-5*sqrt(pi)*sqrt(d/b)*(c + d*x)**2*sin(2*a - 2*b*c/d)*fresnelc(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(1/4)/(32*d*gamma(9/4)) + sqrt(pi)*sqrt(d/b)*(c + d*x)**2*sin(2*a - 2*b*c/d)*fresnelc(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) - 21*sqrt(pi)*sqrt(d/b)*(c + d*x)**2*cos(2*a - 2*b*c/d)*fresnels(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(3/4)/(32*d*gamma(11/4)) + sqrt(pi)*sqrt(d/b)*(c + d*x)**2*cos(2*a - 2*b*c/d)*fresnels(2*b*sqrt(c + d*x)/(sqrt(pi)*d*sqrt(b/d)))/(2*d) - 15*sqrt(pi)*d*sqrt(d/b)*sin(2*a - 2*b*c/d)*fresnelc(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(1/4)/(512*b**2*gamma(9/4)) - 63*sqrt(pi)*d*sqrt(d/b)*cos(2*a - 2*b*c/d)*fresnels(2*sqrt(b)*sqrt(c + d*x)/(sqrt(pi)*sqrt(d)))*gamma(3/4)/(512*b**2*gamma(11/4)) + 5*sqrt(d/b)*(c + d*x)**(3/2)*sin(2*a - 2*b*c/d)*sin(2*b*c/d + 2*b*x)*gamma(1/4)/(64*sqrt(b)*sqrt(d)*gamma(9/4)) - 21*sqrt(d/b)*(c + d*x)**(3/2)*cos(2*a - 2*b*c/d)*cos(2*b*c/d + 2*b*x)*gamma(3/4)/(64*sqrt(b)*sqrt(d)*gamma(11/4)) + 15*sqrt(d)*sqrt(d/b)*sqrt(c + d*x)*sin(2*a - 2*b*c/d)*cos(2*b*c/d + 2*b*x)*gamma(1/4)/(256*b**(3/2)*gamma(9/4)) + 63*sqrt(d)*sqrt(d/b)*sqrt(c + d*x)*sin(2*b*c/d + 2*b*x)*cos(2*a - 2*b*c/d)*gamma(3/4)/(256*b**(3/2)*gamma(11/4))","B",0
57,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)**2*cos(a + b*x), x)","F",0
60,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2*cos(a + b*x), x)","F",0
61,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2*cos(a + b*x), x)","F",0
62,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)**2*cos(a + b*x), x)","F",0
63,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)*sin(b*x+a)**3,x)","\int \sqrt{c + d x} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**3*cos(a + b*x), x)","F",0
67,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)*sin(b*x+a)**3,x)","\int \sqrt{c + d x} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**3*cos(a + b*x), x)","F",0
68,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**2*sin(b*x+a),x)","\int \left(c + d x\right)^{m} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)*cos(a + b*x)**2, x)","F",0
71,1,646,0,7.187240," ","integrate((d*x+c)**4*cos(b*x+a)**2*sin(b*x+a),x)","\begin{cases} - \frac{c^{4} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{4 c^{3} d x \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c^{2} d^{2} x^{2} \cos^{3}{\left(a + b x \right)}}{b} - \frac{4 c d^{3} x^{3} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{d^{4} x^{4} \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{8 c^{3} d \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{4 c^{3} d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{8 c^{2} d^{2} x \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 c^{2} d^{2} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{8 c d^{3} x^{2} \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 c d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{8 d^{4} x^{3} \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{4 d^{4} x^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{8 c^{2} d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{28 c^{2} d^{2} \cos^{3}{\left(a + b x \right)}}{9 b^{3}} + \frac{16 c d^{3} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{56 c d^{3} x \cos^{3}{\left(a + b x \right)}}{9 b^{3}} + \frac{8 d^{4} x^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{28 d^{4} x^{2} \cos^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{160 c d^{3} \sin^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{56 c d^{3} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{4}} - \frac{160 d^{4} x \sin^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{56 d^{4} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{4}} - \frac{160 d^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{27 b^{5}} - \frac{488 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{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**4*cos(a + b*x)**3/(3*b) - 4*c**3*d*x*cos(a + b*x)**3/(3*b) - 2*c**2*d**2*x**2*cos(a + b*x)**3/b - 4*c*d**3*x**3*cos(a + b*x)**3/(3*b) - d**4*x**4*cos(a + b*x)**3/(3*b) + 8*c**3*d*sin(a + b*x)**3/(9*b**2) + 4*c**3*d*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 8*c**2*d**2*x*sin(a + b*x)**3/(3*b**2) + 4*c**2*d**2*x*sin(a + b*x)*cos(a + b*x)**2/b**2 + 8*c*d**3*x**2*sin(a + b*x)**3/(3*b**2) + 4*c*d**3*x**2*sin(a + b*x)*cos(a + b*x)**2/b**2 + 8*d**4*x**3*sin(a + b*x)**3/(9*b**2) + 4*d**4*x**3*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 8*c**2*d**2*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 28*c**2*d**2*cos(a + b*x)**3/(9*b**3) + 16*c*d**3*x*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 56*c*d**3*x*cos(a + b*x)**3/(9*b**3) + 8*d**4*x**2*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 28*d**4*x**2*cos(a + b*x)**3/(9*b**3) - 160*c*d**3*sin(a + b*x)**3/(27*b**4) - 56*c*d**3*sin(a + b*x)*cos(a + b*x)**2/(9*b**4) - 160*d**4*x*sin(a + b*x)**3/(27*b**4) - 56*d**4*x*sin(a + b*x)*cos(a + b*x)**2/(9*b**4) - 160*d**4*sin(a + b*x)**2*cos(a + b*x)/(27*b**5) - 488*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)*cos(a)**2, True))","A",0
72,1,391,0,3.950740," ","integrate((d*x+c)**3*cos(b*x+a)**2*sin(b*x+a),x)","\begin{cases} - \frac{c^{3} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{c^{2} d x \cos^{3}{\left(a + b x \right)}}{b} - \frac{c d^{2} x^{2} \cos^{3}{\left(a + b x \right)}}{b} - \frac{d^{3} x^{3} \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{2 c^{2} d \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{c^{2} d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{4 c d^{2} x \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 c d^{2} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{2 d^{3} x^{2} \sin^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b^{2}} + \frac{4 c d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{14 c d^{2} \cos^{3}{\left(a + b x \right)}}{9 b^{3}} + \frac{4 d^{3} x \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{3 b^{3}} + \frac{14 d^{3} x \cos^{3}{\left(a + b x \right)}}{9 b^{3}} - \frac{40 d^{3} \sin^{3}{\left(a + b x \right)}}{27 b^{4}} - \frac{14 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{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**3*cos(a + b*x)**3/(3*b) - c**2*d*x*cos(a + b*x)**3/b - c*d**2*x**2*cos(a + b*x)**3/b - d**3*x**3*cos(a + b*x)**3/(3*b) + 2*c**2*d*sin(a + b*x)**3/(3*b**2) + c**2*d*sin(a + b*x)*cos(a + b*x)**2/b**2 + 4*c*d**2*x*sin(a + b*x)**3/(3*b**2) + 2*c*d**2*x*sin(a + b*x)*cos(a + b*x)**2/b**2 + 2*d**3*x**2*sin(a + b*x)**3/(3*b**2) + d**3*x**2*sin(a + b*x)*cos(a + b*x)**2/b**2 + 4*c*d**2*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 14*c*d**2*cos(a + b*x)**3/(9*b**3) + 4*d**3*x*sin(a + b*x)**2*cos(a + b*x)/(3*b**3) + 14*d**3*x*cos(a + b*x)**3/(9*b**3) - 40*d**3*sin(a + b*x)**3/(27*b**4) - 14*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)*cos(a)**2, True))","A",0
73,1,216,0,2.033903," ","integrate((d*x+c)**2*cos(b*x+a)**2*sin(b*x+a),x)","\begin{cases} - \frac{c^{2} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c d x \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{d^{2} x^{2} \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{4 c d \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{2 c d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 d^{2} x \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{2 d^{2} x \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{2}} + \frac{4 d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{9 b^{3}} + \frac{14 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{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**2*cos(a + b*x)**3/(3*b) - 2*c*d*x*cos(a + b*x)**3/(3*b) - d**2*x**2*cos(a + b*x)**3/(3*b) + 4*c*d*sin(a + b*x)**3/(9*b**2) + 2*c*d*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 4*d**2*x*sin(a + b*x)**3/(9*b**2) + 2*d**2*x*sin(a + b*x)*cos(a + b*x)**2/(3*b**2) + 4*d**2*sin(a + b*x)**2*cos(a + b*x)/(9*b**3) + 14*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)*cos(a)**2, True))","A",0
74,1,85,0,0.866854," ","integrate((d*x+c)*cos(b*x+a)**2*sin(b*x+a),x)","\begin{cases} - \frac{c \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{d x \cos^{3}{\left(a + b x \right)}}{3 b} + \frac{2 d \sin^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{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{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*cos(a + b*x)**3/(3*b) - d*x*cos(a + b*x)**3/(3*b) + 2*d*sin(a + b*x)**3/(9*b**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)*cos(a)**2, True))","A",0
75,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)/(d*x+c),x)","\int \frac{\sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**2/(c + d*x), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)/(d*x+c)**2,x)","\int \frac{\sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**2/(c + d*x)**2, x)","F",0
77,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)/(d*x+c)**3,x)","\int \frac{\sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**2/(c + d*x)**3, x)","F",0
78,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)/(d*x+c)**4,x)","\int \frac{\sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**2/(c + d*x)**4, x)","F",0
79,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**2*sin(b*x+a)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
80,1,1231,0,13.618756," ","integrate((d*x+c)**4*cos(b*x+a)**2*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{4} x \sin^{4}{\left(a + b x \right)}}{8} + \frac{c^{4} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c^{4} x \cos^{4}{\left(a + b x \right)}}{8} + \frac{c^{3} d x^{2} \sin^{4}{\left(a + b x \right)}}{4} + \frac{c^{3} d x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{2} + \frac{c^{3} d x^{2} \cos^{4}{\left(a + b x \right)}}{4} + \frac{c^{2} d^{2} x^{3} \sin^{4}{\left(a + b x \right)}}{4} + \frac{c^{2} d^{2} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{2} + \frac{c^{2} d^{2} x^{3} \cos^{4}{\left(a + b x \right)}}{4} + \frac{c d^{3} x^{4} \sin^{4}{\left(a + b x \right)}}{8} + \frac{c d^{3} x^{4} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c d^{3} x^{4} \cos^{4}{\left(a + b x \right)}}{8} + \frac{d^{4} x^{5} \sin^{4}{\left(a + b x \right)}}{40} + \frac{d^{4} x^{5} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{20} + \frac{d^{4} x^{5} \cos^{4}{\left(a + b x \right)}}{40} + \frac{c^{4} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{c^{4} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} + \frac{c^{3} d x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{c^{3} d x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{2 b} + \frac{3 c^{2} d^{2} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b} - \frac{3 c^{2} d^{2} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{4 b} + \frac{c d^{3} x^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{c d^{3} x^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{2 b} + \frac{d^{4} x^{4} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{d^{4} x^{4} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{c^{3} d \sin^{4}{\left(a + b x \right)}}{8 b^{2}} - \frac{c^{3} d \cos^{4}{\left(a + b x \right)}}{8 b^{2}} - \frac{3 c^{2} d^{2} x \sin^{4}{\left(a + b x \right)}}{32 b^{2}} + \frac{9 c^{2} d^{2} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b^{2}} - \frac{3 c^{2} d^{2} x \cos^{4}{\left(a + b x \right)}}{32 b^{2}} - \frac{3 c d^{3} x^{2} \sin^{4}{\left(a + b x \right)}}{32 b^{2}} + \frac{9 c d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b^{2}} - \frac{3 c d^{3} x^{2} \cos^{4}{\left(a + b x \right)}}{32 b^{2}} - \frac{d^{4} x^{3} \sin^{4}{\left(a + b x \right)}}{32 b^{2}} + \frac{3 d^{4} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b^{2}} - \frac{d^{4} x^{3} \cos^{4}{\left(a + b x \right)}}{32 b^{2}} - \frac{3 c^{2} d^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{3}} + \frac{3 c^{2} d^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{3}} - \frac{3 c d^{3} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{3}} + \frac{3 c d^{3} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{3}} - \frac{3 d^{4} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{3}} + \frac{3 d^{4} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{3}} + \frac{3 c d^{3} \sin^{4}{\left(a + b x \right)}}{64 b^{4}} + \frac{3 c d^{3} \cos^{4}{\left(a + b x \right)}}{64 b^{4}} + \frac{3 d^{4} x \sin^{4}{\left(a + b x \right)}}{256 b^{4}} - \frac{9 d^{4} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{128 b^{4}} + \frac{3 d^{4} x \cos^{4}{\left(a + b x \right)}}{256 b^{4}} + \frac{3 d^{4} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{256 b^{5}} - \frac{3 d^{4} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{256 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)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x*sin(a + b*x)**4/8 + c**4*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + c**4*x*cos(a + b*x)**4/8 + c**3*d*x**2*sin(a + b*x)**4/4 + c**3*d*x**2*sin(a + b*x)**2*cos(a + b*x)**2/2 + c**3*d*x**2*cos(a + b*x)**4/4 + c**2*d**2*x**3*sin(a + b*x)**4/4 + c**2*d**2*x**3*sin(a + b*x)**2*cos(a + b*x)**2/2 + c**2*d**2*x**3*cos(a + b*x)**4/4 + c*d**3*x**4*sin(a + b*x)**4/8 + c*d**3*x**4*sin(a + b*x)**2*cos(a + b*x)**2/4 + c*d**3*x**4*cos(a + b*x)**4/8 + d**4*x**5*sin(a + b*x)**4/40 + d**4*x**5*sin(a + b*x)**2*cos(a + b*x)**2/20 + d**4*x**5*cos(a + b*x)**4/40 + c**4*sin(a + b*x)**3*cos(a + b*x)/(8*b) - c**4*sin(a + b*x)*cos(a + b*x)**3/(8*b) + c**3*d*x*sin(a + b*x)**3*cos(a + b*x)/(2*b) - c**3*d*x*sin(a + b*x)*cos(a + b*x)**3/(2*b) + 3*c**2*d**2*x**2*sin(a + b*x)**3*cos(a + b*x)/(4*b) - 3*c**2*d**2*x**2*sin(a + b*x)*cos(a + b*x)**3/(4*b) + c*d**3*x**3*sin(a + b*x)**3*cos(a + b*x)/(2*b) - c*d**3*x**3*sin(a + b*x)*cos(a + b*x)**3/(2*b) + d**4*x**4*sin(a + b*x)**3*cos(a + b*x)/(8*b) - d**4*x**4*sin(a + b*x)*cos(a + b*x)**3/(8*b) - c**3*d*sin(a + b*x)**4/(8*b**2) - c**3*d*cos(a + b*x)**4/(8*b**2) - 3*c**2*d**2*x*sin(a + b*x)**4/(32*b**2) + 9*c**2*d**2*x*sin(a + b*x)**2*cos(a + b*x)**2/(16*b**2) - 3*c**2*d**2*x*cos(a + b*x)**4/(32*b**2) - 3*c*d**3*x**2*sin(a + b*x)**4/(32*b**2) + 9*c*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(16*b**2) - 3*c*d**3*x**2*cos(a + b*x)**4/(32*b**2) - d**4*x**3*sin(a + b*x)**4/(32*b**2) + 3*d**4*x**3*sin(a + b*x)**2*cos(a + b*x)**2/(16*b**2) - d**4*x**3*cos(a + b*x)**4/(32*b**2) - 3*c**2*d**2*sin(a + b*x)**3*cos(a + b*x)/(32*b**3) + 3*c**2*d**2*sin(a + b*x)*cos(a + b*x)**3/(32*b**3) - 3*c*d**3*x*sin(a + b*x)**3*cos(a + b*x)/(16*b**3) + 3*c*d**3*x*sin(a + b*x)*cos(a + b*x)**3/(16*b**3) - 3*d**4*x**2*sin(a + b*x)**3*cos(a + b*x)/(32*b**3) + 3*d**4*x**2*sin(a + b*x)*cos(a + b*x)**3/(32*b**3) + 3*c*d**3*sin(a + b*x)**4/(64*b**4) + 3*c*d**3*cos(a + b*x)**4/(64*b**4) + 3*d**4*x*sin(a + b*x)**4/(256*b**4) - 9*d**4*x*sin(a + b*x)**2*cos(a + b*x)**2/(128*b**4) + 3*d**4*x*cos(a + b*x)**4/(256*b**4) + 3*d**4*sin(a + b*x)**3*cos(a + b*x)/(256*b**5) - 3*d**4*sin(a + b*x)*cos(a + b*x)**3/(256*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*cos(a)**2, True))","A",0
81,1,835,0,7.943460," ","integrate((d*x+c)**3*cos(b*x+a)**2*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{3} x \sin^{4}{\left(a + b x \right)}}{8} + \frac{c^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c^{3} x \cos^{4}{\left(a + b x \right)}}{8} + \frac{3 c^{2} d x^{2} \sin^{4}{\left(a + b x \right)}}{16} + \frac{3 c^{2} d x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8} + \frac{3 c^{2} d x^{2} \cos^{4}{\left(a + b x \right)}}{16} + \frac{c d^{2} x^{3} \sin^{4}{\left(a + b x \right)}}{8} + \frac{c d^{2} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c d^{2} x^{3} \cos^{4}{\left(a + b x \right)}}{8} + \frac{d^{3} x^{4} \sin^{4}{\left(a + b x \right)}}{32} + \frac{d^{3} x^{4} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{d^{3} x^{4} \cos^{4}{\left(a + b x \right)}}{32} + \frac{c^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{c^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} + \frac{3 c^{2} d x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{3 c^{2} d x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} + \frac{3 c d^{2} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{3 c d^{2} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} + \frac{d^{3} x^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{d^{3} x^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{3 c^{2} d \sin^{4}{\left(a + b x \right)}}{32 b^{2}} - \frac{3 c^{2} d \cos^{4}{\left(a + b x \right)}}{32 b^{2}} - \frac{3 c d^{2} x \sin^{4}{\left(a + b x \right)}}{64 b^{2}} + \frac{9 c d^{2} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32 b^{2}} - \frac{3 c d^{2} x \cos^{4}{\left(a + b x \right)}}{64 b^{2}} - \frac{3 d^{3} x^{2} \sin^{4}{\left(a + b x \right)}}{128 b^{2}} + \frac{9 d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{64 b^{2}} - \frac{3 d^{3} x^{2} \cos^{4}{\left(a + b x \right)}}{128 b^{2}} - \frac{3 c d^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{3}} + \frac{3 c d^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{3}} - \frac{3 d^{3} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{3}} + \frac{3 d^{3} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{3}} + \frac{3 d^{3} \sin^{4}{\left(a + b x \right)}}{256 b^{4}} + \frac{3 d^{3} \cos^{4}{\left(a + b x \right)}}{256 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)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*x*sin(a + b*x)**4/8 + c**3*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + c**3*x*cos(a + b*x)**4/8 + 3*c**2*d*x**2*sin(a + b*x)**4/16 + 3*c**2*d*x**2*sin(a + b*x)**2*cos(a + b*x)**2/8 + 3*c**2*d*x**2*cos(a + b*x)**4/16 + c*d**2*x**3*sin(a + b*x)**4/8 + c*d**2*x**3*sin(a + b*x)**2*cos(a + b*x)**2/4 + c*d**2*x**3*cos(a + b*x)**4/8 + d**3*x**4*sin(a + b*x)**4/32 + d**3*x**4*sin(a + b*x)**2*cos(a + b*x)**2/16 + d**3*x**4*cos(a + b*x)**4/32 + c**3*sin(a + b*x)**3*cos(a + b*x)/(8*b) - c**3*sin(a + b*x)*cos(a + b*x)**3/(8*b) + 3*c**2*d*x*sin(a + b*x)**3*cos(a + b*x)/(8*b) - 3*c**2*d*x*sin(a + b*x)*cos(a + b*x)**3/(8*b) + 3*c*d**2*x**2*sin(a + b*x)**3*cos(a + b*x)/(8*b) - 3*c*d**2*x**2*sin(a + b*x)*cos(a + b*x)**3/(8*b) + d**3*x**3*sin(a + b*x)**3*cos(a + b*x)/(8*b) - d**3*x**3*sin(a + b*x)*cos(a + b*x)**3/(8*b) - 3*c**2*d*sin(a + b*x)**4/(32*b**2) - 3*c**2*d*cos(a + b*x)**4/(32*b**2) - 3*c*d**2*x*sin(a + b*x)**4/(64*b**2) + 9*c*d**2*x*sin(a + b*x)**2*cos(a + b*x)**2/(32*b**2) - 3*c*d**2*x*cos(a + b*x)**4/(64*b**2) - 3*d**3*x**2*sin(a + b*x)**4/(128*b**2) + 9*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(64*b**2) - 3*d**3*x**2*cos(a + b*x)**4/(128*b**2) - 3*c*d**2*sin(a + b*x)**3*cos(a + b*x)/(64*b**3) + 3*c*d**2*sin(a + b*x)*cos(a + b*x)**3/(64*b**3) - 3*d**3*x*sin(a + b*x)**3*cos(a + b*x)/(64*b**3) + 3*d**3*x*sin(a + b*x)*cos(a + b*x)**3/(64*b**3) + 3*d**3*sin(a + b*x)**4/(256*b**4) + 3*d**3*cos(a + b*x)**4/(256*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*cos(a)**2, True))","A",0
82,1,493,0,3.977852," ","integrate((d*x+c)**2*cos(b*x+a)**2*sin(b*x+a)**2,x)","\begin{cases} \frac{c^{2} x \sin^{4}{\left(a + b x \right)}}{8} + \frac{c^{2} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c^{2} x \cos^{4}{\left(a + b x \right)}}{8} + \frac{c d x^{2} \sin^{4}{\left(a + b x \right)}}{8} + \frac{c d x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c d x^{2} \cos^{4}{\left(a + b x \right)}}{8} + \frac{d^{2} x^{3} \sin^{4}{\left(a + b x \right)}}{24} + \frac{d^{2} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{12} + \frac{d^{2} x^{3} \cos^{4}{\left(a + b x \right)}}{24} + \frac{c^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{c^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} + \frac{c d x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b} - \frac{c d x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{4 b} + \frac{d^{2} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{d^{2} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{c d \sin^{4}{\left(a + b x \right)}}{16 b^{2}} - \frac{c d \cos^{4}{\left(a + b x \right)}}{16 b^{2}} - \frac{d^{2} x \sin^{4}{\left(a + b x \right)}}{64 b^{2}} + \frac{3 d^{2} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32 b^{2}} - \frac{d^{2} x \cos^{4}{\left(a + b x \right)}}{64 b^{2}} - \frac{d^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{3}} + \frac{d^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 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)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*x*sin(a + b*x)**4/8 + c**2*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + c**2*x*cos(a + b*x)**4/8 + c*d*x**2*sin(a + b*x)**4/8 + c*d*x**2*sin(a + b*x)**2*cos(a + b*x)**2/4 + c*d*x**2*cos(a + b*x)**4/8 + d**2*x**3*sin(a + b*x)**4/24 + d**2*x**3*sin(a + b*x)**2*cos(a + b*x)**2/12 + d**2*x**3*cos(a + b*x)**4/24 + c**2*sin(a + b*x)**3*cos(a + b*x)/(8*b) - c**2*sin(a + b*x)*cos(a + b*x)**3/(8*b) + c*d*x*sin(a + b*x)**3*cos(a + b*x)/(4*b) - c*d*x*sin(a + b*x)*cos(a + b*x)**3/(4*b) + d**2*x**2*sin(a + b*x)**3*cos(a + b*x)/(8*b) - d**2*x**2*sin(a + b*x)*cos(a + b*x)**3/(8*b) - c*d*sin(a + b*x)**4/(16*b**2) - c*d*cos(a + b*x)**4/(16*b**2) - d**2*x*sin(a + b*x)**4/(64*b**2) + 3*d**2*x*sin(a + b*x)**2*cos(a + b*x)**2/(32*b**2) - d**2*x*cos(a + b*x)**4/(64*b**2) - d**2*sin(a + b*x)**3*cos(a + b*x)/(64*b**3) + d**2*sin(a + b*x)*cos(a + b*x)**3/(64*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**2*cos(a)**2, True))","A",0
83,1,238,0,1.998265," ","integrate((d*x+c)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\begin{cases} \frac{c x \sin^{4}{\left(a + b x \right)}}{8} + \frac{c x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{c x \cos^{4}{\left(a + b x \right)}}{8} + \frac{d x^{2} \sin^{4}{\left(a + b x \right)}}{16} + \frac{d x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8} + \frac{d x^{2} \cos^{4}{\left(a + b x \right)}}{16} + \frac{c \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{c \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} + \frac{d x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{d x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{d \sin^{4}{\left(a + b x \right)}}{32 b^{2}} - \frac{d \cos^{4}{\left(a + b x \right)}}{32 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x*sin(a + b*x)**4/8 + c*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + c*x*cos(a + b*x)**4/8 + d*x**2*sin(a + b*x)**4/16 + d*x**2*sin(a + b*x)**2*cos(a + b*x)**2/8 + d*x**2*cos(a + b*x)**4/16 + c*sin(a + b*x)**3*cos(a + b*x)/(8*b) - c*sin(a + b*x)*cos(a + b*x)**3/(8*b) + d*x*sin(a + b*x)**3*cos(a + b*x)/(8*b) - d*x*sin(a + b*x)*cos(a + b*x)**3/(8*b) - d*sin(a + b*x)**4/(32*b**2) - d*cos(a + b*x)**4/(32*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**2*cos(a)**2, True))","A",0
84,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**2/(d*x+c),x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**2/(c + d*x), x)","F",0
85,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**2/(c + d*x)**2, x)","F",0
86,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**2/(d*x+c)**3,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**2/(c + d*x)**3, x)","F",0
87,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**2/(d*x+c)**4,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**2/(c + d*x)**4, x)","F",0
88,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**2*sin(b*x+a)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
89,1,1098,0,20.155898," ","integrate((d*x+c)**4*cos(b*x+a)**2*sin(b*x+a)**3,x)","\begin{cases} - \frac{c^{4} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c^{4} \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{4 c^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{8 c^{3} d x \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{2 c^{2} d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{b} - \frac{4 c^{2} d^{2} x^{2} \cos^{5}{\left(a + b x \right)}}{5 b} - \frac{4 c d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{8 c d^{3} x^{3} \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{d^{4} x^{4} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 d^{4} x^{4} \cos^{5}{\left(a + b x \right)}}{15 b} + \frac{104 c^{3} d \sin^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{52 c^{3} d \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{45 b^{2}} + \frac{8 c^{3} d \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{15 b^{2}} + \frac{104 c^{2} d^{2} x \sin^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{52 c^{2} d^{2} x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{15 b^{2}} + \frac{8 c^{2} d^{2} x \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b^{2}} + \frac{104 c d^{3} x^{2} \sin^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{52 c d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{15 b^{2}} + \frac{8 c d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b^{2}} + \frac{104 d^{4} x^{3} \sin^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{52 d^{4} x^{3} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{45 b^{2}} + \frac{8 d^{4} x^{3} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{15 b^{2}} + \frac{104 c^{2} d^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{75 b^{3}} + \frac{676 c^{2} d^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{225 b^{3}} + \frac{1712 c^{2} d^{2} \cos^{5}{\left(a + b x \right)}}{1125 b^{3}} + \frac{208 c d^{3} x \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{75 b^{3}} + \frac{1352 c d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{225 b^{3}} + \frac{3424 c d^{3} x \cos^{5}{\left(a + b x \right)}}{1125 b^{3}} + \frac{104 d^{4} x^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{75 b^{3}} + \frac{676 d^{4} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{225 b^{3}} + \frac{1712 d^{4} x^{2} \cos^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{50272 c d^{3} \sin^{5}{\left(a + b x \right)}}{16875 b^{4}} - \frac{20456 c d^{3} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3375 b^{4}} - \frac{3424 c d^{3} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{1125 b^{4}} - \frac{50272 d^{4} x \sin^{5}{\left(a + b x \right)}}{16875 b^{4}} - \frac{20456 d^{4} x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3375 b^{4}} - \frac{3424 d^{4} x \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{1125 b^{4}} - \frac{50272 d^{4} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16875 b^{5}} - \frac{303368 d^{4} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{50625 b^{5}} - \frac{760816 d^{4} \cos^{5}{\left(a + b x \right)}}{253125 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)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**4*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*c**4*cos(a + b*x)**5/(15*b) - 4*c**3*d*x*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 8*c**3*d*x*cos(a + b*x)**5/(15*b) - 2*c**2*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**3/b - 4*c**2*d**2*x**2*cos(a + b*x)**5/(5*b) - 4*c*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 8*c*d**3*x**3*cos(a + b*x)**5/(15*b) - d**4*x**4*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*d**4*x**4*cos(a + b*x)**5/(15*b) + 104*c**3*d*sin(a + b*x)**5/(225*b**2) + 52*c**3*d*sin(a + b*x)**3*cos(a + b*x)**2/(45*b**2) + 8*c**3*d*sin(a + b*x)*cos(a + b*x)**4/(15*b**2) + 104*c**2*d**2*x*sin(a + b*x)**5/(75*b**2) + 52*c**2*d**2*x*sin(a + b*x)**3*cos(a + b*x)**2/(15*b**2) + 8*c**2*d**2*x*sin(a + b*x)*cos(a + b*x)**4/(5*b**2) + 104*c*d**3*x**2*sin(a + b*x)**5/(75*b**2) + 52*c*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)**2/(15*b**2) + 8*c*d**3*x**2*sin(a + b*x)*cos(a + b*x)**4/(5*b**2) + 104*d**4*x**3*sin(a + b*x)**5/(225*b**2) + 52*d**4*x**3*sin(a + b*x)**3*cos(a + b*x)**2/(45*b**2) + 8*d**4*x**3*sin(a + b*x)*cos(a + b*x)**4/(15*b**2) + 104*c**2*d**2*sin(a + b*x)**4*cos(a + b*x)/(75*b**3) + 676*c**2*d**2*sin(a + b*x)**2*cos(a + b*x)**3/(225*b**3) + 1712*c**2*d**2*cos(a + b*x)**5/(1125*b**3) + 208*c*d**3*x*sin(a + b*x)**4*cos(a + b*x)/(75*b**3) + 1352*c*d**3*x*sin(a + b*x)**2*cos(a + b*x)**3/(225*b**3) + 3424*c*d**3*x*cos(a + b*x)**5/(1125*b**3) + 104*d**4*x**2*sin(a + b*x)**4*cos(a + b*x)/(75*b**3) + 676*d**4*x**2*sin(a + b*x)**2*cos(a + b*x)**3/(225*b**3) + 1712*d**4*x**2*cos(a + b*x)**5/(1125*b**3) - 50272*c*d**3*sin(a + b*x)**5/(16875*b**4) - 20456*c*d**3*sin(a + b*x)**3*cos(a + b*x)**2/(3375*b**4) - 3424*c*d**3*sin(a + b*x)*cos(a + b*x)**4/(1125*b**4) - 50272*d**4*x*sin(a + b*x)**5/(16875*b**4) - 20456*d**4*x*sin(a + b*x)**3*cos(a + b*x)**2/(3375*b**4) - 3424*d**4*x*sin(a + b*x)*cos(a + b*x)**4/(1125*b**4) - 50272*d**4*sin(a + b*x)**4*cos(a + b*x)/(16875*b**5) - 303368*d**4*sin(a + b*x)**2*cos(a + b*x)**3/(50625*b**5) - 760816*d**4*cos(a + b*x)**5/(253125*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*cos(a)**2, True))","A",0
90,1,690,0,11.140464," ","integrate((d*x+c)**3*cos(b*x+a)**2*sin(b*x+a)**3,x)","\begin{cases} - \frac{c^{3} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c^{3} \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{c^{2} d x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{b} - \frac{2 c^{2} d x \cos^{5}{\left(a + b x \right)}}{5 b} - \frac{c d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{b} - \frac{2 c d^{2} x^{2} \cos^{5}{\left(a + b x \right)}}{5 b} - \frac{d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 d^{3} x^{3} \cos^{5}{\left(a + b x \right)}}{15 b} + \frac{26 c^{2} d \sin^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{13 c^{2} d \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{15 b^{2}} + \frac{2 c^{2} d \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b^{2}} + \frac{52 c d^{2} x \sin^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{26 c d^{2} x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{15 b^{2}} + \frac{4 c d^{2} x \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b^{2}} + \frac{26 d^{3} x^{2} \sin^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{13 d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{15 b^{2}} + \frac{2 d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b^{2}} + \frac{52 c d^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{75 b^{3}} + \frac{338 c d^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{225 b^{3}} + \frac{856 c d^{2} \cos^{5}{\left(a + b x \right)}}{1125 b^{3}} + \frac{52 d^{3} x \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{75 b^{3}} + \frac{338 d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{225 b^{3}} + \frac{856 d^{3} x \cos^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{12568 d^{3} \sin^{5}{\left(a + b x \right)}}{16875 b^{4}} - \frac{5114 d^{3} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3375 b^{4}} - \frac{856 d^{3} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{1125 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)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**3*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*c**3*cos(a + b*x)**5/(15*b) - c**2*d*x*sin(a + b*x)**2*cos(a + b*x)**3/b - 2*c**2*d*x*cos(a + b*x)**5/(5*b) - c*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**3/b - 2*c*d**2*x**2*cos(a + b*x)**5/(5*b) - d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*d**3*x**3*cos(a + b*x)**5/(15*b) + 26*c**2*d*sin(a + b*x)**5/(75*b**2) + 13*c**2*d*sin(a + b*x)**3*cos(a + b*x)**2/(15*b**2) + 2*c**2*d*sin(a + b*x)*cos(a + b*x)**4/(5*b**2) + 52*c*d**2*x*sin(a + b*x)**5/(75*b**2) + 26*c*d**2*x*sin(a + b*x)**3*cos(a + b*x)**2/(15*b**2) + 4*c*d**2*x*sin(a + b*x)*cos(a + b*x)**4/(5*b**2) + 26*d**3*x**2*sin(a + b*x)**5/(75*b**2) + 13*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)**2/(15*b**2) + 2*d**3*x**2*sin(a + b*x)*cos(a + b*x)**4/(5*b**2) + 52*c*d**2*sin(a + b*x)**4*cos(a + b*x)/(75*b**3) + 338*c*d**2*sin(a + b*x)**2*cos(a + b*x)**3/(225*b**3) + 856*c*d**2*cos(a + b*x)**5/(1125*b**3) + 52*d**3*x*sin(a + b*x)**4*cos(a + b*x)/(75*b**3) + 338*d**3*x*sin(a + b*x)**2*cos(a + b*x)**3/(225*b**3) + 856*d**3*x*cos(a + b*x)**5/(1125*b**3) - 12568*d**3*sin(a + b*x)**5/(16875*b**4) - 5114*d**3*sin(a + b*x)**3*cos(a + b*x)**2/(3375*b**4) - 856*d**3*sin(a + b*x)*cos(a + b*x)**4/(1125*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*cos(a)**2, True))","A",0
91,1,382,0,5.958915," ","integrate((d*x+c)**2*cos(b*x+a)**2*sin(b*x+a)**3,x)","\begin{cases} - \frac{c^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c^{2} \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{2 c d x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{4 c d x \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 d^{2} x^{2} \cos^{5}{\left(a + b x \right)}}{15 b} + \frac{52 c d \sin^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{26 c d \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{45 b^{2}} + \frac{4 c d \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{15 b^{2}} + \frac{52 d^{2} x \sin^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{26 d^{2} x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{45 b^{2}} + \frac{4 d^{2} x \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{15 b^{2}} + \frac{52 d^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{225 b^{3}} + \frac{338 d^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{675 b^{3}} + \frac{856 d^{2} \cos^{5}{\left(a + b x \right)}}{3375 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)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**2*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*c**2*cos(a + b*x)**5/(15*b) - 2*c*d*x*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 4*c*d*x*cos(a + b*x)**5/(15*b) - d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*d**2*x**2*cos(a + b*x)**5/(15*b) + 52*c*d*sin(a + b*x)**5/(225*b**2) + 26*c*d*sin(a + b*x)**3*cos(a + b*x)**2/(45*b**2) + 4*c*d*sin(a + b*x)*cos(a + b*x)**4/(15*b**2) + 52*d**2*x*sin(a + b*x)**5/(225*b**2) + 26*d**2*x*sin(a + b*x)**3*cos(a + b*x)**2/(45*b**2) + 4*d**2*x*sin(a + b*x)*cos(a + b*x)**4/(15*b**2) + 52*d**2*sin(a + b*x)**4*cos(a + b*x)/(225*b**3) + 338*d**2*sin(a + b*x)**2*cos(a + b*x)**3/(675*b**3) + 856*d**2*cos(a + b*x)**5/(3375*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**3*cos(a)**2, True))","A",0
92,1,163,0,3.051226," ","integrate((d*x+c)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\begin{cases} - \frac{c \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 c \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{d x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 d x \cos^{5}{\left(a + b x \right)}}{15 b} + \frac{26 d \sin^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{13 d \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{45 b^{2}} + \frac{2 d \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{15 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{3}{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*c*cos(a + b*x)**5/(15*b) - d*x*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*d*x*cos(a + b*x)**5/(15*b) + 26*d*sin(a + b*x)**5/(225*b**2) + 13*d*sin(a + b*x)**3*cos(a + b*x)**2/(45*b**2) + 2*d*sin(a + b*x)*cos(a + b*x)**4/(15*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**3*cos(a)**2, True))","A",0
93,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**3/(d*x+c),x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)**2/(c + d*x), x)","F",0
94,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)**2/(c + d*x)**2, x)","F",0
95,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**3/(d*x+c)**3,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)**2/(c + d*x)**3, x)","F",0
96,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**3/(d*x+c)**4,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)**2/(c + d*x)**4, x)","F",0
97,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*cot(b*x+a),x)","\int \left(c + d x\right)^{m} \cos{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)*cot(a + b*x), x)","F",0
98,0,0,0,0.000000," ","integrate((d*x+c)**4*cos(b*x+a)*cot(b*x+a),x)","\int \left(c + d x\right)^{4} \cos{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cos(a + b*x)*cot(a + b*x), x)","F",0
99,0,0,0,0.000000," ","integrate((d*x+c)**3*cos(b*x+a)*cot(b*x+a),x)","\int \left(c + d x\right)^{3} \cos{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cos(a + b*x)*cot(a + b*x), x)","F",0
100,0,0,0,0.000000," ","integrate((d*x+c)**2*cos(b*x+a)*cot(b*x+a),x)","\int \left(c + d x\right)^{2} \cos{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cos(a + b*x)*cot(a + b*x), x)","F",0
101,0,0,0,0.000000," ","integrate((d*x+c)*cos(b*x+a)*cot(b*x+a),x)","\int \left(c + d x\right) \cos{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cos(a + b*x)*cot(a + b*x), x)","F",0
102,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)/(d*x+c),x)","\int \frac{\cos{\left(a + b x \right)} \cot{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)*cot(a + b*x)/(c + d*x), x)","F",0
103,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)/(d*x+c)**2,x)","\int \frac{\cos{\left(a + b x \right)} \cot{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)*cot(a + b*x)/(c + d*x)**2, x)","F",0
104,0,0,0,0.000000," ","integrate((d*x+c)**m*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cot(a + b*x)**2, x)","F",0
105,0,0,0,0.000000," ","integrate((d*x+c)**4*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{4} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cot(a + b*x)**2, x)","F",0
106,0,0,0,0.000000," ","integrate((d*x+c)**3*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cot(a + b*x)**2, x)","F",0
107,0,0,0,0.000000," ","integrate((d*x+c)**2*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cot(a + b*x)**2, x)","F",0
108,1,104,0,0.480114," ","integrate((d*x+c)*cot(b*x+a)**2,x)","\begin{cases} \tilde{\infty} \left(c x + \frac{d x^{2}}{2}\right) & \text{for}\: a = 0 \wedge b = 0 \\\left(c x + \frac{d x^{2}}{2}\right) \cot^{2}{\left(a \right)} & \text{for}\: b = 0 \\\tilde{\infty} \left(c x + \frac{d x^{2}}{2}\right) & \text{for}\: a = - b x \\- c x - \frac{d x^{2}}{2} - \frac{c}{b \tan{\left(a + b x \right)}} - \frac{d x}{b \tan{\left(a + b x \right)}} - \frac{d \log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b^{2}} + \frac{d \log{\left(\tan{\left(a + b x \right)} \right)}}{b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(c*x + d*x**2/2), Eq(a, 0) & Eq(b, 0)), ((c*x + d*x**2/2)*cot(a)**2, Eq(b, 0)), (zoo*(c*x + d*x**2/2), Eq(a, -b*x)), (-c*x - d*x**2/2 - c/(b*tan(a + b*x)) - d*x/(b*tan(a + b*x)) - d*log(tan(a + b*x)**2 + 1)/(2*b**2) + d*log(tan(a + b*x))/b**2, True))","A",0
109,0,0,0,0.000000," ","integrate(cot(b*x+a)**2/(d*x+c),x)","\int \frac{\cot^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cot(a + b*x)**2/(c + d*x), x)","F",0
110,0,0,0,0.000000," ","integrate(cot(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\cot^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cot(a + b*x)**2/(c + d*x)**2, x)","F",0
111,0,0,0,0.000000," ","integrate((d*x+c)**m*cot(b*x+a)**2*csc(b*x+a),x)","\int \left(c + d x\right)^{m} \cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cot(a + b*x)**2*csc(a + b*x), x)","F",0
112,0,0,0,0.000000," ","integrate((d*x+c)**4*cot(b*x+a)**2*csc(b*x+a),x)","\int \left(c + d x\right)^{4} \cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cot(a + b*x)**2*csc(a + b*x), x)","F",0
113,0,0,0,0.000000," ","integrate((d*x+c)**3*cot(b*x+a)**2*csc(b*x+a),x)","\int \left(c + d x\right)^{3} \cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cot(a + b*x)**2*csc(a + b*x), x)","F",0
114,0,0,0,0.000000," ","integrate((d*x+c)**2*cot(b*x+a)**2*csc(b*x+a),x)","\int \left(c + d x\right)^{2} \cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cot(a + b*x)**2*csc(a + b*x), x)","F",0
115,0,0,0,0.000000," ","integrate((d*x+c)*cot(b*x+a)**2*csc(b*x+a),x)","\int \left(c + d x\right) \cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cot(a + b*x)**2*csc(a + b*x), x)","F",0
116,0,0,0,0.000000," ","integrate(cot(b*x+a)**2*csc(b*x+a)/(d*x+c),x)","\int \frac{\cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cot(a + b*x)**2*csc(a + b*x)/(c + d*x), x)","F",0
117,0,0,0,0.000000," ","integrate(cot(b*x+a)**2*csc(b*x+a)/(d*x+c)**2,x)","\int \frac{\cot^{2}{\left(a + b x \right)} \csc{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cot(a + b*x)**2*csc(a + b*x)/(c + d*x)**2, x)","F",0
118,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2*sin(b*x+a),x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)*cos(a + b*x)**2, x)","F",0
120,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2*sin(b*x+a),x)","\int \sqrt{c + d x} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)*cos(a + b*x)**2, x)","F",0
121,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2*sin(b*x+a),x)","\int \sqrt{c + d x} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)*cos(a + b*x)**2, x)","F",0
122,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2*sin(b*x+a),x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)*cos(a + b*x)**2, x)","F",0
123,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)**2*cos(a + b*x)**2, x)","F",0
126,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2*cos(a + b*x)**2, x)","F",0
127,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2*cos(a + b*x)**2, x)","F",0
128,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{\frac{3}{2}} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**(3/2)*sin(a + b*x)**2*cos(a + b*x)**2, x)","F",0
129,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\int \sqrt{c + d x} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**3*cos(a + b*x)**2, x)","F",0
133,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\int \sqrt{c + d x} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**3*cos(a + b*x)**2, x)","F",0
134,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**2*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**3*sin(b*x+a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
137,1,935,0,13.230219," ","integrate((d*x+c)**4*cos(b*x+a)**3*sin(b*x+a),x)","\begin{cases} - \frac{c^{4} \cos^{4}{\left(a + b x \right)}}{4 b} + \frac{3 c^{3} d x \sin^{4}{\left(a + b x \right)}}{8 b} + \frac{3 c^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} - \frac{5 c^{3} d x \cos^{4}{\left(a + b x \right)}}{8 b} + \frac{9 c^{2} d^{2} x^{2} \sin^{4}{\left(a + b x \right)}}{16 b} + \frac{9 c^{2} d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{15 c^{2} d^{2} x^{2} \cos^{4}{\left(a + b x \right)}}{16 b} + \frac{3 c d^{3} x^{3} \sin^{4}{\left(a + b x \right)}}{8 b} + \frac{3 c d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} - \frac{5 c d^{3} x^{3} \cos^{4}{\left(a + b x \right)}}{8 b} + \frac{3 d^{4} x^{4} \sin^{4}{\left(a + b x \right)}}{32 b} + \frac{3 d^{4} x^{4} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{5 d^{4} x^{4} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{3 c^{3} d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{5 c^{3} d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} + \frac{9 c^{2} d^{2} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{15 c^{2} d^{2} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} + \frac{9 c d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{15 c d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} + \frac{3 d^{4} x^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{5 d^{4} x^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b^{2}} - \frac{9 c^{2} d^{2} \sin^{4}{\left(a + b x \right)}}{32 b^{3}} + \frac{15 c^{2} d^{2} \cos^{4}{\left(a + b x \right)}}{32 b^{3}} - \frac{45 c d^{3} x \sin^{4}{\left(a + b x \right)}}{64 b^{3}} - \frac{9 c d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32 b^{3}} + \frac{51 c d^{3} x \cos^{4}{\left(a + b x \right)}}{64 b^{3}} - \frac{45 d^{4} x^{2} \sin^{4}{\left(a + b x \right)}}{128 b^{3}} - \frac{9 d^{4} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{64 b^{3}} + \frac{51 d^{4} x^{2} \cos^{4}{\left(a + b x \right)}}{128 b^{3}} - \frac{45 c d^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{4}} - \frac{51 c d^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{4}} - \frac{45 d^{4} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{64 b^{4}} - \frac{51 d^{4} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{64 b^{4}} + \frac{45 d^{4} \sin^{4}{\left(a + b x \right)}}{256 b^{5}} - \frac{51 d^{4} \cos^{4}{\left(a + b x \right)}}{256 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**4*cos(a + b*x)**4/(4*b) + 3*c**3*d*x*sin(a + b*x)**4/(8*b) + 3*c**3*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(4*b) - 5*c**3*d*x*cos(a + b*x)**4/(8*b) + 9*c**2*d**2*x**2*sin(a + b*x)**4/(16*b) + 9*c**2*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(8*b) - 15*c**2*d**2*x**2*cos(a + b*x)**4/(16*b) + 3*c*d**3*x**3*sin(a + b*x)**4/(8*b) + 3*c*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**2/(4*b) - 5*c*d**3*x**3*cos(a + b*x)**4/(8*b) + 3*d**4*x**4*sin(a + b*x)**4/(32*b) + 3*d**4*x**4*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 5*d**4*x**4*cos(a + b*x)**4/(32*b) + 3*c**3*d*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 5*c**3*d*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) + 9*c**2*d**2*x*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 15*c**2*d**2*x*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) + 9*c*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 15*c*d**3*x**2*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) + 3*d**4*x**3*sin(a + b*x)**3*cos(a + b*x)/(8*b**2) + 5*d**4*x**3*sin(a + b*x)*cos(a + b*x)**3/(8*b**2) - 9*c**2*d**2*sin(a + b*x)**4/(32*b**3) + 15*c**2*d**2*cos(a + b*x)**4/(32*b**3) - 45*c*d**3*x*sin(a + b*x)**4/(64*b**3) - 9*c*d**3*x*sin(a + b*x)**2*cos(a + b*x)**2/(32*b**3) + 51*c*d**3*x*cos(a + b*x)**4/(64*b**3) - 45*d**4*x**2*sin(a + b*x)**4/(128*b**3) - 9*d**4*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(64*b**3) + 51*d**4*x**2*cos(a + b*x)**4/(128*b**3) - 45*c*d**3*sin(a + b*x)**3*cos(a + b*x)/(64*b**4) - 51*c*d**3*sin(a + b*x)*cos(a + b*x)**3/(64*b**4) - 45*d**4*x*sin(a + b*x)**3*cos(a + b*x)/(64*b**4) - 51*d**4*x*sin(a + b*x)*cos(a + b*x)**3/(64*b**4) + 45*d**4*sin(a + b*x)**4/(256*b**5) - 51*d**4*cos(a + b*x)**4/(256*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)*cos(a)**3, True))","A",0
138,1,602,0,7.632831," ","integrate((d*x+c)**3*cos(b*x+a)**3*sin(b*x+a),x)","\begin{cases} - \frac{c^{3} \cos^{4}{\left(a + b x \right)}}{4 b} + \frac{9 c^{2} d x \sin^{4}{\left(a + b x \right)}}{32 b} + \frac{9 c^{2} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{15 c^{2} d x \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{9 c d^{2} x^{2} \sin^{4}{\left(a + b x \right)}}{32 b} + \frac{9 c d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{15 c d^{2} x^{2} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{3 d^{3} x^{3} \sin^{4}{\left(a + b x \right)}}{32 b} + \frac{3 d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{5 d^{3} x^{3} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{9 c^{2} d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{2}} + \frac{15 c^{2} d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{2}} + \frac{9 c d^{2} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{2}} + \frac{15 c d^{2} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{2}} + \frac{9 d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{2}} + \frac{15 d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{2}} - \frac{9 c d^{2} \sin^{4}{\left(a + b x \right)}}{64 b^{3}} + \frac{15 c d^{2} \cos^{4}{\left(a + b x \right)}}{64 b^{3}} - \frac{45 d^{3} x \sin^{4}{\left(a + b x \right)}}{256 b^{3}} - \frac{9 d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{128 b^{3}} + \frac{51 d^{3} x \cos^{4}{\left(a + b x \right)}}{256 b^{3}} - \frac{45 d^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{256 b^{4}} - \frac{51 d^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{256 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**3*cos(a + b*x)**4/(4*b) + 9*c**2*d*x*sin(a + b*x)**4/(32*b) + 9*c**2*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 15*c**2*d*x*cos(a + b*x)**4/(32*b) + 9*c*d**2*x**2*sin(a + b*x)**4/(32*b) + 9*c*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 15*c*d**2*x**2*cos(a + b*x)**4/(32*b) + 3*d**3*x**3*sin(a + b*x)**4/(32*b) + 3*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 5*d**3*x**3*cos(a + b*x)**4/(32*b) + 9*c**2*d*sin(a + b*x)**3*cos(a + b*x)/(32*b**2) + 15*c**2*d*sin(a + b*x)*cos(a + b*x)**3/(32*b**2) + 9*c*d**2*x*sin(a + b*x)**3*cos(a + b*x)/(16*b**2) + 15*c*d**2*x*sin(a + b*x)*cos(a + b*x)**3/(16*b**2) + 9*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)/(32*b**2) + 15*d**3*x**2*sin(a + b*x)*cos(a + b*x)**3/(32*b**2) - 9*c*d**2*sin(a + b*x)**4/(64*b**3) + 15*c*d**2*cos(a + b*x)**4/(64*b**3) - 45*d**3*x*sin(a + b*x)**4/(256*b**3) - 9*d**3*x*sin(a + b*x)**2*cos(a + b*x)**2/(128*b**3) + 51*d**3*x*cos(a + b*x)**4/(256*b**3) - 45*d**3*sin(a + b*x)**3*cos(a + b*x)/(256*b**4) - 51*d**3*sin(a + b*x)*cos(a + b*x)**3/(256*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)*cos(a)**3, True))","A",0
139,1,320,0,3.791965," ","integrate((d*x+c)**2*cos(b*x+a)**3*sin(b*x+a),x)","\begin{cases} - \frac{c^{2} \cos^{4}{\left(a + b x \right)}}{4 b} + \frac{3 c d x \sin^{4}{\left(a + b x \right)}}{16 b} + \frac{3 c d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{5 c d x \cos^{4}{\left(a + b x \right)}}{16 b} + \frac{3 d^{2} x^{2} \sin^{4}{\left(a + b x \right)}}{32 b} + \frac{3 d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{5 d^{2} x^{2} \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{3 c d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{2}} + \frac{5 c d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{2}} + \frac{3 d^{2} x \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b^{2}} + \frac{5 d^{2} x \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{16 b^{2}} - \frac{3 d^{2} \sin^{4}{\left(a + b x \right)}}{64 b^{3}} + \frac{5 d^{2} \cos^{4}{\left(a + b x \right)}}{64 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**2*cos(a + b*x)**4/(4*b) + 3*c*d*x*sin(a + b*x)**4/(16*b) + 3*c*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(8*b) - 5*c*d*x*cos(a + b*x)**4/(16*b) + 3*d**2*x**2*sin(a + b*x)**4/(32*b) + 3*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 5*d**2*x**2*cos(a + b*x)**4/(32*b) + 3*c*d*sin(a + b*x)**3*cos(a + b*x)/(16*b**2) + 5*c*d*sin(a + b*x)*cos(a + b*x)**3/(16*b**2) + 3*d**2*x*sin(a + b*x)**3*cos(a + b*x)/(16*b**2) + 5*d**2*x*sin(a + b*x)*cos(a + b*x)**3/(16*b**2) - 3*d**2*sin(a + b*x)**4/(64*b**3) + 5*d**2*cos(a + b*x)**4/(64*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)*cos(a)**3, True))","A",0
140,1,138,0,1.936418," ","integrate((d*x+c)*cos(b*x+a)**3*sin(b*x+a),x)","\begin{cases} - \frac{c \cos^{4}{\left(a + b x \right)}}{4 b} + \frac{3 d x \sin^{4}{\left(a + b x \right)}}{32 b} + \frac{3 d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16 b} - \frac{5 d x \cos^{4}{\left(a + b x \right)}}{32 b} + \frac{3 d \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{32 b^{2}} + \frac{5 d \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{32 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*cos(a + b*x)**4/(4*b) + 3*d*x*sin(a + b*x)**4/(32*b) + 3*d*x*sin(a + b*x)**2*cos(a + b*x)**2/(16*b) - 5*d*x*cos(a + b*x)**4/(32*b) + 3*d*sin(a + b*x)**3*cos(a + b*x)/(32*b**2) + 5*d*sin(a + b*x)*cos(a + b*x)**3/(32*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)*cos(a)**3, True))","A",0
141,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)/(d*x+c),x)","\int \frac{\sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**3/(c + d*x), x)","F",0
142,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)/(d*x+c)**2,x)","\int \frac{\sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**3/(c + d*x)**2, x)","F",0
143,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)/(d*x+c)**3,x)","\int \frac{\sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**3/(c + d*x)**3, x)","F",0
144,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)/(d*x+c)**4,x)","\int \frac{\sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)*cos(a + b*x)**3/(c + d*x)**4, x)","F",0
145,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**3*sin(b*x+a)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
146,1,1098,0,20.951665," ","integrate((d*x+c)**4*cos(b*x+a)**3*sin(b*x+a)**2,x)","\begin{cases} \frac{2 c^{4} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{c^{4} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{8 c^{3} d x \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{4 c^{3} d x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{4 c^{2} d^{2} x^{2} \sin^{5}{\left(a + b x \right)}}{5 b} + \frac{2 c^{2} d^{2} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{8 c d^{3} x^{3} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{4 c d^{3} x^{3} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{2 d^{4} x^{4} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{d^{4} x^{4} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{8 c^{3} d \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{15 b^{2}} + \frac{52 c^{3} d \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{45 b^{2}} + \frac{104 c^{3} d \cos^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{8 c^{2} d^{2} x \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{5 b^{2}} + \frac{52 c^{2} d^{2} x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{15 b^{2}} + \frac{104 c^{2} d^{2} x \cos^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{8 c d^{3} x^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{5 b^{2}} + \frac{52 c d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{15 b^{2}} + \frac{104 c d^{3} x^{2} \cos^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{8 d^{4} x^{3} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{15 b^{2}} + \frac{52 d^{4} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{45 b^{2}} + \frac{104 d^{4} x^{3} \cos^{5}{\left(a + b x \right)}}{225 b^{2}} - \frac{1712 c^{2} d^{2} \sin^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{676 c^{2} d^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{225 b^{3}} - \frac{104 c^{2} d^{2} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{75 b^{3}} - \frac{3424 c d^{3} x \sin^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{1352 c d^{3} x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{225 b^{3}} - \frac{208 c d^{3} x \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{75 b^{3}} - \frac{1712 d^{4} x^{2} \sin^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{676 d^{4} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{225 b^{3}} - \frac{104 d^{4} x^{2} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{75 b^{3}} - \frac{3424 c d^{3} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{1125 b^{4}} - \frac{20456 c d^{3} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3375 b^{4}} - \frac{50272 c d^{3} \cos^{5}{\left(a + b x \right)}}{16875 b^{4}} - \frac{3424 d^{4} x \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{1125 b^{4}} - \frac{20456 d^{4} x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3375 b^{4}} - \frac{50272 d^{4} x \cos^{5}{\left(a + b x \right)}}{16875 b^{4}} + \frac{760816 d^{4} \sin^{5}{\left(a + b x \right)}}{253125 b^{5}} + \frac{303368 d^{4} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{50625 b^{5}} + \frac{50272 d^{4} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{16875 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**4*sin(a + b*x)**5/(15*b) + c**4*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 8*c**3*d*x*sin(a + b*x)**5/(15*b) + 4*c**3*d*x*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 4*c**2*d**2*x**2*sin(a + b*x)**5/(5*b) + 2*c**2*d**2*x**2*sin(a + b*x)**3*cos(a + b*x)**2/b + 8*c*d**3*x**3*sin(a + b*x)**5/(15*b) + 4*c*d**3*x**3*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 2*d**4*x**4*sin(a + b*x)**5/(15*b) + d**4*x**4*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 8*c**3*d*sin(a + b*x)**4*cos(a + b*x)/(15*b**2) + 52*c**3*d*sin(a + b*x)**2*cos(a + b*x)**3/(45*b**2) + 104*c**3*d*cos(a + b*x)**5/(225*b**2) + 8*c**2*d**2*x*sin(a + b*x)**4*cos(a + b*x)/(5*b**2) + 52*c**2*d**2*x*sin(a + b*x)**2*cos(a + b*x)**3/(15*b**2) + 104*c**2*d**2*x*cos(a + b*x)**5/(75*b**2) + 8*c*d**3*x**2*sin(a + b*x)**4*cos(a + b*x)/(5*b**2) + 52*c*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)**3/(15*b**2) + 104*c*d**3*x**2*cos(a + b*x)**5/(75*b**2) + 8*d**4*x**3*sin(a + b*x)**4*cos(a + b*x)/(15*b**2) + 52*d**4*x**3*sin(a + b*x)**2*cos(a + b*x)**3/(45*b**2) + 104*d**4*x**3*cos(a + b*x)**5/(225*b**2) - 1712*c**2*d**2*sin(a + b*x)**5/(1125*b**3) - 676*c**2*d**2*sin(a + b*x)**3*cos(a + b*x)**2/(225*b**3) - 104*c**2*d**2*sin(a + b*x)*cos(a + b*x)**4/(75*b**3) - 3424*c*d**3*x*sin(a + b*x)**5/(1125*b**3) - 1352*c*d**3*x*sin(a + b*x)**3*cos(a + b*x)**2/(225*b**3) - 208*c*d**3*x*sin(a + b*x)*cos(a + b*x)**4/(75*b**3) - 1712*d**4*x**2*sin(a + b*x)**5/(1125*b**3) - 676*d**4*x**2*sin(a + b*x)**3*cos(a + b*x)**2/(225*b**3) - 104*d**4*x**2*sin(a + b*x)*cos(a + b*x)**4/(75*b**3) - 3424*c*d**3*sin(a + b*x)**4*cos(a + b*x)/(1125*b**4) - 20456*c*d**3*sin(a + b*x)**2*cos(a + b*x)**3/(3375*b**4) - 50272*c*d**3*cos(a + b*x)**5/(16875*b**4) - 3424*d**4*x*sin(a + b*x)**4*cos(a + b*x)/(1125*b**4) - 20456*d**4*x*sin(a + b*x)**2*cos(a + b*x)**3/(3375*b**4) - 50272*d**4*x*cos(a + b*x)**5/(16875*b**4) + 760816*d**4*sin(a + b*x)**5/(253125*b**5) + 303368*d**4*sin(a + b*x)**3*cos(a + b*x)**2/(50625*b**5) + 50272*d**4*sin(a + b*x)*cos(a + b*x)**4/(16875*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*cos(a)**3, True))","A",0
147,1,690,0,11.353512," ","integrate((d*x+c)**3*cos(b*x+a)**3*sin(b*x+a)**2,x)","\begin{cases} \frac{2 c^{3} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{c^{3} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{2 c^{2} d x \sin^{5}{\left(a + b x \right)}}{5 b} + \frac{c^{2} d x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 c d^{2} x^{2} \sin^{5}{\left(a + b x \right)}}{5 b} + \frac{c d^{2} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 d^{3} x^{3} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{d^{3} x^{3} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{2 c^{2} d \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{5 b^{2}} + \frac{13 c^{2} d \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{15 b^{2}} + \frac{26 c^{2} d \cos^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{4 c d^{2} x \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{5 b^{2}} + \frac{26 c d^{2} x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{15 b^{2}} + \frac{52 c d^{2} x \cos^{5}{\left(a + b x \right)}}{75 b^{2}} + \frac{2 d^{3} x^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{5 b^{2}} + \frac{13 d^{3} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{15 b^{2}} + \frac{26 d^{3} x^{2} \cos^{5}{\left(a + b x \right)}}{75 b^{2}} - \frac{856 c d^{2} \sin^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{338 c d^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{225 b^{3}} - \frac{52 c d^{2} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{75 b^{3}} - \frac{856 d^{3} x \sin^{5}{\left(a + b x \right)}}{1125 b^{3}} - \frac{338 d^{3} x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{225 b^{3}} - \frac{52 d^{3} x \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{75 b^{3}} - \frac{856 d^{3} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{1125 b^{4}} - \frac{5114 d^{3} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3375 b^{4}} - \frac{12568 d^{3} \cos^{5}{\left(a + b x \right)}}{16875 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**3*sin(a + b*x)**5/(15*b) + c**3*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 2*c**2*d*x*sin(a + b*x)**5/(5*b) + c**2*d*x*sin(a + b*x)**3*cos(a + b*x)**2/b + 2*c*d**2*x**2*sin(a + b*x)**5/(5*b) + c*d**2*x**2*sin(a + b*x)**3*cos(a + b*x)**2/b + 2*d**3*x**3*sin(a + b*x)**5/(15*b) + d**3*x**3*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 2*c**2*d*sin(a + b*x)**4*cos(a + b*x)/(5*b**2) + 13*c**2*d*sin(a + b*x)**2*cos(a + b*x)**3/(15*b**2) + 26*c**2*d*cos(a + b*x)**5/(75*b**2) + 4*c*d**2*x*sin(a + b*x)**4*cos(a + b*x)/(5*b**2) + 26*c*d**2*x*sin(a + b*x)**2*cos(a + b*x)**3/(15*b**2) + 52*c*d**2*x*cos(a + b*x)**5/(75*b**2) + 2*d**3*x**2*sin(a + b*x)**4*cos(a + b*x)/(5*b**2) + 13*d**3*x**2*sin(a + b*x)**2*cos(a + b*x)**3/(15*b**2) + 26*d**3*x**2*cos(a + b*x)**5/(75*b**2) - 856*c*d**2*sin(a + b*x)**5/(1125*b**3) - 338*c*d**2*sin(a + b*x)**3*cos(a + b*x)**2/(225*b**3) - 52*c*d**2*sin(a + b*x)*cos(a + b*x)**4/(75*b**3) - 856*d**3*x*sin(a + b*x)**5/(1125*b**3) - 338*d**3*x*sin(a + b*x)**3*cos(a + b*x)**2/(225*b**3) - 52*d**3*x*sin(a + b*x)*cos(a + b*x)**4/(75*b**3) - 856*d**3*sin(a + b*x)**4*cos(a + b*x)/(1125*b**4) - 5114*d**3*sin(a + b*x)**2*cos(a + b*x)**3/(3375*b**4) - 12568*d**3*cos(a + b*x)**5/(16875*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*cos(a)**3, True))","A",0
148,1,382,0,6.227726," ","integrate((d*x+c)**2*cos(b*x+a)**3*sin(b*x+a)**2,x)","\begin{cases} \frac{2 c^{2} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{c^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{4 c d x \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{2 c d x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{2 d^{2} x^{2} \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{d^{2} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{4 c d \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{15 b^{2}} + \frac{26 c d \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{45 b^{2}} + \frac{52 c d \cos^{5}{\left(a + b x \right)}}{225 b^{2}} + \frac{4 d^{2} x \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{15 b^{2}} + \frac{26 d^{2} x \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{45 b^{2}} + \frac{52 d^{2} x \cos^{5}{\left(a + b x \right)}}{225 b^{2}} - \frac{856 d^{2} \sin^{5}{\left(a + b x \right)}}{3375 b^{3}} - \frac{338 d^{2} \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{675 b^{3}} - \frac{52 d^{2} \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{225 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c**2*sin(a + b*x)**5/(15*b) + c**2*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 4*c*d*x*sin(a + b*x)**5/(15*b) + 2*c*d*x*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 2*d**2*x**2*sin(a + b*x)**5/(15*b) + d**2*x**2*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 4*c*d*sin(a + b*x)**4*cos(a + b*x)/(15*b**2) + 26*c*d*sin(a + b*x)**2*cos(a + b*x)**3/(45*b**2) + 52*c*d*cos(a + b*x)**5/(225*b**2) + 4*d**2*x*sin(a + b*x)**4*cos(a + b*x)/(15*b**2) + 26*d**2*x*sin(a + b*x)**2*cos(a + b*x)**3/(45*b**2) + 52*d**2*x*cos(a + b*x)**5/(225*b**2) - 856*d**2*sin(a + b*x)**5/(3375*b**3) - 338*d**2*sin(a + b*x)**3*cos(a + b*x)**2/(675*b**3) - 52*d**2*sin(a + b*x)*cos(a + b*x)**4/(225*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**2*cos(a)**3, True))","A",0
149,1,163,0,3.100956," ","integrate((d*x+c)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\begin{cases} \frac{2 c \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{c \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{2 d x \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{d x \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{2 d \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{15 b^{2}} + \frac{13 d \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{45 b^{2}} + \frac{26 d \cos^{5}{\left(a + b x \right)}}{225 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{2}{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*c*sin(a + b*x)**5/(15*b) + c*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 2*d*x*sin(a + b*x)**5/(15*b) + d*x*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 2*d*sin(a + b*x)**4*cos(a + b*x)/(15*b**2) + 13*d*sin(a + b*x)**2*cos(a + b*x)**3/(45*b**2) + 26*d*cos(a + b*x)**5/(225*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**2*cos(a)**3, True))","A",0
150,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**2/(d*x+c),x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**3/(c + d*x), x)","F",0
151,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**3/(c + d*x)**2, x)","F",0
152,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**2/(d*x+c)**3,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**3/(c + d*x)**3, x)","F",0
153,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**2/(d*x+c)**4,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral(sin(a + b*x)**2*cos(a + b*x)**3/(c + d*x)**4, x)","F",0
154,-2,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
155,1,1334,0,31.302336," ","integrate((d*x+c)**4*cos(b*x+a)**3*sin(b*x+a)**3,x)","\begin{cases} \frac{c^{4} \sin^{6}{\left(a + b x \right)}}{12 b} + \frac{c^{4} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{c^{3} d x \sin^{6}{\left(a + b x \right)}}{6 b} + \frac{c^{3} d x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{2 b} - \frac{c^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{2 b} - \frac{c^{3} d x \cos^{6}{\left(a + b x \right)}}{6 b} + \frac{c^{2} d^{2} x^{2} \sin^{6}{\left(a + b x \right)}}{4 b} + \frac{3 c^{2} d^{2} x^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} - \frac{3 c^{2} d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{4 b} - \frac{c^{2} d^{2} x^{2} \cos^{6}{\left(a + b x \right)}}{4 b} + \frac{c d^{3} x^{3} \sin^{6}{\left(a + b x \right)}}{6 b} + \frac{c d^{3} x^{3} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{2 b} - \frac{c d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{2 b} - \frac{c d^{3} x^{3} \cos^{6}{\left(a + b x \right)}}{6 b} + \frac{d^{4} x^{4} \sin^{6}{\left(a + b x \right)}}{24 b} + \frac{d^{4} x^{4} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{d^{4} x^{4} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{8 b} - \frac{d^{4} x^{4} \cos^{6}{\left(a + b x \right)}}{24 b} + \frac{c^{3} d \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{6 b^{2}} + \frac{4 c^{3} d \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{c^{3} d \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{6 b^{2}} + \frac{c^{2} d^{2} x \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{2}} + \frac{4 c^{2} d^{2} x \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{c^{2} d^{2} x \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{2 b^{2}} + \frac{c d^{3} x^{2} \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b^{2}} + \frac{4 c d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{c d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{2 b^{2}} + \frac{d^{4} x^{3} \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{6 b^{2}} + \frac{4 d^{4} x^{3} \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{d^{4} x^{3} \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{6 b^{2}} - \frac{7 c^{2} d^{2} \sin^{6}{\left(a + b x \right)}}{36 b^{3}} - \frac{c^{2} d^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} + \frac{c^{2} d^{2} \cos^{6}{\left(a + b x \right)}}{12 b^{3}} - \frac{5 c d^{3} x \sin^{6}{\left(a + b x \right)}}{18 b^{3}} - \frac{c d^{3} x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b^{3}} + \frac{c d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{3 b^{3}} + \frac{5 c d^{3} x \cos^{6}{\left(a + b x \right)}}{18 b^{3}} - \frac{5 d^{4} x^{2} \sin^{6}{\left(a + b x \right)}}{36 b^{3}} - \frac{d^{4} x^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{6 b^{3}} + \frac{d^{4} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{6 b^{3}} + \frac{5 d^{4} x^{2} \cos^{6}{\left(a + b x \right)}}{36 b^{3}} - \frac{5 c d^{3} \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{18 b^{4}} - \frac{31 c d^{3} \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{54 b^{4}} - \frac{5 c d^{3} \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{18 b^{4}} - \frac{5 d^{4} x \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{18 b^{4}} - \frac{31 d^{4} x \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{54 b^{4}} - \frac{5 d^{4} x \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{18 b^{4}} + \frac{61 d^{4} \sin^{6}{\left(a + b x \right)}}{648 b^{5}} + \frac{31 d^{4} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{216 b^{5}} - \frac{5 d^{4} \cos^{6}{\left(a + b x \right)}}{108 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*sin(a + b*x)**6/(12*b) + c**4*sin(a + b*x)**4*cos(a + b*x)**2/(4*b) + c**3*d*x*sin(a + b*x)**6/(6*b) + c**3*d*x*sin(a + b*x)**4*cos(a + b*x)**2/(2*b) - c**3*d*x*sin(a + b*x)**2*cos(a + b*x)**4/(2*b) - c**3*d*x*cos(a + b*x)**6/(6*b) + c**2*d**2*x**2*sin(a + b*x)**6/(4*b) + 3*c**2*d**2*x**2*sin(a + b*x)**4*cos(a + b*x)**2/(4*b) - 3*c**2*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**4/(4*b) - c**2*d**2*x**2*cos(a + b*x)**6/(4*b) + c*d**3*x**3*sin(a + b*x)**6/(6*b) + c*d**3*x**3*sin(a + b*x)**4*cos(a + b*x)**2/(2*b) - c*d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**4/(2*b) - c*d**3*x**3*cos(a + b*x)**6/(6*b) + d**4*x**4*sin(a + b*x)**6/(24*b) + d**4*x**4*sin(a + b*x)**4*cos(a + b*x)**2/(8*b) - d**4*x**4*sin(a + b*x)**2*cos(a + b*x)**4/(8*b) - d**4*x**4*cos(a + b*x)**6/(24*b) + c**3*d*sin(a + b*x)**5*cos(a + b*x)/(6*b**2) + 4*c**3*d*sin(a + b*x)**3*cos(a + b*x)**3/(9*b**2) + c**3*d*sin(a + b*x)*cos(a + b*x)**5/(6*b**2) + c**2*d**2*x*sin(a + b*x)**5*cos(a + b*x)/(2*b**2) + 4*c**2*d**2*x*sin(a + b*x)**3*cos(a + b*x)**3/(3*b**2) + c**2*d**2*x*sin(a + b*x)*cos(a + b*x)**5/(2*b**2) + c*d**3*x**2*sin(a + b*x)**5*cos(a + b*x)/(2*b**2) + 4*c*d**3*x**2*sin(a + b*x)**3*cos(a + b*x)**3/(3*b**2) + c*d**3*x**2*sin(a + b*x)*cos(a + b*x)**5/(2*b**2) + d**4*x**3*sin(a + b*x)**5*cos(a + b*x)/(6*b**2) + 4*d**4*x**3*sin(a + b*x)**3*cos(a + b*x)**3/(9*b**2) + d**4*x**3*sin(a + b*x)*cos(a + b*x)**5/(6*b**2) - 7*c**2*d**2*sin(a + b*x)**6/(36*b**3) - c**2*d**2*sin(a + b*x)**4*cos(a + b*x)**2/(3*b**3) + c**2*d**2*cos(a + b*x)**6/(12*b**3) - 5*c*d**3*x*sin(a + b*x)**6/(18*b**3) - c*d**3*x*sin(a + b*x)**4*cos(a + b*x)**2/(3*b**3) + c*d**3*x*sin(a + b*x)**2*cos(a + b*x)**4/(3*b**3) + 5*c*d**3*x*cos(a + b*x)**6/(18*b**3) - 5*d**4*x**2*sin(a + b*x)**6/(36*b**3) - d**4*x**2*sin(a + b*x)**4*cos(a + b*x)**2/(6*b**3) + d**4*x**2*sin(a + b*x)**2*cos(a + b*x)**4/(6*b**3) + 5*d**4*x**2*cos(a + b*x)**6/(36*b**3) - 5*c*d**3*sin(a + b*x)**5*cos(a + b*x)/(18*b**4) - 31*c*d**3*sin(a + b*x)**3*cos(a + b*x)**3/(54*b**4) - 5*c*d**3*sin(a + b*x)*cos(a + b*x)**5/(18*b**4) - 5*d**4*x*sin(a + b*x)**5*cos(a + b*x)/(18*b**4) - 31*d**4*x*sin(a + b*x)**3*cos(a + b*x)**3/(54*b**4) - 5*d**4*x*sin(a + b*x)*cos(a + b*x)**5/(18*b**4) + 61*d**4*sin(a + b*x)**6/(648*b**5) + 31*d**4*sin(a + b*x)**4*cos(a + b*x)**2/(216*b**5) - 5*d**4*cos(a + b*x)**6/(108*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*cos(a)**3, True))","A",0
156,1,857,0,18.631839," ","integrate((d*x+c)**3*cos(b*x+a)**3*sin(b*x+a)**3,x)","\begin{cases} \frac{c^{3} \sin^{6}{\left(a + b x \right)}}{12 b} + \frac{c^{3} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{c^{2} d x \sin^{6}{\left(a + b x \right)}}{8 b} + \frac{3 c^{2} d x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{3 c^{2} d x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{8 b} - \frac{c^{2} d x \cos^{6}{\left(a + b x \right)}}{8 b} + \frac{c d^{2} x^{2} \sin^{6}{\left(a + b x \right)}}{8 b} + \frac{3 c d^{2} x^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{3 c d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{8 b} - \frac{c d^{2} x^{2} \cos^{6}{\left(a + b x \right)}}{8 b} + \frac{d^{3} x^{3} \sin^{6}{\left(a + b x \right)}}{24 b} + \frac{d^{3} x^{3} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{d^{3} x^{3} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{8 b} - \frac{d^{3} x^{3} \cos^{6}{\left(a + b x \right)}}{24 b} + \frac{c^{2} d \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{c^{2} d \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{c^{2} d \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{8 b^{2}} + \frac{c d^{2} x \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{2}} + \frac{2 c d^{2} x \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{c d^{2} x \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{4 b^{2}} + \frac{d^{3} x^{2} \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b^{2}} + \frac{d^{3} x^{2} \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b^{2}} + \frac{d^{3} x^{2} \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{8 b^{2}} - \frac{7 c d^{2} \sin^{6}{\left(a + b x \right)}}{72 b^{3}} - \frac{c d^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{6 b^{3}} + \frac{c d^{2} \cos^{6}{\left(a + b x \right)}}{24 b^{3}} - \frac{5 d^{3} x \sin^{6}{\left(a + b x \right)}}{72 b^{3}} - \frac{d^{3} x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{12 b^{3}} + \frac{d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{12 b^{3}} + \frac{5 d^{3} x \cos^{6}{\left(a + b x \right)}}{72 b^{3}} - \frac{5 d^{3} \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{72 b^{4}} - \frac{31 d^{3} \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{216 b^{4}} - \frac{5 d^{3} \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{72 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*sin(a + b*x)**6/(12*b) + c**3*sin(a + b*x)**4*cos(a + b*x)**2/(4*b) + c**2*d*x*sin(a + b*x)**6/(8*b) + 3*c**2*d*x*sin(a + b*x)**4*cos(a + b*x)**2/(8*b) - 3*c**2*d*x*sin(a + b*x)**2*cos(a + b*x)**4/(8*b) - c**2*d*x*cos(a + b*x)**6/(8*b) + c*d**2*x**2*sin(a + b*x)**6/(8*b) + 3*c*d**2*x**2*sin(a + b*x)**4*cos(a + b*x)**2/(8*b) - 3*c*d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**4/(8*b) - c*d**2*x**2*cos(a + b*x)**6/(8*b) + d**3*x**3*sin(a + b*x)**6/(24*b) + d**3*x**3*sin(a + b*x)**4*cos(a + b*x)**2/(8*b) - d**3*x**3*sin(a + b*x)**2*cos(a + b*x)**4/(8*b) - d**3*x**3*cos(a + b*x)**6/(24*b) + c**2*d*sin(a + b*x)**5*cos(a + b*x)/(8*b**2) + c**2*d*sin(a + b*x)**3*cos(a + b*x)**3/(3*b**2) + c**2*d*sin(a + b*x)*cos(a + b*x)**5/(8*b**2) + c*d**2*x*sin(a + b*x)**5*cos(a + b*x)/(4*b**2) + 2*c*d**2*x*sin(a + b*x)**3*cos(a + b*x)**3/(3*b**2) + c*d**2*x*sin(a + b*x)*cos(a + b*x)**5/(4*b**2) + d**3*x**2*sin(a + b*x)**5*cos(a + b*x)/(8*b**2) + d**3*x**2*sin(a + b*x)**3*cos(a + b*x)**3/(3*b**2) + d**3*x**2*sin(a + b*x)*cos(a + b*x)**5/(8*b**2) - 7*c*d**2*sin(a + b*x)**6/(72*b**3) - c*d**2*sin(a + b*x)**4*cos(a + b*x)**2/(6*b**3) + c*d**2*cos(a + b*x)**6/(24*b**3) - 5*d**3*x*sin(a + b*x)**6/(72*b**3) - d**3*x*sin(a + b*x)**4*cos(a + b*x)**2/(12*b**3) + d**3*x*sin(a + b*x)**2*cos(a + b*x)**4/(12*b**3) + 5*d**3*x*cos(a + b*x)**6/(72*b**3) - 5*d**3*sin(a + b*x)**5*cos(a + b*x)/(72*b**4) - 31*d**3*sin(a + b*x)**3*cos(a + b*x)**3/(216*b**4) - 5*d**3*sin(a + b*x)*cos(a + b*x)**5/(72*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*cos(a)**3, True))","A",0
157,1,461,0,9.992009," ","integrate((d*x+c)**2*cos(b*x+a)**3*sin(b*x+a)**3,x)","\begin{cases} \frac{c^{2} \sin^{6}{\left(a + b x \right)}}{12 b} + \frac{c^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{c d x \sin^{6}{\left(a + b x \right)}}{12 b} + \frac{c d x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} - \frac{c d x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{4 b} - \frac{c d x \cos^{6}{\left(a + b x \right)}}{12 b} + \frac{d^{2} x^{2} \sin^{6}{\left(a + b x \right)}}{24 b} + \frac{d^{2} x^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{d^{2} x^{2} \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{8 b} - \frac{d^{2} x^{2} \cos^{6}{\left(a + b x \right)}}{24 b} + \frac{c d \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{12 b^{2}} + \frac{2 c d \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{c d \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{12 b^{2}} + \frac{d^{2} x \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{12 b^{2}} + \frac{2 d^{2} x \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{d^{2} x \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{12 b^{2}} - \frac{7 d^{2} \sin^{6}{\left(a + b x \right)}}{216 b^{3}} - \frac{d^{2} \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{18 b^{3}} + \frac{d^{2} \cos^{6}{\left(a + b x \right)}}{72 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)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*sin(a + b*x)**6/(12*b) + c**2*sin(a + b*x)**4*cos(a + b*x)**2/(4*b) + c*d*x*sin(a + b*x)**6/(12*b) + c*d*x*sin(a + b*x)**4*cos(a + b*x)**2/(4*b) - c*d*x*sin(a + b*x)**2*cos(a + b*x)**4/(4*b) - c*d*x*cos(a + b*x)**6/(12*b) + d**2*x**2*sin(a + b*x)**6/(24*b) + d**2*x**2*sin(a + b*x)**4*cos(a + b*x)**2/(8*b) - d**2*x**2*sin(a + b*x)**2*cos(a + b*x)**4/(8*b) - d**2*x**2*cos(a + b*x)**6/(24*b) + c*d*sin(a + b*x)**5*cos(a + b*x)/(12*b**2) + 2*c*d*sin(a + b*x)**3*cos(a + b*x)**3/(9*b**2) + c*d*sin(a + b*x)*cos(a + b*x)**5/(12*b**2) + d**2*x*sin(a + b*x)**5*cos(a + b*x)/(12*b**2) + 2*d**2*x*sin(a + b*x)**3*cos(a + b*x)**3/(9*b**2) + d**2*x*sin(a + b*x)*cos(a + b*x)**5/(12*b**2) - 7*d**2*sin(a + b*x)**6/(216*b**3) - d**2*sin(a + b*x)**4*cos(a + b*x)**2/(18*b**3) + d**2*cos(a + b*x)**6/(72*b**3), Ne(b, 0)), ((c**2*x + c*d*x**2 + d**2*x**3/3)*sin(a)**3*cos(a)**3, True))","A",0
158,1,201,0,5.331925," ","integrate((d*x+c)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\begin{cases} \frac{c \sin^{6}{\left(a + b x \right)}}{12 b} + \frac{c \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4 b} + \frac{d x \sin^{6}{\left(a + b x \right)}}{24 b} + \frac{d x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{8 b} - \frac{d x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{8 b} - \frac{d x \cos^{6}{\left(a + b x \right)}}{24 b} + \frac{d \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{24 b^{2}} + \frac{d \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{9 b^{2}} + \frac{d \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{24 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \sin^{3}{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*sin(a + b*x)**6/(12*b) + c*sin(a + b*x)**4*cos(a + b*x)**2/(4*b) + d*x*sin(a + b*x)**6/(24*b) + d*x*sin(a + b*x)**4*cos(a + b*x)**2/(8*b) - d*x*sin(a + b*x)**2*cos(a + b*x)**4/(8*b) - d*x*cos(a + b*x)**6/(24*b) + d*sin(a + b*x)**5*cos(a + b*x)/(24*b**2) + d*sin(a + b*x)**3*cos(a + b*x)**3/(9*b**2) + d*sin(a + b*x)*cos(a + b*x)**5/(24*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*sin(a)**3*cos(a)**3, True))","A",0
159,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**3/(d*x+c),x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)**3/(c + d*x), x)","F",0
160,0,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**3*cos(a + b*x)**3/(c + d*x)**2, x)","F",0
161,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**3/(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(b*x+a)**3/(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)**2*cot(b*x+a),x)","\int \left(c + d x\right)^{m} \cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)**2*cot(a + b*x), x)","F",0
164,0,0,0,0.000000," ","integrate((d*x+c)**4*cos(b*x+a)**2*cot(b*x+a),x)","\int \left(c + d x\right)^{4} \cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cos(a + b*x)**2*cot(a + b*x), x)","F",0
165,0,0,0,0.000000," ","integrate((d*x+c)**3*cos(b*x+a)**2*cot(b*x+a),x)","\int \left(c + d x\right)^{3} \cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cos(a + b*x)**2*cot(a + b*x), x)","F",0
166,0,0,0,0.000000," ","integrate((d*x+c)**2*cos(b*x+a)**2*cot(b*x+a),x)","\int \left(c + d x\right)^{2} \cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cos(a + b*x)**2*cot(a + b*x), x)","F",0
167,0,0,0,0.000000," ","integrate((d*x+c)*cos(b*x+a)**2*cot(b*x+a),x)","\int \left(c + d x\right) \cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cos(a + b*x)**2*cot(a + b*x), x)","F",0
168,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*cot(b*x+a)/(d*x+c),x)","\int \frac{\cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)**2*cot(a + b*x)/(c + d*x), x)","F",0
169,0,0,0,0.000000," ","integrate(cos(b*x+a)**2*cot(b*x+a)/(d*x+c)**2,x)","\int \frac{\cos^{2}{\left(a + b x \right)} \cot{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)**2*cot(a + b*x)/(c + d*x)**2, x)","F",0
170,0,0,0,0.000000," ","integrate((d*x+c)**m*cos(b*x+a)*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cos(a + b*x)*cot(a + b*x)**2, x)","F",0
171,0,0,0,0.000000," ","integrate((d*x+c)**4*cos(b*x+a)*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{4} \cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cos(a + b*x)*cot(a + b*x)**2, x)","F",0
172,0,0,0,0.000000," ","integrate((d*x+c)**3*cos(b*x+a)*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cos(a + b*x)*cot(a + b*x)**2, x)","F",0
173,0,0,0,0.000000," ","integrate((d*x+c)**2*cos(b*x+a)*cot(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cos(a + b*x)*cot(a + b*x)**2, x)","F",0
174,0,0,0,0.000000," ","integrate((d*x+c)*cos(b*x+a)*cot(b*x+a)**2,x)","\int \left(c + d x\right) \cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cos(a + b*x)*cot(a + b*x)**2, x)","F",0
175,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)**2/(d*x+c),x)","\int \frac{\cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cos(a + b*x)*cot(a + b*x)**2/(c + d*x), x)","F",0
176,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\cos{\left(a + b x \right)} \cot^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cos(a + b*x)*cot(a + b*x)**2/(c + d*x)**2, x)","F",0
177,0,0,0,0.000000," ","integrate((d*x+c)**m*cot(b*x+a)**3,x)","\int \left(c + d x\right)^{m} \cot^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*cot(a + b*x)**3, x)","F",0
178,0,0,0,0.000000," ","integrate((d*x+c)**4*cot(b*x+a)**3,x)","\int \left(c + d x\right)^{4} \cot^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*cot(a + b*x)**3, x)","F",0
179,0,0,0,0.000000," ","integrate((d*x+c)**3*cot(b*x+a)**3,x)","\int \left(c + d x\right)^{3} \cot^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*cot(a + b*x)**3, x)","F",0
180,0,0,0,0.000000," ","integrate((d*x+c)**2*cot(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \cot^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*cot(a + b*x)**3, x)","F",0
181,0,0,0,0.000000," ","integrate((d*x+c)*cot(b*x+a)**3,x)","\int \left(c + d x\right) \cot^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*cot(a + b*x)**3, x)","F",0
182,0,0,0,0.000000," ","integrate(cot(b*x+a)**3/(d*x+c),x)","\int \frac{\cot^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(cot(a + b*x)**3/(c + d*x), x)","F",0
183,0,0,0,0.000000," ","integrate(cot(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\cot^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(cot(a + b*x)**3/(c + d*x)**2, x)","F",0
184,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3*sin(b*x+a),x)","\int \sqrt{c + d x} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)*cos(a + b*x)**3, x)","F",0
187,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3*sin(b*x+a),x)","\int \sqrt{c + d x} \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)*cos(a + b*x)**3, x)","F",0
188,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2*cos(a + b*x)**3, x)","F",0
193,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\int \sqrt{c + d x} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x)*sin(a + b*x)**2*cos(a + b*x)**3, x)","F",0
194,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)*cos(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,0,0,0,0.000000," ","integrate(x**3*cos(x)**2*cot(x)**2,x)","\int x^{3} \cos^{2}{\left(x \right)} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral(x**3*cos(x)**2*cot(x)**2, x)","F",0
203,0,0,0,0.000000," ","integrate(x**2*cos(x)**2*cot(x)**2,x)","\int x^{2} \cos^{2}{\left(x \right)} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral(x**2*cos(x)**2*cot(x)**2, x)","F",0
204,0,0,0,0.000000," ","integrate(x*cos(x)**2*cot(x)**2,x)","\int x \cos^{2}{\left(x \right)} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral(x*cos(x)**2*cot(x)**2, x)","F",0
205,0,0,0,0.000000," ","integrate(x**3*cos(x)**2*cot(x)**3,x)","\int x^{3} \cos^{2}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx"," ",0,"Integral(x**3*cos(x)**2*cot(x)**3, x)","F",0
206,0,0,0,0.000000," ","integrate(x**2*cos(x)**2*cot(x)**3,x)","\int x^{2} \cos^{2}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx"," ",0,"Integral(x**2*cos(x)**2*cot(x)**3, x)","F",0
207,0,0,0,0.000000," ","integrate(x*cos(x)**2*cot(x)**3,x)","\int x \cos^{2}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx"," ",0,"Integral(x*cos(x)**2*cot(x)**3, x)","F",0
208,0,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)*sin(b*x+a),x)","\int \left(c + d x\right)^{m} \sin{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)*sec(a + b*x), x)","F",0
209,0,0,0,0.000000," ","integrate((d*x+c)**4*sec(b*x+a)*sin(b*x+a),x)","\int \left(c + d x\right)^{4} \sin{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*sin(a + b*x)*sec(a + b*x), x)","F",0
210,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)*sin(b*x+a),x)","\int \left(c + d x\right)^{3} \sin{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*sin(a + b*x)*sec(a + b*x), x)","F",0
211,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)*sin(b*x+a),x)","\int \left(c + d x\right)^{2} \sin{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sin(a + b*x)*sec(a + b*x), x)","F",0
212,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a),x)","\int \left(c + d x\right) \sin{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sin(a + b*x)*sec(a + b*x), x)","F",0
213,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)/(d*x+c),x)","\int \frac{\sin{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)*sec(a + b*x)/(c + d*x), x)","F",0
214,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)/(d*x+c)**2,x)","\int \frac{\sin{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)*sec(a + b*x)/(c + d*x)**2, x)","F",0
215,-1,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \sin^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*sin(a + b*x)**2*sec(a + b*x), x)","F",0
217,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)*sin(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \sin^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sin(a + b*x)**2*sec(a + b*x), x)","F",0
218,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a)**2,x)","\int \left(c + d x\right) \sin^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sin(a + b*x)**2*sec(a + b*x), x)","F",0
219,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**2/(d*x+c),x)","\int \frac{\sin^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)**2*sec(a + b*x)/(c + d*x), x)","F",0
220,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\sin^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)**2*sec(a + b*x)/(c + d*x)**2, x)","F",0
221,-2,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)*sin(b*x+a)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
222,-1,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)*sin(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \sin^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sin(a + b*x)**3*sec(a + b*x), x)","F",0
224,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a)**3,x)","\int \left(c + d x\right) \sin^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sin(a + b*x)**3*sec(a + b*x), x)","F",0
225,-2,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**3/(d*x+c),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
226,-2,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**3/(d*x+c)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
227,0,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)*sec(b*x+a),x)","\int \left(c + d x\right)^{m} \csc{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*csc(a + b*x)*sec(a + b*x), x)","F",0
228,0,0,0,0.000000," ","integrate((d*x+c)**4*csc(b*x+a)*sec(b*x+a),x)","\int \left(c + d x\right)^{4} \csc{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*csc(a + b*x)*sec(a + b*x), x)","F",0
229,0,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)*sec(b*x+a),x)","\int \left(c + d x\right)^{3} \csc{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*csc(a + b*x)*sec(a + b*x), x)","F",0
230,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)*sec(b*x+a),x)","\int \left(c + d x\right)^{2} \csc{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)*sec(a + b*x), x)","F",0
231,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a),x)","\int \left(c + d x\right) \csc{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)*sec(a + b*x), x)","F",0
232,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)/(d*x+c),x)","\int \frac{\csc{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)*sec(a + b*x)/(c + d*x), x)","F",0
233,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)/(d*x+c)**2,x)","\int \frac{\csc{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)*sec(a + b*x)/(c + d*x)**2, x)","F",0
234,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**2*sec(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,0,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**2*sec(b*x+a),x)","\int \left(c + d x\right)^{3} \csc^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*csc(a + b*x)**2*sec(a + b*x), x)","F",0
236,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**2*sec(b*x+a),x)","\int \left(c + d x\right)^{2} \csc^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)**2*sec(a + b*x), x)","F",0
237,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**2*sec(b*x+a),x)","\int \left(c + d x\right) \csc^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**2*sec(a + b*x), x)","F",0
238,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sec(b*x+a)/(d*x+c),x)","\int \frac{\csc^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**2*sec(a + b*x)/(c + d*x), x)","F",0
239,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sec(b*x+a)/(d*x+c)**2,x)","\int \frac{\csc^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**2*sec(a + b*x)/(c + d*x)**2, x)","F",0
240,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**3*sec(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**3*sec(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**3*sec(b*x+a),x)","\int \left(c + d x\right)^{2} \csc^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)**3*sec(a + b*x), x)","F",0
243,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**3*sec(b*x+a),x)","\int \left(c + d x\right) \csc^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**3*sec(a + b*x), x)","F",0
244,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)/(d*x+c),x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)/(c + d*x), x)","F",0
245,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)/(d*x+c)**2,x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)/(c + d*x)**2, x)","F",0
246,0,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)*tan(b*x+a),x)","\int \left(c + d x\right)^{m} \tan{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*tan(a + b*x)*sec(a + b*x), x)","F",0
247,0,0,0,0.000000," ","integrate((d*x+c)**4*sec(b*x+a)*tan(b*x+a),x)","\int \left(c + d x\right)^{4} \tan{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*tan(a + b*x)*sec(a + b*x), x)","F",0
248,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)*tan(b*x+a),x)","\int \left(c + d x\right)^{3} \tan{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*tan(a + b*x)*sec(a + b*x), x)","F",0
249,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)*tan(b*x+a),x)","\int \left(c + d x\right)^{2} \tan{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*tan(a + b*x)*sec(a + b*x), x)","F",0
250,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*tan(b*x+a),x)","\int \left(c + d x\right) \tan{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*tan(a + b*x)*sec(a + b*x), x)","F",0
251,0,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c),x)","\int \frac{\tan{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(tan(a + b*x)*sec(a + b*x)/(c + d*x), x)","F",0
252,0,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c)**2,x)","\int \frac{\tan{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(tan(a + b*x)*sec(a + b*x)/(c + d*x)**2, x)","F",0
253,0,0,0,0.000000," ","integrate((d*x+c)**m*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*tan(a + b*x)**2, x)","F",0
254,0,0,0,0.000000," ","integrate((d*x+c)**3*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*tan(a + b*x)**2, x)","F",0
255,0,0,0,0.000000," ","integrate((d*x+c)**2*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*tan(a + b*x)**2, x)","F",0
256,1,65,0,0.246092," ","integrate((d*x+c)*tan(b*x+a)**2,x)","\begin{cases} - c x - \frac{d x^{2}}{2} + \frac{c \tan{\left(a + b x \right)}}{b} + \frac{d x \tan{\left(a + b x \right)}}{b} - \frac{d \log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b^{2}} & \text{for}\: b \neq 0 \\\left(c x + \frac{d x^{2}}{2}\right) \tan^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*x - d*x**2/2 + c*tan(a + b*x)/b + d*x*tan(a + b*x)/b - d*log(tan(a + b*x)**2 + 1)/(2*b**2), Ne(b, 0)), ((c*x + d*x**2/2)*tan(a)**2, True))","A",0
257,0,0,0,0.000000," ","integrate(tan(b*x+a)**2/(d*x+c),x)","\int \frac{\tan^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(tan(a + b*x)**2/(c + d*x), x)","F",0
258,0,0,0,0.000000," ","integrate(tan(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\tan^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(tan(a + b*x)**2/(c + d*x)**2, x)","F",0
259,0,0,0,0.000000," ","integrate((d*x+c)**m*sin(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \sin{\left(a + b x \right)} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*sin(a + b*x)*tan(a + b*x)**2, x)","F",0
260,0,0,0,0.000000," ","integrate((d*x+c)**3*sin(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \sin{\left(a + b x \right)} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*sin(a + b*x)*tan(a + b*x)**2, x)","F",0
261,0,0,0,0.000000," ","integrate((d*x+c)**2*sin(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \sin{\left(a + b x \right)} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*sin(a + b*x)*tan(a + b*x)**2, x)","F",0
262,0,0,0,0.000000," ","integrate((d*x+c)*sin(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right) \sin{\left(a + b x \right)} \tan^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sin(a + b*x)*tan(a + b*x)**2, x)","F",0
263,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+a)**2/(d*x+c),x)","\int \frac{\sin{\left(a + b x \right)} \tan^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(a + b*x)*tan(a + b*x)**2/(c + d*x), x)","F",0
264,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\sin{\left(a + b x \right)} \tan^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(a + b*x)*tan(a + b*x)**2/(c + d*x)**2, x)","F",0
265,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate((d*x+c)**4*csc(b*x+a)*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,0,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)*sec(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \csc{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*csc(a + b*x)*sec(a + b*x)**2, x)","F",0
268,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)*sec(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \csc{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)*sec(a + b*x)**2, x)","F",0
269,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a)**2,x)","\int \left(c + d x\right) \csc{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)*sec(a + b*x)**2, x)","F",0
270,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)**2/(d*x+c),x)","\int \frac{\csc{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)*sec(a + b*x)**2/(c + d*x), x)","F",0
271,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\csc{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)*sec(a + b*x)**2/(c + d*x)**2, x)","F",0
272,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**2*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**2*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**2*sec(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \csc^{2}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)**2*sec(a + b*x)**2, x)","F",0
275,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**2*sec(b*x+a)**2,x)","\int \left(c + d x\right) \csc^{2}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**2*sec(a + b*x)**2, x)","F",0
276,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sec(b*x+a)**2/(d*x+c),x)","\int \frac{\csc^{2}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**2*sec(a + b*x)**2/(c + d*x), x)","F",0
277,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sec(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\csc^{2}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**2*sec(a + b*x)**2/(c + d*x)**2, x)","F",0
278,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**3*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**3*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**3*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**3*sec(b*x+a)**2,x)","\int \left(c + d x\right) \csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**3*sec(a + b*x)**2, x)","F",0
282,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)**2/(d*x+c),x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)**2/(c + d*x), x)","F",0
283,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)**2/(c + d*x)**2, x)","F",0
284,-1,0,0,0.000000," ","integrate(x**m*csc(b*x+a)**3*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate(x**3*csc(b*x+a)**3*sec(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,0,0,0,0.000000," ","integrate(x**2*csc(b*x+a)**3*sec(b*x+a)**2,x)","\int x^{2} \csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x**2*csc(a + b*x)**3*sec(a + b*x)**2, x)","F",0
287,0,0,0,0.000000," ","integrate(x*csc(b*x+a)**3*sec(b*x+a)**2,x)","\int x \csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(x*csc(a + b*x)**3*sec(a + b*x)**2, x)","F",0
288,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)**2/x,x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)**2/x, x)","F",0
289,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)**2/x**2,x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)**2/x**2, x)","F",0
290,0,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)**2*tan(b*x+a),x)","\int \left(c + d x\right)^{m} \tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*tan(a + b*x)*sec(a + b*x)**2, x)","F",0
291,0,0,0,0.000000," ","integrate((d*x+c)**4*sec(b*x+a)**2*tan(b*x+a),x)","\int \left(c + d x\right)^{4} \tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**4*tan(a + b*x)*sec(a + b*x)**2, x)","F",0
292,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)**2*tan(b*x+a),x)","\int \left(c + d x\right)^{3} \tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*tan(a + b*x)*sec(a + b*x)**2, x)","F",0
293,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)**2*tan(b*x+a),x)","\int \left(c + d x\right)^{2} \tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*tan(a + b*x)*sec(a + b*x)**2, x)","F",0
294,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)**2*tan(b*x+a),x)","\int \left(c + d x\right) \tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*tan(a + b*x)*sec(a + b*x)**2, x)","F",0
295,0,0,0,0.000000," ","integrate(sec(b*x+a)**2*tan(b*x+a)/(d*x+c),x)","\int \frac{\tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(tan(a + b*x)*sec(a + b*x)**2/(c + d*x), x)","F",0
296,0,0,0,0.000000," ","integrate(sec(b*x+a)**2*tan(b*x+a)/(d*x+c)**2,x)","\int \frac{\tan{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(tan(a + b*x)*sec(a + b*x)**2/(c + d*x)**2, x)","F",0
297,0,0,0,0.000000," ","integrate((d*x+c)**m*sec(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{m} \tan^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*tan(a + b*x)**2*sec(a + b*x), x)","F",0
298,0,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{3} \tan^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*tan(a + b*x)**2*sec(a + b*x), x)","F",0
299,0,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right)^{2} \tan^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*tan(a + b*x)**2*sec(a + b*x), x)","F",0
300,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*tan(b*x+a)**2,x)","\int \left(c + d x\right) \tan^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*tan(a + b*x)**2*sec(a + b*x), x)","F",0
301,0,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)**2/(d*x+c),x)","\int \frac{\tan^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(tan(a + b*x)**2*sec(a + b*x)/(c + d*x), x)","F",0
302,0,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)**2/(d*x+c)**2,x)","\int \frac{\tan^{2}{\left(a + b x \right)} \sec{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(tan(a + b*x)**2*sec(a + b*x)/(c + d*x)**2, x)","F",0
303,0,0,0,0.000000," ","integrate((d*x+c)**m*tan(b*x+a)**3,x)","\int \left(c + d x\right)^{m} \tan^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**m*tan(a + b*x)**3, x)","F",0
304,0,0,0,0.000000," ","integrate((d*x+c)**3*tan(b*x+a)**3,x)","\int \left(c + d x\right)^{3} \tan^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**3*tan(a + b*x)**3, x)","F",0
305,0,0,0,0.000000," ","integrate((d*x+c)**2*tan(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \tan^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*tan(a + b*x)**3, x)","F",0
306,0,0,0,0.000000," ","integrate((d*x+c)*tan(b*x+a)**3,x)","\int \left(c + d x\right) \tan^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*tan(a + b*x)**3, x)","F",0
307,0,0,0,0.000000," ","integrate(tan(b*x+a)**3/(d*x+c),x)","\int \frac{\tan^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(tan(a + b*x)**3/(c + d*x), x)","F",0
308,0,0,0,0.000000," ","integrate(tan(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\tan^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(tan(a + b*x)**3/(c + d*x)**2, x)","F",0
309,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate((d*x+c)**4*csc(b*x+a)*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,0,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)*sec(b*x+a)**3,x)","\int \left(c + d x\right)^{2} \csc{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)**2*csc(a + b*x)*sec(a + b*x)**3, x)","F",0
313,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a)**3,x)","\int \left(c + d x\right) \csc{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)*sec(a + b*x)**3, x)","F",0
314,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)**3/(d*x+c),x)","\int \frac{\csc{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)*sec(a + b*x)**3/(c + d*x), x)","F",0
315,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\csc{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)*sec(a + b*x)**3/(c + d*x)**2, x)","F",0
316,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**2*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**2*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**2*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**2*sec(b*x+a)**3,x)","\int \left(c + d x\right) \csc^{2}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*csc(a + b*x)**2*sec(a + b*x)**3, x)","F",0
320,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sec(b*x+a)**3/(d*x+c),x)","\int \frac{\csc^{2}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**2*sec(a + b*x)**3/(c + d*x), x)","F",0
321,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sec(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\csc^{2}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**2*sec(a + b*x)**3/(c + d*x)**2, x)","F",0
322,-1,0,0,0.000000," ","integrate((d*x+c)**m*csc(b*x+a)**3*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**3*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**3*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**3*sec(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)**3/(d*x+c),x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}}{c + d x}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)**3/(c + d*x), x)","F",0
327,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sec(b*x+a)**3/(d*x+c)**2,x)","\int \frac{\csc^{3}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(csc(a + b*x)**3*sec(a + b*x)**3/(c + d*x)**2, x)","F",0
328,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)**(5/2)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)**(3/2)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,0,0,0,0.000000," ","integrate(x*sin(b*x+a)*cos(b*x+a)**(1/2),x)","\int x \sin{\left(a + b x \right)} \sqrt{\cos{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sin(a + b*x)*sqrt(cos(a + b*x)), x)","F",0
331,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)**(1/2),x)","\int \frac{x \sin{\left(a + b x \right)}}{\sqrt{\cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x*sin(a + b*x)/sqrt(cos(a + b*x)), x)","F",0
332,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)**(3/2),x)","\int \frac{x \sin{\left(a + b x \right)}}{\cos^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sin(a + b*x)/cos(a + b*x)**(3/2), x)","F",0
333,-1,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(x*sec(b*x+a)**(9/2)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(x*sec(b*x+a)**(7/2)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(x*sec(b*x+a)**(5/2)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(x*sec(b*x+a)**(3/2)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,0,0,0,0.000000," ","integrate(x*sin(b*x+a)*sec(b*x+a)**(1/2),x)","\int x \sin{\left(a + b x \right)} \sqrt{\sec{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sin(a + b*x)*sqrt(sec(a + b*x)), x)","F",0
341,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)**(1/2),x)","\int \frac{x \sin{\left(a + b x \right)}}{\sqrt{\sec{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x*sin(a + b*x)/sqrt(sec(a + b*x)), x)","F",0
342,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)**(3/2),x)","\int \frac{x \sin{\left(a + b x \right)}}{\sec^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sin(a + b*x)/sec(a + b*x)**(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)**(5/2),x)","\int \frac{x \sin{\left(a + b x \right)}}{\sec^{\frac{5}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*sin(a + b*x)/sec(a + b*x)**(5/2), x)","F",0
344,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)**(3/2),x)","\int x \sin^{\frac{3}{2}}{\left(a + b x \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x*sin(a + b*x)**(3/2)*cos(a + b*x), x)","F",0
346,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)**(1/2),x)","\int x \sqrt{\sin{\left(a + b x \right)}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(x*sqrt(sin(a + b*x))*cos(a + b*x), x)","F",0
347,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)**(1/2),x)","\int \frac{x \cos{\left(a + b x \right)}}{\sqrt{\sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x*cos(a + b*x)/sqrt(sin(a + b*x)), x)","F",0
348,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)**(3/2),x)","\int \frac{x \cos{\left(a + b x \right)}}{\sin^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*cos(a + b*x)/sin(a + b*x)**(3/2), x)","F",0
349,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)**(5/2),x)","\int \frac{x \cos{\left(a + b x \right)}}{\sin^{\frac{5}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*cos(a + b*x)/sin(a + b*x)**(5/2), x)","F",0
350,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)**(1/2),x)","\int x \cos{\left(a + b x \right)} \sqrt{\csc{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*cos(a + b*x)*sqrt(csc(a + b*x)), x)","F",0
357,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)**(1/2),x)","\int \frac{x \cos{\left(a + b x \right)}}{\sqrt{\csc{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x*cos(a + b*x)/sqrt(csc(a + b*x)), x)","F",0
358,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)**(3/2),x)","\int \frac{x \cos{\left(a + b x \right)}}{\csc^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*cos(a + b*x)/csc(a + b*x)**(3/2), x)","F",0
359,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)**(5/2),x)","\int \frac{x \cos{\left(a + b x \right)}}{\csc^{\frac{5}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*cos(a + b*x)/csc(a + b*x)**(5/2), x)","F",0
360,1,37,0,1.884037," ","integrate(x*csc(x)*sin(3*x),x)","- x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} + \frac{3 x^{2}}{2} + 2 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}"," ",0,"-x**2*sin(x)**2 - x**2*cos(x)**2 + 3*x**2/2 + 2*x*sin(x)*cos(x) + cos(x)**2","A",0
361,1,440,0,25.349179," ","integrate((d*x+c)**4*csc(x)*sin(3*x),x)","c^{4} x + c^{4} \sin{\left(2 x \right)} - 4 c^{3} d x^{2} \sin^{2}{\left(x \right)} - 4 c^{3} d x^{2} \cos^{2}{\left(x \right)} + 6 c^{3} d x^{2} + 8 c^{3} d x \sin{\left(x \right)} \cos{\left(x \right)} + 4 c^{3} d \cos^{2}{\left(x \right)} - 4 c^{2} d^{2} x^{3} \sin^{2}{\left(x \right)} - 4 c^{2} d^{2} x^{3} \cos^{2}{\left(x \right)} + 6 c^{2} d^{2} x^{3} + 12 c^{2} d^{2} x^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 6 c^{2} d^{2} x \sin^{2}{\left(x \right)} + 6 c^{2} d^{2} x \cos^{2}{\left(x \right)} - 6 c^{2} d^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 2 c d^{3} x^{4} \sin^{2}{\left(x \right)} - 2 c d^{3} x^{4} \cos^{2}{\left(x \right)} + 3 c d^{3} x^{4} + 8 c d^{3} x^{3} \sin{\left(x \right)} \cos{\left(x \right)} - 6 c d^{3} x^{2} \sin^{2}{\left(x \right)} + 6 c d^{3} x^{2} \cos^{2}{\left(x \right)} - 12 c d^{3} x \sin{\left(x \right)} \cos{\left(x \right)} - 6 c d^{3} \cos^{2}{\left(x \right)} - \frac{2 d^{4} x^{5} \sin^{2}{\left(x \right)}}{5} - \frac{2 d^{4} x^{5} \cos^{2}{\left(x \right)}}{5} + \frac{3 d^{4} x^{5}}{5} + 2 d^{4} x^{4} \sin{\left(x \right)} \cos{\left(x \right)} - 2 d^{4} x^{3} \sin^{2}{\left(x \right)} + 2 d^{4} x^{3} \cos^{2}{\left(x \right)} - 6 d^{4} x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 3 d^{4} x \sin^{2}{\left(x \right)} - 3 d^{4} x \cos^{2}{\left(x \right)} + 3 d^{4} \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"c**4*x + c**4*sin(2*x) - 4*c**3*d*x**2*sin(x)**2 - 4*c**3*d*x**2*cos(x)**2 + 6*c**3*d*x**2 + 8*c**3*d*x*sin(x)*cos(x) + 4*c**3*d*cos(x)**2 - 4*c**2*d**2*x**3*sin(x)**2 - 4*c**2*d**2*x**3*cos(x)**2 + 6*c**2*d**2*x**3 + 12*c**2*d**2*x**2*sin(x)*cos(x) - 6*c**2*d**2*x*sin(x)**2 + 6*c**2*d**2*x*cos(x)**2 - 6*c**2*d**2*sin(x)*cos(x) - 2*c*d**3*x**4*sin(x)**2 - 2*c*d**3*x**4*cos(x)**2 + 3*c*d**3*x**4 + 8*c*d**3*x**3*sin(x)*cos(x) - 6*c*d**3*x**2*sin(x)**2 + 6*c*d**3*x**2*cos(x)**2 - 12*c*d**3*x*sin(x)*cos(x) - 6*c*d**3*cos(x)**2 - 2*d**4*x**5*sin(x)**2/5 - 2*d**4*x**5*cos(x)**2/5 + 3*d**4*x**5/5 + 2*d**4*x**4*sin(x)*cos(x) - 2*d**4*x**3*sin(x)**2 + 2*d**4*x**3*cos(x)**2 - 6*d**4*x**2*sin(x)*cos(x) + 3*d**4*x*sin(x)**2 - 3*d**4*x*cos(x)**2 + 3*d**4*sin(x)*cos(x)","B",0
362,1,289,0,13.049221," ","integrate((d*x+c)**3*csc(x)*sin(3*x),x)","c^{3} x + c^{3} \sin{\left(2 x \right)} - 3 c^{2} d x^{2} \sin^{2}{\left(x \right)} - 3 c^{2} d x^{2} \cos^{2}{\left(x \right)} + \frac{9 c^{2} d x^{2}}{2} + 6 c^{2} d x \sin{\left(x \right)} \cos{\left(x \right)} + 3 c^{2} d \cos^{2}{\left(x \right)} - 2 c d^{2} x^{3} \sin^{2}{\left(x \right)} - 2 c d^{2} x^{3} \cos^{2}{\left(x \right)} + 3 c d^{2} x^{3} + 6 c d^{2} x^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 3 c d^{2} x \sin^{2}{\left(x \right)} + 3 c d^{2} x \cos^{2}{\left(x \right)} - 3 c d^{2} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{d^{3} x^{4} \sin^{2}{\left(x \right)}}{2} - \frac{d^{3} x^{4} \cos^{2}{\left(x \right)}}{2} + \frac{3 d^{3} x^{4}}{4} + 2 d^{3} x^{3} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{3 d^{3} x^{2} \sin^{2}{\left(x \right)}}{2} + \frac{3 d^{3} x^{2} \cos^{2}{\left(x \right)}}{2} - 3 d^{3} x \sin{\left(x \right)} \cos{\left(x \right)} - \frac{3 d^{3} \cos^{2}{\left(x \right)}}{2}"," ",0,"c**3*x + c**3*sin(2*x) - 3*c**2*d*x**2*sin(x)**2 - 3*c**2*d*x**2*cos(x)**2 + 9*c**2*d*x**2/2 + 6*c**2*d*x*sin(x)*cos(x) + 3*c**2*d*cos(x)**2 - 2*c*d**2*x**3*sin(x)**2 - 2*c*d**2*x**3*cos(x)**2 + 3*c*d**2*x**3 + 6*c*d**2*x**2*sin(x)*cos(x) - 3*c*d**2*x*sin(x)**2 + 3*c*d**2*x*cos(x)**2 - 3*c*d**2*sin(x)*cos(x) - d**3*x**4*sin(x)**2/2 - d**3*x**4*cos(x)**2/2 + 3*d**3*x**4/4 + 2*d**3*x**3*sin(x)*cos(x) - 3*d**3*x**2*sin(x)**2/2 + 3*d**3*x**2*cos(x)**2/2 - 3*d**3*x*sin(x)*cos(x) - 3*d**3*cos(x)**2/2","B",0
363,1,155,0,6.972035," ","integrate((d*x+c)**2*csc(x)*sin(3*x),x)","c^{2} x + c^{2} \sin{\left(2 x \right)} - 2 c d x^{2} \sin^{2}{\left(x \right)} - 2 c d x^{2} \cos^{2}{\left(x \right)} + 3 c d x^{2} + 4 c d x \sin{\left(x \right)} \cos{\left(x \right)} + 2 c d \cos^{2}{\left(x \right)} - \frac{2 d^{2} x^{3} \sin^{2}{\left(x \right)}}{3} - \frac{2 d^{2} x^{3} \cos^{2}{\left(x \right)}}{3} + d^{2} x^{3} + 2 d^{2} x^{2} \sin{\left(x \right)} \cos{\left(x \right)} - d^{2} x \sin^{2}{\left(x \right)} + d^{2} x \cos^{2}{\left(x \right)} - d^{2} \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"c**2*x + c**2*sin(2*x) - 2*c*d*x**2*sin(x)**2 - 2*c*d*x**2*cos(x)**2 + 3*c*d*x**2 + 4*c*d*x*sin(x)*cos(x) + 2*c*d*cos(x)**2 - 2*d**2*x**3*sin(x)**2/3 - 2*d**2*x**3*cos(x)**2/3 + d**2*x**3 + 2*d**2*x**2*sin(x)*cos(x) - d**2*x*sin(x)**2 + d**2*x*cos(x)**2 - d**2*sin(x)*cos(x)","B",0
364,1,56,0,3.851622," ","integrate((d*x+c)*csc(x)*sin(3*x),x)","c x + c \sin{\left(2 x \right)} - d x^{2} \sin^{2}{\left(x \right)} - d x^{2} \cos^{2}{\left(x \right)} + \frac{3 d x^{2}}{2} + 2 d x \sin{\left(x \right)} \cos{\left(x \right)} + d \cos^{2}{\left(x \right)}"," ",0,"c*x + c*sin(2*x) - d*x**2*sin(x)**2 - d*x**2*cos(x)**2 + 3*d*x**2/2 + 2*d*x*sin(x)*cos(x) + d*cos(x)**2","A",0
365,0,0,0,0.000000," ","integrate(csc(x)*sin(3*x)/(d*x+c),x)","\int \frac{\sin{\left(3 x \right)} \csc{\left(x \right)}}{c + d x}\, dx"," ",0,"Integral(sin(3*x)*csc(x)/(c + d*x), x)","F",0
366,0,0,0,0.000000," ","integrate(csc(x)*sin(3*x)/(d*x+c)**2,x)","\int \frac{\sin{\left(3 x \right)} \csc{\left(x \right)}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral(sin(3*x)*csc(x)/(c + d*x)**2, x)","F",0
367,0,0,0,0.000000," ","integrate(csc(x)*sin(3*x)/(d*x+c)**3,x)","\int \frac{\sin{\left(3 x \right)} \csc{\left(x \right)}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral(sin(3*x)*csc(x)/(c + d*x)**3, x)","F",0
368,-1,0,0,0.000000," ","integrate((d*x+c)**4*csc(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)*sin(3*b*x+3*a),x)","\int \left(c + d x\right) \sin{\left(3 a + 3 b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((c + d*x)*sin(3*a + 3*b*x)*csc(a + b*x), x)","F",0
372,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((d*x+c)**3*csc(b*x+a)**2*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((d*x+c)**2*csc(b*x+a)**2*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)**2*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(3*b*x+3*a)/(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(3*b*x+3*a)/(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(3*b*x+3*a)/(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((d*x+c)**4*sec(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*sin(3*b*x+3*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-2,0,0,0.000000," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
387,-2,0,0,0.000000," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
388,-1,0,0,0.000000," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-2,0,0,0.000000," ","integrate((d*x+c)**3*sec(b*x+a)**2*sin(3*b*x+3*a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
390,-2,0,0,0.000000," ","integrate((d*x+c)**2*sec(b*x+a)**2*sin(3*b*x+3*a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
391,-2,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)**2*sin(3*b*x+3*a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
392,-1,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(3*b*x+3*a)/(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(3*b*x+3*a)/(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(3*b*x+3*a)/(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,0,0,0,0.000000," ","integrate(x*cos(2*x)*sec(x),x)","\int x \cos{\left(2 x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x*cos(2*x)*sec(x), x)","F",0
396,1,144,0,5.739020," ","integrate(x*cos(2*x)*sec(x)**2,x)","x^{2} + \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}"," ",0,"x**2 + 2*x*tan(x/2)/(tan(x/2)**2 - 1) - log(tan(x/2) - 1)*tan(x/2)**2/(tan(x/2)**2 - 1) + log(tan(x/2) - 1)/(tan(x/2)**2 - 1) - log(tan(x/2) + 1)*tan(x/2)**2/(tan(x/2)**2 - 1) + log(tan(x/2) + 1)/(tan(x/2)**2 - 1) + log(tan(x/2)**2 + 1)*tan(x/2)**2/(tan(x/2)**2 - 1) - log(tan(x/2)**2 + 1)/(tan(x/2)**2 - 1)","B",0
397,0,0,0,0.000000," ","integrate(x*cos(2*x)*sec(x)**3,x)","\int x \cos{\left(2 x \right)} \sec^{3}{\left(x \right)}\, dx"," ",0,"Integral(x*cos(2*x)*sec(x)**3, x)","F",0
