1,1,394,0,0.806317," ","integrate(x**m*(B*x+A)*(c*x**2+b*x),x)","\begin{cases} - \frac{A b}{2 x^{2}} - \frac{A c}{x} - \frac{B b}{x} + B c \log{\left(x \right)} & \text{for}\: m = -4 \\- \frac{A b}{x} + A c \log{\left(x \right)} + B b \log{\left(x \right)} + B c x & \text{for}\: m = -3 \\A b \log{\left(x \right)} + A c x + B b x + \frac{B c x^{2}}{2} & \text{for}\: m = -2 \\\frac{A b m^{2} x^{2} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{7 A b m x^{2} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{12 A b x^{2} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{A c m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{6 A c m x^{3} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{8 A c x^{3} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{B b m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{6 B b m x^{3} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{8 B b x^{3} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{B c m^{2} x^{4} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{5 B c m x^{4} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{6 B c x^{4} x^{m}}{m^{3} + 9 m^{2} + 26 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*b/(2*x**2) - A*c/x - B*b/x + B*c*log(x), Eq(m, -4)), (-A*b/x + A*c*log(x) + B*b*log(x) + B*c*x, Eq(m, -3)), (A*b*log(x) + A*c*x + B*b*x + B*c*x**2/2, Eq(m, -2)), (A*b*m**2*x**2*x**m/(m**3 + 9*m**2 + 26*m + 24) + 7*A*b*m*x**2*x**m/(m**3 + 9*m**2 + 26*m + 24) + 12*A*b*x**2*x**m/(m**3 + 9*m**2 + 26*m + 24) + A*c*m**2*x**3*x**m/(m**3 + 9*m**2 + 26*m + 24) + 6*A*c*m*x**3*x**m/(m**3 + 9*m**2 + 26*m + 24) + 8*A*c*x**3*x**m/(m**3 + 9*m**2 + 26*m + 24) + B*b*m**2*x**3*x**m/(m**3 + 9*m**2 + 26*m + 24) + 6*B*b*m*x**3*x**m/(m**3 + 9*m**2 + 26*m + 24) + 8*B*b*x**3*x**m/(m**3 + 9*m**2 + 26*m + 24) + B*c*m**2*x**4*x**m/(m**3 + 9*m**2 + 26*m + 24) + 5*B*c*m*x**4*x**m/(m**3 + 9*m**2 + 26*m + 24) + 6*B*c*x**4*x**m/(m**3 + 9*m**2 + 26*m + 24), True))","A",0
2,1,29,0,0.065364," ","integrate(x**3*(B*x+A)*(c*x**2+b*x),x)","\frac{A b x^{5}}{5} + \frac{B c x^{7}}{7} + x^{6} \left(\frac{A c}{6} + \frac{B b}{6}\right)"," ",0,"A*b*x**5/5 + B*c*x**7/7 + x**6*(A*c/6 + B*b/6)","A",0
3,1,29,0,0.064786," ","integrate(x**2*(B*x+A)*(c*x**2+b*x),x)","\frac{A b x^{4}}{4} + \frac{B c x^{6}}{6} + x^{5} \left(\frac{A c}{5} + \frac{B b}{5}\right)"," ",0,"A*b*x**4/4 + B*c*x**6/6 + x**5*(A*c/5 + B*b/5)","A",0
4,1,29,0,0.066243," ","integrate(x*(B*x+A)*(c*x**2+b*x),x)","\frac{A b x^{3}}{3} + \frac{B c x^{5}}{5} + x^{4} \left(\frac{A c}{4} + \frac{B b}{4}\right)"," ",0,"A*b*x**3/3 + B*c*x**5/5 + x**4*(A*c/4 + B*b/4)","A",0
5,1,29,0,0.063992," ","integrate((B*x+A)*(c*x**2+b*x),x)","\frac{A b x^{2}}{2} + \frac{B c x^{4}}{4} + x^{3} \left(\frac{A c}{3} + \frac{B b}{3}\right)"," ",0,"A*b*x**2/2 + B*c*x**4/4 + x**3*(A*c/3 + B*b/3)","A",0
6,1,26,0,0.063764," ","integrate((B*x+A)*(c*x**2+b*x)/x,x)","A b x + \frac{B c x^{3}}{3} + x^{2} \left(\frac{A c}{2} + \frac{B b}{2}\right)"," ",0,"A*b*x + B*c*x**3/3 + x**2*(A*c/2 + B*b/2)","A",0
7,1,22,0,0.113120," ","integrate((B*x+A)*(c*x**2+b*x)/x**2,x)","A b \log{\left(x \right)} + \frac{B c x^{2}}{2} + x \left(A c + B b\right)"," ",0,"A*b*log(x) + B*c*x**2/2 + x*(A*c + B*b)","A",0
8,1,19,0,0.148136," ","integrate((B*x+A)*(c*x**2+b*x)/x**3,x)","- \frac{A b}{x} + B c x + \left(A c + B b\right) \log{\left(x \right)}"," ",0,"-A*b/x + B*c*x + (A*c + B*b)*log(x)","A",0
9,1,27,0,0.224406," ","integrate((B*x+A)*(c*x**2+b*x)/x**4,x)","B c \log{\left(x \right)} + \frac{- A b + x \left(- 2 A c - 2 B b\right)}{2 x^{2}}"," ",0,"B*c*log(x) + (-A*b + x*(-2*A*c - 2*B*b))/(2*x**2)","A",0
10,1,31,0,0.279895," ","integrate((B*x+A)*(c*x**2+b*x)/x**5,x)","\frac{- 2 A b - 6 B c x^{2} + x \left(- 3 A c - 3 B b\right)}{6 x^{3}}"," ",0,"(-2*A*b - 6*B*c*x**2 + x*(-3*A*c - 3*B*b))/(6*x**3)","A",0
11,1,31,0,0.337719," ","integrate((B*x+A)*(c*x**2+b*x)/x**6,x)","\frac{- 3 A b - 6 B c x^{2} + x \left(- 4 A c - 4 B b\right)}{12 x^{4}}"," ",0,"(-3*A*b - 6*B*c*x**2 + x*(-4*A*c - 4*B*b))/(12*x**4)","A",0
12,1,31,0,0.409711," ","integrate((B*x+A)*(c*x**2+b*x)/x**7,x)","\frac{- 12 A b - 20 B c x^{2} + x \left(- 15 A c - 15 B b\right)}{60 x^{5}}"," ",0,"(-12*A*b - 20*B*c*x**2 + x*(-15*A*c - 15*B*b))/(60*x**5)","A",0
13,1,31,0,0.485346," ","integrate((B*x+A)*(c*x**2+b*x)/x**8,x)","\frac{- 10 A b - 15 B c x^{2} + x \left(- 12 A c - 12 B b\right)}{60 x^{6}}"," ",0,"(-10*A*b - 15*B*c*x**2 + x*(-12*A*c - 12*B*b))/(60*x**6)","A",0
14,1,1027,0,1.551794," ","integrate(x**m*(B*x+A)*(c*x**2+b*x)**2,x)","\begin{cases} - \frac{A b^{2}}{3 x^{3}} - \frac{A b c}{x^{2}} - \frac{A c^{2}}{x} - \frac{B b^{2}}{2 x^{2}} - \frac{2 B b c}{x} + B c^{2} \log{\left(x \right)} & \text{for}\: m = -6 \\- \frac{A b^{2}}{2 x^{2}} - \frac{2 A b c}{x} + A c^{2} \log{\left(x \right)} - \frac{B b^{2}}{x} + 2 B b c \log{\left(x \right)} + B c^{2} x & \text{for}\: m = -5 \\- \frac{A b^{2}}{x} + 2 A b c \log{\left(x \right)} + A c^{2} x + B b^{2} \log{\left(x \right)} + 2 B b c x + \frac{B c^{2} x^{2}}{2} & \text{for}\: m = -4 \\A b^{2} \log{\left(x \right)} + 2 A b c x + \frac{A c^{2} x^{2}}{2} + B b^{2} x + B b c x^{2} + \frac{B c^{2} x^{3}}{3} & \text{for}\: m = -3 \\\frac{A b^{2} m^{3} x^{3} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{15 A b^{2} m^{2} x^{3} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{74 A b^{2} m x^{3} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{120 A b^{2} x^{3} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{2 A b c m^{3} x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{28 A b c m^{2} x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{126 A b c m x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{180 A b c x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{A c^{2} m^{3} x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{13 A c^{2} m^{2} x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{54 A c^{2} m x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{72 A c^{2} x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{B b^{2} m^{3} x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{14 B b^{2} m^{2} x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{63 B b^{2} m x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{90 B b^{2} x^{4} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{2 B b c m^{3} x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{26 B b c m^{2} x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{108 B b c m x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{144 B b c x^{5} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{B c^{2} m^{3} x^{6} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{12 B c^{2} m^{2} x^{6} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{47 B c^{2} m x^{6} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} + \frac{60 B c^{2} x^{6} x^{m}}{m^{4} + 18 m^{3} + 119 m^{2} + 342 m + 360} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*b**2/(3*x**3) - A*b*c/x**2 - A*c**2/x - B*b**2/(2*x**2) - 2*B*b*c/x + B*c**2*log(x), Eq(m, -6)), (-A*b**2/(2*x**2) - 2*A*b*c/x + A*c**2*log(x) - B*b**2/x + 2*B*b*c*log(x) + B*c**2*x, Eq(m, -5)), (-A*b**2/x + 2*A*b*c*log(x) + A*c**2*x + B*b**2*log(x) + 2*B*b*c*x + B*c**2*x**2/2, Eq(m, -4)), (A*b**2*log(x) + 2*A*b*c*x + A*c**2*x**2/2 + B*b**2*x + B*b*c*x**2 + B*c**2*x**3/3, Eq(m, -3)), (A*b**2*m**3*x**3*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 15*A*b**2*m**2*x**3*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 74*A*b**2*m*x**3*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 120*A*b**2*x**3*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 2*A*b*c*m**3*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 28*A*b*c*m**2*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 126*A*b*c*m*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 180*A*b*c*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + A*c**2*m**3*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 13*A*c**2*m**2*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 54*A*c**2*m*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 72*A*c**2*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + B*b**2*m**3*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 14*B*b**2*m**2*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 63*B*b**2*m*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 90*B*b**2*x**4*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 2*B*b*c*m**3*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 26*B*b*c*m**2*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 108*B*b*c*m*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 144*B*b*c*x**5*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + B*c**2*m**3*x**6*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 12*B*c**2*m**2*x**6*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 47*B*c**2*m*x**6*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360) + 60*B*c**2*x**6*x**m/(m**4 + 18*m**3 + 119*m**2 + 342*m + 360), True))","A",0
15,1,54,0,0.075551," ","integrate(x**3*(B*x+A)*(c*x**2+b*x)**2,x)","\frac{A b^{2} x^{6}}{6} + \frac{B c^{2} x^{9}}{9} + x^{8} \left(\frac{A c^{2}}{8} + \frac{B b c}{4}\right) + x^{7} \left(\frac{2 A b c}{7} + \frac{B b^{2}}{7}\right)"," ",0,"A*b**2*x**6/6 + B*c**2*x**9/9 + x**8*(A*c**2/8 + B*b*c/4) + x**7*(2*A*b*c/7 + B*b**2/7)","A",0
16,1,54,0,0.080526," ","integrate(x**2*(B*x+A)*(c*x**2+b*x)**2,x)","\frac{A b^{2} x^{5}}{5} + \frac{B c^{2} x^{8}}{8} + x^{7} \left(\frac{A c^{2}}{7} + \frac{2 B b c}{7}\right) + x^{6} \left(\frac{A b c}{3} + \frac{B b^{2}}{6}\right)"," ",0,"A*b**2*x**5/5 + B*c**2*x**8/8 + x**7*(A*c**2/7 + 2*B*b*c/7) + x**6*(A*b*c/3 + B*b**2/6)","A",0
17,1,54,0,0.076827," ","integrate(x*(B*x+A)*(c*x**2+b*x)**2,x)","\frac{A b^{2} x^{4}}{4} + \frac{B c^{2} x^{7}}{7} + x^{6} \left(\frac{A c^{2}}{6} + \frac{B b c}{3}\right) + x^{5} \left(\frac{2 A b c}{5} + \frac{B b^{2}}{5}\right)"," ",0,"A*b**2*x**4/4 + B*c**2*x**7/7 + x**6*(A*c**2/6 + B*b*c/3) + x**5*(2*A*b*c/5 + B*b**2/5)","A",0
18,1,54,0,0.075674," ","integrate((B*x+A)*(c*x**2+b*x)**2,x)","\frac{A b^{2} x^{3}}{3} + \frac{B c^{2} x^{6}}{6} + x^{5} \left(\frac{A c^{2}}{5} + \frac{2 B b c}{5}\right) + x^{4} \left(\frac{A b c}{2} + \frac{B b^{2}}{4}\right)"," ",0,"A*b**2*x**3/3 + B*c**2*x**6/6 + x**5*(A*c**2/5 + 2*B*b*c/5) + x**4*(A*b*c/2 + B*b**2/4)","A",0
19,1,54,0,0.077732," ","integrate((B*x+A)*(c*x**2+b*x)**2/x,x)","\frac{A b^{2} x^{2}}{2} + \frac{B c^{2} x^{5}}{5} + x^{4} \left(\frac{A c^{2}}{4} + \frac{B b c}{2}\right) + x^{3} \left(\frac{2 A b c}{3} + \frac{B b^{2}}{3}\right)"," ",0,"A*b**2*x**2/2 + B*c**2*x**5/5 + x**4*(A*c**2/4 + B*b*c/2) + x**3*(2*A*b*c/3 + B*b**2/3)","A",0
20,1,49,0,0.078051," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**2,x)","A b^{2} x + \frac{B c^{2} x^{4}}{4} + x^{3} \left(\frac{A c^{2}}{3} + \frac{2 B b c}{3}\right) + x^{2} \left(A b c + \frac{B b^{2}}{2}\right)"," ",0,"A*b**2*x + B*c**2*x**4/4 + x**3*(A*c**2/3 + 2*B*b*c/3) + x**2*(A*b*c + B*b**2/2)","A",0
21,1,46,0,0.143613," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**3,x)","A b^{2} \log{\left(x \right)} + \frac{B c^{2} x^{3}}{3} + x^{2} \left(\frac{A c^{2}}{2} + B b c\right) + x \left(2 A b c + B b^{2}\right)"," ",0,"A*b**2*log(x) + B*c**2*x**3/3 + x**2*(A*c**2/2 + B*b*c) + x*(2*A*b*c + B*b**2)","A",0
22,1,42,0,0.186786," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**4,x)","- \frac{A b^{2}}{x} + \frac{B c^{2} x^{2}}{2} + b \left(2 A c + B b\right) \log{\left(x \right)} + x \left(A c^{2} + 2 B b c\right)"," ",0,"-A*b**2/x + B*c**2*x**2/2 + b*(2*A*c + B*b)*log(x) + x*(A*c**2 + 2*B*b*c)","A",0
23,1,46,0,0.332035," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**5,x)","B c^{2} x + c \left(A c + 2 B b\right) \log{\left(x \right)} + \frac{- A b^{2} + x \left(- 4 A b c - 2 B b^{2}\right)}{2 x^{2}}"," ",0,"B*c**2*x + c*(A*c + 2*B*b)*log(x) + (-A*b**2 + x*(-4*A*b*c - 2*B*b**2))/(2*x**2)","A",0
24,1,54,0,0.534428," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**6,x)","B c^{2} \log{\left(x \right)} + \frac{- 2 A b^{2} + x^{2} \left(- 6 A c^{2} - 12 B b c\right) + x \left(- 6 A b c - 3 B b^{2}\right)}{6 x^{3}}"," ",0,"B*c**2*log(x) + (-2*A*b**2 + x**2*(-6*A*c**2 - 12*B*b*c) + x*(-6*A*b*c - 3*B*b**2))/(6*x**3)","A",0
25,1,56,0,0.679837," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**7,x)","\frac{- 3 A b^{2} - 12 B c^{2} x^{3} + x^{2} \left(- 6 A c^{2} - 12 B b c\right) + x \left(- 8 A b c - 4 B b^{2}\right)}{12 x^{4}}"," ",0,"(-3*A*b**2 - 12*B*c**2*x**3 + x**2*(-6*A*c**2 - 12*B*b*c) + x*(-8*A*b*c - 4*B*b**2))/(12*x**4)","A",0
26,1,56,0,0.856848," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**8,x)","\frac{- 12 A b^{2} - 30 B c^{2} x^{3} + x^{2} \left(- 20 A c^{2} - 40 B b c\right) + x \left(- 30 A b c - 15 B b^{2}\right)}{60 x^{5}}"," ",0,"(-12*A*b**2 - 30*B*c**2*x**3 + x**2*(-20*A*c**2 - 40*B*b*c) + x*(-30*A*b*c - 15*B*b**2))/(60*x**5)","A",0
27,1,2026,0,2.761460," ","integrate(x**m*(B*x+A)*(c*x**2+b*x)**3,x)","\begin{cases} - \frac{A b^{3}}{4 x^{4}} - \frac{A b^{2} c}{x^{3}} - \frac{3 A b c^{2}}{2 x^{2}} - \frac{A c^{3}}{x} - \frac{B b^{3}}{3 x^{3}} - \frac{3 B b^{2} c}{2 x^{2}} - \frac{3 B b c^{2}}{x} + B c^{3} \log{\left(x \right)} & \text{for}\: m = -8 \\- \frac{A b^{3}}{3 x^{3}} - \frac{3 A b^{2} c}{2 x^{2}} - \frac{3 A b c^{2}}{x} + A c^{3} \log{\left(x \right)} - \frac{B b^{3}}{2 x^{2}} - \frac{3 B b^{2} c}{x} + 3 B b c^{2} \log{\left(x \right)} + B c^{3} x & \text{for}\: m = -7 \\- \frac{A b^{3}}{2 x^{2}} - \frac{3 A b^{2} c}{x} + 3 A b c^{2} \log{\left(x \right)} + A c^{3} x - \frac{B b^{3}}{x} + 3 B b^{2} c \log{\left(x \right)} + 3 B b c^{2} x + \frac{B c^{3} x^{2}}{2} & \text{for}\: m = -6 \\- \frac{A b^{3}}{x} + 3 A b^{2} c \log{\left(x \right)} + 3 A b c^{2} x + \frac{A c^{3} x^{2}}{2} + B b^{3} \log{\left(x \right)} + 3 B b^{2} c x + \frac{3 B b c^{2} x^{2}}{2} + \frac{B c^{3} x^{3}}{3} & \text{for}\: m = -5 \\A b^{3} \log{\left(x \right)} + 3 A b^{2} c x + \frac{3 A b c^{2} x^{2}}{2} + \frac{A c^{3} x^{3}}{3} + B b^{3} x + \frac{3 B b^{2} c x^{2}}{2} + B b c^{2} x^{3} + \frac{B c^{3} x^{4}}{4} & \text{for}\: m = -4 \\\frac{A b^{3} m^{4} x^{4} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{26 A b^{3} m^{3} x^{4} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{251 A b^{3} m^{2} x^{4} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{1066 A b^{3} m x^{4} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{1680 A b^{3} x^{4} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{3 A b^{2} c m^{4} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{75 A b^{2} c m^{3} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{690 A b^{2} c m^{2} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{2760 A b^{2} c m x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{4032 A b^{2} c x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{3 A b c^{2} m^{4} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{72 A b c^{2} m^{3} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{633 A b c^{2} m^{2} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{2412 A b c^{2} m x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{3360 A b c^{2} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{A c^{3} m^{4} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{23 A c^{3} m^{3} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{194 A c^{3} m^{2} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{712 A c^{3} m x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{960 A c^{3} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{B b^{3} m^{4} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{25 B b^{3} m^{3} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{230 B b^{3} m^{2} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{920 B b^{3} m x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{1344 B b^{3} x^{5} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{3 B b^{2} c m^{4} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{72 B b^{2} c m^{3} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{633 B b^{2} c m^{2} x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{2412 B b^{2} c m x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{3360 B b^{2} c x^{6} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{3 B b c^{2} m^{4} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{69 B b c^{2} m^{3} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{582 B b c^{2} m^{2} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{2136 B b c^{2} m x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{2880 B b c^{2} x^{7} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{B c^{3} m^{4} x^{8} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{22 B c^{3} m^{3} x^{8} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{179 B c^{3} m^{2} x^{8} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{638 B c^{3} m x^{8} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} + \frac{840 B c^{3} x^{8} x^{m}}{m^{5} + 30 m^{4} + 355 m^{3} + 2070 m^{2} + 5944 m + 6720} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*b**3/(4*x**4) - A*b**2*c/x**3 - 3*A*b*c**2/(2*x**2) - A*c**3/x - B*b**3/(3*x**3) - 3*B*b**2*c/(2*x**2) - 3*B*b*c**2/x + B*c**3*log(x), Eq(m, -8)), (-A*b**3/(3*x**3) - 3*A*b**2*c/(2*x**2) - 3*A*b*c**2/x + A*c**3*log(x) - B*b**3/(2*x**2) - 3*B*b**2*c/x + 3*B*b*c**2*log(x) + B*c**3*x, Eq(m, -7)), (-A*b**3/(2*x**2) - 3*A*b**2*c/x + 3*A*b*c**2*log(x) + A*c**3*x - B*b**3/x + 3*B*b**2*c*log(x) + 3*B*b*c**2*x + B*c**3*x**2/2, Eq(m, -6)), (-A*b**3/x + 3*A*b**2*c*log(x) + 3*A*b*c**2*x + A*c**3*x**2/2 + B*b**3*log(x) + 3*B*b**2*c*x + 3*B*b*c**2*x**2/2 + B*c**3*x**3/3, Eq(m, -5)), (A*b**3*log(x) + 3*A*b**2*c*x + 3*A*b*c**2*x**2/2 + A*c**3*x**3/3 + B*b**3*x + 3*B*b**2*c*x**2/2 + B*b*c**2*x**3 + B*c**3*x**4/4, Eq(m, -4)), (A*b**3*m**4*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 26*A*b**3*m**3*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 251*A*b**3*m**2*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 1066*A*b**3*m*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 1680*A*b**3*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3*A*b**2*c*m**4*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 75*A*b**2*c*m**3*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 690*A*b**2*c*m**2*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2760*A*b**2*c*m*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 4032*A*b**2*c*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3*A*b*c**2*m**4*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 72*A*b*c**2*m**3*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 633*A*b*c**2*m**2*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2412*A*b*c**2*m*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3360*A*b*c**2*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + A*c**3*m**4*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 23*A*c**3*m**3*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 194*A*c**3*m**2*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 712*A*c**3*m*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 960*A*c**3*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + B*b**3*m**4*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 25*B*b**3*m**3*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 230*B*b**3*m**2*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 920*B*b**3*m*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 1344*B*b**3*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3*B*b**2*c*m**4*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 72*B*b**2*c*m**3*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 633*B*b**2*c*m**2*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2412*B*b**2*c*m*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3360*B*b**2*c*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3*B*b*c**2*m**4*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 69*B*b*c**2*m**3*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 582*B*b*c**2*m**2*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2136*B*b*c**2*m*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2880*B*b*c**2*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + B*c**3*m**4*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 22*B*c**3*m**3*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 179*B*c**3*m**2*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 638*B*c**3*m*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 840*B*c**3*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720), True))","A",0
28,1,80,0,0.083964," ","integrate(x**3*(B*x+A)*(c*x**2+b*x)**3,x)","\frac{A b^{3} x^{7}}{7} + \frac{B c^{3} x^{11}}{11} + x^{10} \left(\frac{A c^{3}}{10} + \frac{3 B b c^{2}}{10}\right) + x^{9} \left(\frac{A b c^{2}}{3} + \frac{B b^{2} c}{3}\right) + x^{8} \left(\frac{3 A b^{2} c}{8} + \frac{B b^{3}}{8}\right)"," ",0,"A*b**3*x**7/7 + B*c**3*x**11/11 + x**10*(A*c**3/10 + 3*B*b*c**2/10) + x**9*(A*b*c**2/3 + B*b**2*c/3) + x**8*(3*A*b**2*c/8 + B*b**3/8)","A",0
29,1,82,0,0.082935," ","integrate(x**2*(B*x+A)*(c*x**2+b*x)**3,x)","\frac{A b^{3} x^{6}}{6} + \frac{B c^{3} x^{10}}{10} + x^{9} \left(\frac{A c^{3}}{9} + \frac{B b c^{2}}{3}\right) + x^{8} \left(\frac{3 A b c^{2}}{8} + \frac{3 B b^{2} c}{8}\right) + x^{7} \left(\frac{3 A b^{2} c}{7} + \frac{B b^{3}}{7}\right)"," ",0,"A*b**3*x**6/6 + B*c**3*x**10/10 + x**9*(A*c**3/9 + B*b*c**2/3) + x**8*(3*A*b*c**2/8 + 3*B*b**2*c/8) + x**7*(3*A*b**2*c/7 + B*b**3/7)","A",0
30,1,82,0,0.082644," ","integrate(x*(B*x+A)*(c*x**2+b*x)**3,x)","\frac{A b^{3} x^{5}}{5} + \frac{B c^{3} x^{9}}{9} + x^{8} \left(\frac{A c^{3}}{8} + \frac{3 B b c^{2}}{8}\right) + x^{7} \left(\frac{3 A b c^{2}}{7} + \frac{3 B b^{2} c}{7}\right) + x^{6} \left(\frac{A b^{2} c}{2} + \frac{B b^{3}}{6}\right)"," ",0,"A*b**3*x**5/5 + B*c**3*x**9/9 + x**8*(A*c**3/8 + 3*B*b*c**2/8) + x**7*(3*A*b*c**2/7 + 3*B*b**2*c/7) + x**6*(A*b**2*c/2 + B*b**3/6)","A",0
31,1,80,0,0.082782," ","integrate((B*x+A)*(c*x**2+b*x)**3,x)","\frac{A b^{3} x^{4}}{4} + \frac{B c^{3} x^{8}}{8} + x^{7} \left(\frac{A c^{3}}{7} + \frac{3 B b c^{2}}{7}\right) + x^{6} \left(\frac{A b c^{2}}{2} + \frac{B b^{2} c}{2}\right) + x^{5} \left(\frac{3 A b^{2} c}{5} + \frac{B b^{3}}{5}\right)"," ",0,"A*b**3*x**4/4 + B*c**3*x**8/8 + x**7*(A*c**3/7 + 3*B*b*c**2/7) + x**6*(A*b*c**2/2 + B*b**2*c/2) + x**5*(3*A*b**2*c/5 + B*b**3/5)","A",0
32,1,82,0,0.084512," ","integrate((B*x+A)*(c*x**2+b*x)**3/x,x)","\frac{A b^{3} x^{3}}{3} + \frac{B c^{3} x^{7}}{7} + x^{6} \left(\frac{A c^{3}}{6} + \frac{B b c^{2}}{2}\right) + x^{5} \left(\frac{3 A b c^{2}}{5} + \frac{3 B b^{2} c}{5}\right) + x^{4} \left(\frac{3 A b^{2} c}{4} + \frac{B b^{3}}{4}\right)"," ",0,"A*b**3*x**3/3 + B*c**3*x**7/7 + x**6*(A*c**3/6 + B*b*c**2/2) + x**5*(3*A*b*c**2/5 + 3*B*b**2*c/5) + x**4*(3*A*b**2*c/4 + B*b**3/4)","A",0
33,1,80,0,0.084453," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**2,x)","\frac{A b^{3} x^{2}}{2} + \frac{B c^{3} x^{6}}{6} + x^{5} \left(\frac{A c^{3}}{5} + \frac{3 B b c^{2}}{5}\right) + x^{4} \left(\frac{3 A b c^{2}}{4} + \frac{3 B b^{2} c}{4}\right) + x^{3} \left(A b^{2} c + \frac{B b^{3}}{3}\right)"," ",0,"A*b**3*x**2/2 + B*c**3*x**6/6 + x**5*(A*c**3/5 + 3*B*b*c**2/5) + x**4*(3*A*b*c**2/4 + 3*B*b**2*c/4) + x**3*(A*b**2*c + B*b**3/3)","A",0
34,1,73,0,0.083050," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**3,x)","A b^{3} x + \frac{B c^{3} x^{5}}{5} + x^{4} \left(\frac{A c^{3}}{4} + \frac{3 B b c^{2}}{4}\right) + x^{3} \left(A b c^{2} + B b^{2} c\right) + x^{2} \left(\frac{3 A b^{2} c}{2} + \frac{B b^{3}}{2}\right)"," ",0,"A*b**3*x + B*c**3*x**5/5 + x**4*(A*c**3/4 + 3*B*b*c**2/4) + x**3*(A*b*c**2 + B*b**2*c) + x**2*(3*A*b**2*c/2 + B*b**3/2)","B",0
35,1,73,0,0.171531," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**4,x)","A b^{3} \log{\left(x \right)} + \frac{B c^{3} x^{4}}{4} + x^{3} \left(\frac{A c^{3}}{3} + B b c^{2}\right) + x^{2} \left(\frac{3 A b c^{2}}{2} + \frac{3 B b^{2} c}{2}\right) + x \left(3 A b^{2} c + B b^{3}\right)"," ",0,"A*b**3*log(x) + B*c**3*x**4/4 + x**3*(A*c**3/3 + B*b*c**2) + x**2*(3*A*b*c**2/2 + 3*B*b**2*c/2) + x*(3*A*b**2*c + B*b**3)","A",0
36,1,70,0,0.218963," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**5,x)","- \frac{A b^{3}}{x} + \frac{B c^{3} x^{3}}{3} + b^{2} \left(3 A c + B b\right) \log{\left(x \right)} + x^{2} \left(\frac{A c^{3}}{2} + \frac{3 B b c^{2}}{2}\right) + x \left(3 A b c^{2} + 3 B b^{2} c\right)"," ",0,"-A*b**3/x + B*c**3*x**3/3 + b**2*(3*A*c + B*b)*log(x) + x**2*(A*c**3/2 + 3*B*b*c**2/2) + x*(3*A*b*c**2 + 3*B*b**2*c)","A",0
37,1,68,0,0.361014," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**6,x)","\frac{B c^{3} x^{2}}{2} + 3 b c \left(A c + B b\right) \log{\left(x \right)} + x \left(A c^{3} + 3 B b c^{2}\right) + \frac{- A b^{3} + x \left(- 6 A b^{2} c - 2 B b^{3}\right)}{2 x^{2}}"," ",0,"B*c**3*x**2/2 + 3*b*c*(A*c + B*b)*log(x) + x*(A*c**3 + 3*B*b*c**2) + (-A*b**3 + x*(-6*A*b**2*c - 2*B*b**3))/(2*x**2)","A",0
38,1,73,0,0.663411," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**7,x)","B c^{3} x + c^{2} \left(A c + 3 B b\right) \log{\left(x \right)} + \frac{- 2 A b^{3} + x^{2} \left(- 18 A b c^{2} - 18 B b^{2} c\right) + x \left(- 9 A b^{2} c - 3 B b^{3}\right)}{6 x^{3}}"," ",0,"B*c**3*x + c**2*(A*c + 3*B*b)*log(x) + (-2*A*b**3 + x**2*(-18*A*b*c**2 - 18*B*b**2*c) + x*(-9*A*b**2*c - 3*B*b**3))/(6*x**3)","A",0
39,1,80,0,0.993244," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**8,x)","B c^{3} \log{\left(x \right)} + \frac{- 3 A b^{3} + x^{3} \left(- 12 A c^{3} - 36 B b c^{2}\right) + x^{2} \left(- 18 A b c^{2} - 18 B b^{2} c\right) + x \left(- 12 A b^{2} c - 4 B b^{3}\right)}{12 x^{4}}"," ",0,"B*c**3*log(x) + (-3*A*b**3 + x**3*(-12*A*c**3 - 36*B*b*c**2) + x**2*(-18*A*b*c**2 - 18*B*b**2*c) + x*(-12*A*b**2*c - 4*B*b**3))/(12*x**4)","A",0
40,1,82,0,1.297991," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**9,x)","\frac{- 4 A b^{3} - 20 B c^{3} x^{4} + x^{3} \left(- 10 A c^{3} - 30 B b c^{2}\right) + x^{2} \left(- 20 A b c^{2} - 20 B b^{2} c\right) + x \left(- 15 A b^{2} c - 5 B b^{3}\right)}{20 x^{5}}"," ",0,"(-4*A*b**3 - 20*B*c**3*x**4 + x**3*(-10*A*c**3 - 30*B*b*c**2) + x**2*(-20*A*b*c**2 - 20*B*b**2*c) + x*(-15*A*b**2*c - 5*B*b**3))/(20*x**5)","A",0
41,1,82,0,1.629623," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**10,x)","\frac{- 10 A b^{3} - 30 B c^{3} x^{4} + x^{3} \left(- 20 A c^{3} - 60 B b c^{2}\right) + x^{2} \left(- 45 A b c^{2} - 45 B b^{2} c\right) + x \left(- 36 A b^{2} c - 12 B b^{3}\right)}{60 x^{6}}"," ",0,"(-10*A*b**3 - 30*B*c**3*x**4 + x**3*(-20*A*c**3 - 60*B*b*c**2) + x**2*(-45*A*b*c**2 - 45*B*b**2*c) + x*(-36*A*b**2*c - 12*B*b**3))/(60*x**6)","A",0
42,1,82,0,2.040479," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**11,x)","\frac{- 60 A b^{3} - 140 B c^{3} x^{4} + x^{3} \left(- 105 A c^{3} - 315 B b c^{2}\right) + x^{2} \left(- 252 A b c^{2} - 252 B b^{2} c\right) + x \left(- 210 A b^{2} c - 70 B b^{3}\right)}{420 x^{7}}"," ",0,"(-60*A*b**3 - 140*B*c**3*x**4 + x**3*(-105*A*c**3 - 315*B*b*c**2) + x**2*(-252*A*b*c**2 - 252*B*b**2*c) + x*(-210*A*b**2*c - 70*B*b**3))/(420*x**7)","A",0
43,1,85,0,0.243344," ","integrate(x**4*(e*x+d)/(c*x**2+b*x),x)","\frac{b^{3} \left(b e - c d\right) \log{\left(b + c x \right)}}{c^{5}} + x^{3} \left(- \frac{b e}{3 c^{2}} + \frac{d}{3 c}\right) + x^{2} \left(\frac{b^{2} e}{2 c^{3}} - \frac{b d}{2 c^{2}}\right) + x \left(- \frac{b^{3} e}{c^{4}} + \frac{b^{2} d}{c^{3}}\right) + \frac{e x^{4}}{4 c}"," ",0,"b**3*(b*e - c*d)*log(b + c*x)/c**5 + x**3*(-b*e/(3*c**2) + d/(3*c)) + x**2*(b**2*e/(2*c**3) - b*d/(2*c**2)) + x*(-b**3*e/c**4 + b**2*d/c**3) + e*x**4/(4*c)","A",0
44,1,61,0,0.219373," ","integrate(x**3*(e*x+d)/(c*x**2+b*x),x)","- \frac{b^{2} \left(b e - c d\right) \log{\left(b + c x \right)}}{c^{4}} + x^{2} \left(- \frac{b e}{2 c^{2}} + \frac{d}{2 c}\right) + x \left(\frac{b^{2} e}{c^{3}} - \frac{b d}{c^{2}}\right) + \frac{e x^{3}}{3 c}"," ",0,"-b**2*(b*e - c*d)*log(b + c*x)/c**4 + x**2*(-b*e/(2*c**2) + d/(2*c)) + x*(b**2*e/c**3 - b*d/c**2) + e*x**3/(3*c)","A",0
45,1,37,0,0.187545," ","integrate(x**2*(e*x+d)/(c*x**2+b*x),x)","\frac{b \left(b e - c d\right) \log{\left(b + c x \right)}}{c^{3}} + x \left(- \frac{b e}{c^{2}} + \frac{d}{c}\right) + \frac{e x^{2}}{2 c}"," ",0,"b*(b*e - c*d)*log(b + c*x)/c**3 + x*(-b*e/c**2 + d/c) + e*x**2/(2*c)","A",0
46,1,20,0,0.158298," ","integrate(x*(e*x+d)/(c*x**2+b*x),x)","\frac{e x}{c} - \frac{\left(b e - c d\right) \log{\left(b + c x \right)}}{c^{2}}"," ",0,"e*x/c - (b*e - c*d)*log(b + c*x)/c**2","A",0
47,1,41,0,0.416306," ","integrate((e*x+d)/(c*x**2+b*x),x)","\frac{d \log{\left(x \right)}}{b} + \frac{\left(b e - c d\right) \log{\left(x + \frac{- b d + \frac{b \left(b e - c d\right)}{c}}{b e - 2 c d} \right)}}{b c}"," ",0,"d*log(x)/b + (b*e - c*d)*log(x + (-b*d + b*(b*e - c*d)/c)/(b*e - 2*c*d))/(b*c)","A",0
48,1,95,0,0.368361," ","integrate((e*x+d)/x/(c*x**2+b*x),x)","- \frac{d}{b x} + \frac{\left(b e - c d\right) \log{\left(x + \frac{b^{2} e - b c d - b \left(b e - c d\right)}{2 b c e - 2 c^{2} d} \right)}}{b^{2}} - \frac{\left(b e - c d\right) \log{\left(x + \frac{b^{2} e - b c d + b \left(b e - c d\right)}{2 b c e - 2 c^{2} d} \right)}}{b^{2}}"," ",0,"-d/(b*x) + (b*e - c*d)*log(x + (b**2*e - b*c*d - b*(b*e - c*d))/(2*b*c*e - 2*c**2*d))/b**2 - (b*e - c*d)*log(x + (b**2*e - b*c*d + b*(b*e - c*d))/(2*b*c*e - 2*c**2*d))/b**2","B",0
49,1,131,0,0.445360," ","integrate((e*x+d)/x**2/(c*x**2+b*x),x)","\frac{- b d + x \left(- 2 b e + 2 c d\right)}{2 b^{2} x^{2}} - \frac{c \left(b e - c d\right) \log{\left(x + \frac{b^{2} c e - b c^{2} d - b c \left(b e - c d\right)}{2 b c^{2} e - 2 c^{3} d} \right)}}{b^{3}} + \frac{c \left(b e - c d\right) \log{\left(x + \frac{b^{2} c e - b c^{2} d + b c \left(b e - c d\right)}{2 b c^{2} e - 2 c^{3} d} \right)}}{b^{3}}"," ",0,"(-b*d + x*(-2*b*e + 2*c*d))/(2*b**2*x**2) - c*(b*e - c*d)*log(x + (b**2*c*e - b*c**2*d - b*c*(b*e - c*d))/(2*b*c**2*e - 2*c**3*d))/b**3 + c*(b*e - c*d)*log(x + (b**2*c*e - b*c**2*d + b*c*(b*e - c*d))/(2*b*c**2*e - 2*c**3*d))/b**3","B",0
50,1,165,0,0.499380," ","integrate((e*x+d)/x**3/(c*x**2+b*x),x)","\frac{- 2 b^{2} d + x^{2} \left(6 b c e - 6 c^{2} d\right) + x \left(- 3 b^{2} e + 3 b c d\right)}{6 b^{3} x^{3}} + \frac{c^{2} \left(b e - c d\right) \log{\left(x + \frac{b^{2} c^{2} e - b c^{3} d - b c^{2} \left(b e - c d\right)}{2 b c^{3} e - 2 c^{4} d} \right)}}{b^{4}} - \frac{c^{2} \left(b e - c d\right) \log{\left(x + \frac{b^{2} c^{2} e - b c^{3} d + b c^{2} \left(b e - c d\right)}{2 b c^{3} e - 2 c^{4} d} \right)}}{b^{4}}"," ",0,"(-2*b**2*d + x**2*(6*b*c*e - 6*c**2*d) + x*(-3*b**2*e + 3*b*c*d))/(6*b**3*x**3) + c**2*(b*e - c*d)*log(x + (b**2*c**2*e - b*c**3*d - b*c**2*(b*e - c*d))/(2*b*c**3*e - 2*c**4*d))/b**4 - c**2*(b*e - c*d)*log(x + (b**2*c**2*e - b*c**3*d + b*c**2*(b*e - c*d))/(2*b*c**3*e - 2*c**4*d))/b**4","B",0
51,1,92,0,0.422879," ","integrate(x**5*(e*x+d)/(c*x**2+b*x)**2,x)","- \frac{b^{2} \left(4 b e - 3 c d\right) \log{\left(b + c x \right)}}{c^{5}} + x^{2} \left(- \frac{b e}{c^{3}} + \frac{d}{2 c^{2}}\right) + x \left(\frac{3 b^{2} e}{c^{4}} - \frac{2 b d}{c^{3}}\right) + \frac{- b^{4} e + b^{3} c d}{b c^{5} + c^{6} x} + \frac{e x^{3}}{3 c^{2}}"," ",0,"-b**2*(4*b*e - 3*c*d)*log(b + c*x)/c**5 + x**2*(-b*e/c**3 + d/(2*c**2)) + x*(3*b**2*e/c**4 - 2*b*d/c**3) + (-b**4*e + b**3*c*d)/(b*c**5 + c**6*x) + e*x**3/(3*c**2)","A",0
52,1,68,0,0.371619," ","integrate(x**4*(e*x+d)/(c*x**2+b*x)**2,x)","\frac{b \left(3 b e - 2 c d\right) \log{\left(b + c x \right)}}{c^{4}} + x \left(- \frac{2 b e}{c^{3}} + \frac{d}{c^{2}}\right) + \frac{b^{3} e - b^{2} c d}{b c^{4} + c^{5} x} + \frac{e x^{2}}{2 c^{2}}"," ",0,"b*(3*b*e - 2*c*d)*log(b + c*x)/c**4 + x*(-2*b*e/c**3 + d/c**2) + (b**3*e - b**2*c*d)/(b*c**4 + c**5*x) + e*x**2/(2*c**2)","A",0
53,1,44,0,0.289325," ","integrate(x**3*(e*x+d)/(c*x**2+b*x)**2,x)","\frac{- b^{2} e + b c d}{b c^{3} + c^{4} x} + \frac{e x}{c^{2}} - \frac{\left(2 b e - c d\right) \log{\left(b + c x \right)}}{c^{3}}"," ",0,"(-b**2*e + b*c*d)/(b*c**3 + c**4*x) + e*x/c**2 - (2*b*e - c*d)*log(b + c*x)/c**3","A",0
54,1,27,0,0.199064," ","integrate(x**2*(e*x+d)/(c*x**2+b*x)**2,x)","\frac{b e - c d}{b c^{2} + c^{3} x} + \frac{e \log{\left(b + c x \right)}}{c^{2}}"," ",0,"(b*e - c*d)/(b*c**2 + c**3*x) + e*log(b + c*x)/c**2","A",0
55,1,32,0,0.293764," ","integrate(x*(e*x+d)/(c*x**2+b*x)**2,x)","\frac{- b e + c d}{b^{2} c + b c^{2} x} + \frac{d \left(\log{\left(x \right)} - \log{\left(\frac{b}{c} + x \right)}\right)}{b^{2}}"," ",0,"(-b*e + c*d)/(b**2*c + b*c**2*x) + d*(log(x) - log(b/c + x))/b**2","A",0
56,1,128,0,0.483959," ","integrate((e*x+d)/(c*x**2+b*x)**2,x)","\frac{- b d + x \left(b e - 2 c d\right)}{b^{3} x + b^{2} c x^{2}} + \frac{\left(b e - 2 c d\right) \log{\left(x + \frac{b^{2} e - 2 b c d - b \left(b e - 2 c d\right)}{2 b c e - 4 c^{2} d} \right)}}{b^{3}} - \frac{\left(b e - 2 c d\right) \log{\left(x + \frac{b^{2} e - 2 b c d + b \left(b e - 2 c d\right)}{2 b c e - 4 c^{2} d} \right)}}{b^{3}}"," ",0,"(-b*d + x*(b*e - 2*c*d))/(b**3*x + b**2*c*x**2) + (b*e - 2*c*d)*log(x + (b**2*e - 2*b*c*d - b*(b*e - 2*c*d))/(2*b*c*e - 4*c**2*d))/b**3 - (b*e - 2*c*d)*log(x + (b**2*e - 2*b*c*d + b*(b*e - 2*c*d))/(2*b*c*e - 4*c**2*d))/b**3","B",0
57,1,184,0,0.593197," ","integrate((e*x+d)/x/(c*x**2+b*x)**2,x)","\frac{- b^{2} d + x^{2} \left(- 4 b c e + 6 c^{2} d\right) + x \left(- 2 b^{2} e + 3 b c d\right)}{2 b^{4} x^{2} + 2 b^{3} c x^{3}} - \frac{c \left(2 b e - 3 c d\right) \log{\left(x + \frac{2 b^{2} c e - 3 b c^{2} d - b c \left(2 b e - 3 c d\right)}{4 b c^{2} e - 6 c^{3} d} \right)}}{b^{4}} + \frac{c \left(2 b e - 3 c d\right) \log{\left(x + \frac{2 b^{2} c e - 3 b c^{2} d + b c \left(2 b e - 3 c d\right)}{4 b c^{2} e - 6 c^{3} d} \right)}}{b^{4}}"," ",0,"(-b**2*d + x**2*(-4*b*c*e + 6*c**2*d) + x*(-2*b**2*e + 3*b*c*d))/(2*b**4*x**2 + 2*b**3*c*x**3) - c*(2*b*e - 3*c*d)*log(x + (2*b**2*c*e - 3*b*c**2*d - b*c*(2*b*e - 3*c*d))/(4*b*c**2*e - 6*c**3*d))/b**4 + c*(2*b*e - 3*c*d)*log(x + (2*b**2*c*e - 3*b*c**2*d + b*c*(2*b*e - 3*c*d))/(4*b*c**2*e - 6*c**3*d))/b**4","B",0
58,1,219,0,0.661368," ","integrate((e*x+d)/x**2/(c*x**2+b*x)**2,x)","\frac{- 2 b^{3} d + x^{3} \left(18 b c^{2} e - 24 c^{3} d\right) + x^{2} \left(9 b^{2} c e - 12 b c^{2} d\right) + x \left(- 3 b^{3} e + 4 b^{2} c d\right)}{6 b^{5} x^{3} + 6 b^{4} c x^{4}} + \frac{c^{2} \left(3 b e - 4 c d\right) \log{\left(x + \frac{3 b^{2} c^{2} e - 4 b c^{3} d - b c^{2} \left(3 b e - 4 c d\right)}{6 b c^{3} e - 8 c^{4} d} \right)}}{b^{5}} - \frac{c^{2} \left(3 b e - 4 c d\right) \log{\left(x + \frac{3 b^{2} c^{2} e - 4 b c^{3} d + b c^{2} \left(3 b e - 4 c d\right)}{6 b c^{3} e - 8 c^{4} d} \right)}}{b^{5}}"," ",0,"(-2*b**3*d + x**3*(18*b*c**2*e - 24*c**3*d) + x**2*(9*b**2*c*e - 12*b*c**2*d) + x*(-3*b**3*e + 4*b**2*c*d))/(6*b**5*x**3 + 6*b**4*c*x**4) + c**2*(3*b*e - 4*c*d)*log(x + (3*b**2*c**2*e - 4*b*c**3*d - b*c**2*(3*b*e - 4*c*d))/(6*b*c**3*e - 8*c**4*d))/b**5 - c**2*(3*b*e - 4*c*d)*log(x + (3*b**2*c**2*e - 4*b*c**3*d + b*c**2*(3*b*e - 4*c*d))/(6*b*c**3*e - 8*c**4*d))/b**5","B",0
59,1,107,0,0.676535," ","integrate(x**6*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{3 b \left(2 b e - c d\right) \log{\left(b + c x \right)}}{c^{5}} + x \left(- \frac{3 b e}{c^{4}} + \frac{d}{c^{3}}\right) + \frac{7 b^{4} e - 5 b^{3} c d + x \left(8 b^{3} c e - 6 b^{2} c^{2} d\right)}{2 b^{2} c^{5} + 4 b c^{6} x + 2 c^{7} x^{2}} + \frac{e x^{2}}{2 c^{3}}"," ",0,"3*b*(2*b*e - c*d)*log(b + c*x)/c**5 + x*(-3*b*e/c**4 + d/c**3) + (7*b**4*e - 5*b**3*c*d + x*(8*b**3*c*e - 6*b**2*c**2*d))/(2*b**2*c**5 + 4*b*c**6*x + 2*c**7*x**2) + e*x**2/(2*c**3)","A",0
60,1,83,0,0.547378," ","integrate(x**5*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{- 5 b^{3} e + 3 b^{2} c d + x \left(- 6 b^{2} c e + 4 b c^{2} d\right)}{2 b^{2} c^{4} + 4 b c^{5} x + 2 c^{6} x^{2}} + \frac{e x}{c^{3}} - \frac{\left(3 b e - c d\right) \log{\left(b + c x \right)}}{c^{4}}"," ",0,"(-5*b**3*e + 3*b**2*c*d + x*(-6*b**2*c*e + 4*b*c**2*d))/(2*b**2*c**4 + 4*b*c**5*x + 2*c**6*x**2) + e*x/c**3 - (3*b*e - c*d)*log(b + c*x)/c**4","A",0
61,1,63,0,0.357219," ","integrate(x**4*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{3 b^{2} e - b c d + x \left(4 b c e - 2 c^{2} d\right)}{2 b^{2} c^{3} + 4 b c^{4} x + 2 c^{5} x^{2}} + \frac{e \log{\left(b + c x \right)}}{c^{3}}"," ",0,"(3*b**2*e - b*c*d + x*(4*b*c*e - 2*c**2*d))/(2*b**2*c**3 + 4*b*c**4*x + 2*c**5*x**2) + e*log(b + c*x)/c**3","A",0
62,1,39,0,0.280958," ","integrate(x**3*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{- b e - c d - 2 c e x}{2 b^{2} c^{2} + 4 b c^{3} x + 2 c^{4} x^{2}}"," ",0,"(-b*e - c*d - 2*c*e*x)/(2*b**2*c**2 + 4*b*c**3*x + 2*c**4*x**2)","A",0
63,1,63,0,0.411034," ","integrate(x**2*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{- b^{2} e + 3 b c d + 2 c^{2} d x}{2 b^{4} c + 4 b^{3} c^{2} x + 2 b^{2} c^{3} x^{2}} + \frac{d \left(\log{\left(x \right)} - \log{\left(\frac{b}{c} + x \right)}\right)}{b^{3}}"," ",0,"(-b**2*e + 3*b*c*d + 2*c**2*d*x)/(2*b**4*c + 4*b**3*c**2*x + 2*b**2*c**3*x**2) + d*(log(x) - log(b/c + x))/b**3","A",0
64,1,168,0,0.638590," ","integrate(x*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{- 2 b^{2} d + x^{2} \left(2 b c e - 6 c^{2} d\right) + x \left(3 b^{2} e - 9 b c d\right)}{2 b^{5} x + 4 b^{4} c x^{2} + 2 b^{3} c^{2} x^{3}} + \frac{\left(b e - 3 c d\right) \log{\left(x + \frac{b^{2} e - 3 b c d - b \left(b e - 3 c d\right)}{2 b c e - 6 c^{2} d} \right)}}{b^{4}} - \frac{\left(b e - 3 c d\right) \log{\left(x + \frac{b^{2} e - 3 b c d + b \left(b e - 3 c d\right)}{2 b c e - 6 c^{2} d} \right)}}{b^{4}}"," ",0,"(-2*b**2*d + x**2*(2*b*c*e - 6*c**2*d) + x*(3*b**2*e - 9*b*c*d))/(2*b**5*x + 4*b**4*c*x**2 + 2*b**3*c**2*x**3) + (b*e - 3*c*d)*log(x + (b**2*e - 3*b*c*d - b*(b*e - 3*c*d))/(2*b*c*e - 6*c**2*d))/b**4 - (b*e - 3*c*d)*log(x + (b**2*e - 3*b*c*d + b*(b*e - 3*c*d))/(2*b*c*e - 6*c**2*d))/b**4","B",0
65,1,219,0,0.737329," ","integrate((e*x+d)/(c*x**2+b*x)**3,x)","\frac{- b^{3} d + x^{3} \left(- 6 b c^{2} e + 12 c^{3} d\right) + x^{2} \left(- 9 b^{2} c e + 18 b c^{2} d\right) + x \left(- 2 b^{3} e + 4 b^{2} c d\right)}{2 b^{6} x^{2} + 4 b^{5} c x^{3} + 2 b^{4} c^{2} x^{4}} - \frac{3 c \left(b e - 2 c d\right) \log{\left(x + \frac{3 b^{2} c e - 6 b c^{2} d - 3 b c \left(b e - 2 c d\right)}{6 b c^{2} e - 12 c^{3} d} \right)}}{b^{5}} + \frac{3 c \left(b e - 2 c d\right) \log{\left(x + \frac{3 b^{2} c e - 6 b c^{2} d + 3 b c \left(b e - 2 c d\right)}{6 b c^{2} e - 12 c^{3} d} \right)}}{b^{5}}"," ",0,"(-b**3*d + x**3*(-6*b*c**2*e + 12*c**3*d) + x**2*(-9*b**2*c*e + 18*b*c**2*d) + x*(-2*b**3*e + 4*b**2*c*d))/(2*b**6*x**2 + 4*b**5*c*x**3 + 2*b**4*c**2*x**4) - 3*c*(b*e - 2*c*d)*log(x + (3*b**2*c*e - 6*b*c**2*d - 3*b*c*(b*e - 2*c*d))/(6*b*c**2*e - 12*c**3*d))/b**5 + 3*c*(b*e - 2*c*d)*log(x + (3*b**2*c*e - 6*b*c**2*d + 3*b*c*(b*e - 2*c*d))/(6*b*c**2*e - 12*c**3*d))/b**5","B",0
66,1,262,0,0.798004," ","integrate((e*x+d)/x/(c*x**2+b*x)**3,x)","\frac{- 2 b^{4} d + x^{4} \left(36 b c^{3} e - 60 c^{4} d\right) + x^{3} \left(54 b^{2} c^{2} e - 90 b c^{3} d\right) + x^{2} \left(12 b^{3} c e - 20 b^{2} c^{2} d\right) + x \left(- 3 b^{4} e + 5 b^{3} c d\right)}{6 b^{7} x^{3} + 12 b^{6} c x^{4} + 6 b^{5} c^{2} x^{5}} + \frac{2 c^{2} \left(3 b e - 5 c d\right) \log{\left(x + \frac{6 b^{2} c^{2} e - 10 b c^{3} d - 2 b c^{2} \left(3 b e - 5 c d\right)}{12 b c^{3} e - 20 c^{4} d} \right)}}{b^{6}} - \frac{2 c^{2} \left(3 b e - 5 c d\right) \log{\left(x + \frac{6 b^{2} c^{2} e - 10 b c^{3} d + 2 b c^{2} \left(3 b e - 5 c d\right)}{12 b c^{3} e - 20 c^{4} d} \right)}}{b^{6}}"," ",0,"(-2*b**4*d + x**4*(36*b*c**3*e - 60*c**4*d) + x**3*(54*b**2*c**2*e - 90*b*c**3*d) + x**2*(12*b**3*c*e - 20*b**2*c**2*d) + x*(-3*b**4*e + 5*b**3*c*d))/(6*b**7*x**3 + 12*b**6*c*x**4 + 6*b**5*c**2*x**5) + 2*c**2*(3*b*e - 5*c*d)*log(x + (6*b**2*c**2*e - 10*b*c**3*d - 2*b*c**2*(3*b*e - 5*c*d))/(12*b*c**3*e - 20*c**4*d))/b**6 - 2*c**2*(3*b*e - 5*c*d)*log(x + (6*b**2*c**2*e - 10*b*c**3*d + 2*b*c**2*(3*b*e - 5*c*d))/(12*b*c**3*e - 20*c**4*d))/b**6","A",0
67,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x)**(1/2),x)","\int x^{3} \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(x**3*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
68,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x)**(1/2),x)","\int x^{2} \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(x**2*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
69,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x)**(1/2),x)","\int x \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(x*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
70,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x), x)","F",0
71,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x, x)","F",0
72,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**2,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{2}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**2, x)","F",0
73,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**3,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{3}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**3, x)","F",0
74,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**4,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{4}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**4, x)","F",0
75,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**5,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{5}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**5, x)","F",0
76,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**6,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{6}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**6, x)","F",0
77,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**7,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{7}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**7, x)","F",0
78,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**8,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{8}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**8, x)","F",0
79,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x)**(3/2),x)","\int x^{3} \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x**3*(x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
80,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x)**(3/2),x)","\int x^{2} \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x**2*(x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
81,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x)**(3/2),x)","\int x \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x*(x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
82,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
83,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x, x)","F",0
84,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**2, x)","F",0
85,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**3, x)","F",0
86,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**4,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{4}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**4, x)","F",0
87,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**5,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{5}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**5, x)","F",0
88,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**6,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{6}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**6, x)","F",0
89,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**7,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{7}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**7, x)","F",0
90,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**8,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{8}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**8, x)","F",0
91,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**9,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{9}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**9, x)","F",0
92,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**10,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{10}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**10, x)","F",0
93,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x)**(5/2),x)","\int x^{3} \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x**3*(x*(b + c*x))**(5/2)*(A + B*x), x)","F",0
94,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x)**(5/2),x)","\int x^{2} \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x**2*(x*(b + c*x))**(5/2)*(A + B*x), x)","F",0
95,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x)**(5/2),x)","\int x \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x*(x*(b + c*x))**(5/2)*(A + B*x), x)","F",0
96,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x), x)","F",0
97,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x, x)","F",0
98,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**2, x)","F",0
99,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**3, x)","F",0
100,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**4,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{4}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**4, x)","F",0
101,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**5,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{5}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**5, x)","F",0
102,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**6,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{6}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**6, x)","F",0
103,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**7,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{7}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**7, x)","F",0
104,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**8,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{8}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**8, x)","F",0
105,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**9,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{9}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**9, x)","F",0
106,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**10,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{10}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**10, x)","F",0
107,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**11,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{11}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**11, x)","F",0
108,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**12,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{12}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**12, x)","F",0
109,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**4*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
110,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**3*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
111,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**2*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
112,0,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
113,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/sqrt(x*(b + c*x)), x)","F",0
114,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x*sqrt(x*(b + c*x))), x)","F",0
115,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{2} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**2*sqrt(x*(b + c*x))), x)","F",0
116,0,0,0,0.000000," ","integrate((B*x+A)/x**3/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{3} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**3*sqrt(x*(b + c*x))), x)","F",0
117,0,0,0,0.000000," ","integrate((B*x+A)/x**4/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{4} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**4*sqrt(x*(b + c*x))), x)","F",0
118,0,0,0,0.000000," ","integrate((B*x+A)/x**5/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{5} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**5*sqrt(x*(b + c*x))), x)","F",0
119,0,0,0,0.000000," ","integrate((B*x+A)/x**6/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{6} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**6*sqrt(x*(b + c*x))), x)","F",0
120,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
121,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{x \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{x \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(x*(b + c*x))**(3/2)), x)","F",0
126,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{x^{2} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**2*(x*(b + c*x))**(3/2)), x)","F",0
127,0,0,0,0.000000," ","integrate((B*x+A)/x**3/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{x^{3} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**3*(x*(b + c*x))**(3/2)), x)","F",0
128,0,0,0,0.000000," ","integrate((B*x+A)/x**4/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{x^{4} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**4*(x*(b + c*x))**(3/2)), x)","F",0
129,0,0,0,0.000000," ","integrate(x**5*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x^{5} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
130,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
131,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
132,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
133,0,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
134,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
135,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x**2+b*x)**(5/2),x)","\int \frac{A + B x}{x \left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(x*(b + c*x))**(5/2)), x)","F",0
136,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(c*x**2+b*x)**(5/2),x)","\int \frac{A + B x}{x^{2} \left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**2*(x*(b + c*x))**(5/2)), x)","F",0
137,0,0,0,0.000000," ","integrate((B*x+A)/x**3/(c*x**2+b*x)**(5/2),x)","\int \frac{A + B x}{x^{3} \left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**3*(x*(b + c*x))**(5/2)), x)","F",0
138,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x)**(7/2),x)","\int \frac{d + e x}{\left(x \left(b + c x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)/(x*(b + c*x))**(7/2), x)","F",0
139,0,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x)**(9/2),x)","\int \frac{d + e x}{\left(x \left(b + c x\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((d + e*x)/(x*(b + c*x))**(9/2), x)","F",0
140,1,46,0,7.885797," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x),x)","\frac{2 A b x^{\frac{11}{2}}}{11} + \frac{2 A c x^{\frac{13}{2}}}{13} + \frac{2 B b x^{\frac{13}{2}}}{13} + \frac{2 B c x^{\frac{15}{2}}}{15}"," ",0,"2*A*b*x**(11/2)/11 + 2*A*c*x**(13/2)/13 + 2*B*b*x**(13/2)/13 + 2*B*c*x**(15/2)/15","A",0
141,1,46,0,3.856701," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x),x)","\frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 A c x^{\frac{11}{2}}}{11} + \frac{2 B b x^{\frac{11}{2}}}{11} + \frac{2 B c x^{\frac{13}{2}}}{13}"," ",0,"2*A*b*x**(9/2)/9 + 2*A*c*x**(11/2)/11 + 2*B*b*x**(11/2)/11 + 2*B*c*x**(13/2)/13","A",0
142,1,46,0,1.624726," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x),x)","\frac{2 A b x^{\frac{7}{2}}}{7} + \frac{2 A c x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{11}{2}}}{11}"," ",0,"2*A*b*x**(7/2)/7 + 2*A*c*x**(9/2)/9 + 2*B*b*x**(9/2)/9 + 2*B*c*x**(11/2)/11","A",0
143,1,37,0,2.332572," ","integrate((B*x+A)*(c*x**2+b*x)*x**(1/2),x)","\frac{2 A b x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{9}{2}}}{9} + \frac{2 x^{\frac{7}{2}} \left(A c + B b\right)}{7}"," ",0,"2*A*b*x**(5/2)/5 + 2*B*c*x**(9/2)/9 + 2*x**(7/2)*(A*c + B*b)/7","A",0
144,1,46,0,0.441431," ","integrate((B*x+A)*(c*x**2+b*x)/x**(1/2),x)","\frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 A c x^{\frac{5}{2}}}{5} + \frac{2 B b x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{7}{2}}}{7}"," ",0,"2*A*b*x**(3/2)/3 + 2*A*c*x**(5/2)/5 + 2*B*b*x**(5/2)/5 + 2*B*c*x**(7/2)/7","A",0
145,1,44,0,0.475456," ","integrate((B*x+A)*(c*x**2+b*x)/x**(3/2),x)","2 A b \sqrt{x} + \frac{2 A c x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{3}{2}}}{3} + \frac{2 B c x^{\frac{5}{2}}}{5}"," ",0,"2*A*b*sqrt(x) + 2*A*c*x**(3/2)/3 + 2*B*b*x**(3/2)/3 + 2*B*c*x**(5/2)/5","A",0
146,1,41,0,0.760747," ","integrate((B*x+A)*(c*x**2+b*x)/x**(5/2),x)","- \frac{2 A b}{\sqrt{x}} + 2 A c \sqrt{x} + 2 B b \sqrt{x} + \frac{2 B c x^{\frac{3}{2}}}{3}"," ",0,"-2*A*b/sqrt(x) + 2*A*c*sqrt(x) + 2*B*b*sqrt(x) + 2*B*c*x**(3/2)/3","A",0
147,1,41,0,1.344513," ","integrate((B*x+A)*(c*x**2+b*x)/x**(7/2),x)","- \frac{2 A b}{3 x^{\frac{3}{2}}} - \frac{2 A c}{\sqrt{x}} - \frac{2 B b}{\sqrt{x}} + 2 B c \sqrt{x}"," ",0,"-2*A*b/(3*x**(3/2)) - 2*A*c/sqrt(x) - 2*B*b/sqrt(x) + 2*B*c*sqrt(x)","A",0
148,1,46,0,2.930129," ","integrate((B*x+A)*(c*x**2+b*x)/x**(9/2),x)","- \frac{2 A b}{5 x^{\frac{5}{2}}} - \frac{2 A c}{3 x^{\frac{3}{2}}} - \frac{2 B b}{3 x^{\frac{3}{2}}} - \frac{2 B c}{\sqrt{x}}"," ",0,"-2*A*b/(5*x**(5/2)) - 2*A*c/(3*x**(3/2)) - 2*B*b/(3*x**(3/2)) - 2*B*c/sqrt(x)","A",0
149,1,80,0,14.982149," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x)**2,x)","\frac{2 A b^{2} x^{\frac{13}{2}}}{13} + \frac{4 A b c x^{\frac{15}{2}}}{15} + \frac{2 A c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} + \frac{4 B b c x^{\frac{17}{2}}}{17} + \frac{2 B c^{2} x^{\frac{19}{2}}}{19}"," ",0,"2*A*b**2*x**(13/2)/13 + 4*A*b*c*x**(15/2)/15 + 2*A*c**2*x**(17/2)/17 + 2*B*b**2*x**(15/2)/15 + 4*B*b*c*x**(17/2)/17 + 2*B*c**2*x**(19/2)/19","A",0
150,1,80,0,8.356514," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x)**2,x)","\frac{2 A b^{2} x^{\frac{11}{2}}}{11} + \frac{4 A b c x^{\frac{13}{2}}}{13} + \frac{2 A c^{2} x^{\frac{15}{2}}}{15} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13} + \frac{4 B b c x^{\frac{15}{2}}}{15} + \frac{2 B c^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*A*b**2*x**(11/2)/11 + 4*A*b*c*x**(13/2)/13 + 2*A*c**2*x**(15/2)/15 + 2*B*b**2*x**(13/2)/13 + 4*B*b*c*x**(15/2)/15 + 2*B*c**2*x**(17/2)/17","A",0
151,1,80,0,4.487191," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**2,x)","\frac{2 A b^{2} x^{\frac{9}{2}}}{9} + \frac{4 A b c x^{\frac{11}{2}}}{11} + \frac{2 A c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} x^{\frac{11}{2}}}{11} + \frac{4 B b c x^{\frac{13}{2}}}{13} + \frac{2 B c^{2} x^{\frac{15}{2}}}{15}"," ",0,"2*A*b**2*x**(9/2)/9 + 4*A*b*c*x**(11/2)/11 + 2*A*c**2*x**(13/2)/13 + 2*B*b**2*x**(11/2)/11 + 4*B*b*c*x**(13/2)/13 + 2*B*c**2*x**(15/2)/15","A",0
152,1,66,0,3.239672," ","integrate((B*x+A)*(c*x**2+b*x)**2*x**(1/2),x)","\frac{2 A b^{2} x^{\frac{7}{2}}}{7} + \frac{2 B c^{2} x^{\frac{13}{2}}}{13} + \frac{2 x^{\frac{11}{2}} \left(A c^{2} + 2 B b c\right)}{11} + \frac{2 x^{\frac{9}{2}} \left(2 A b c + B b^{2}\right)}{9}"," ",0,"2*A*b**2*x**(7/2)/7 + 2*B*c**2*x**(13/2)/13 + 2*x**(11/2)*(A*c**2 + 2*B*b*c)/11 + 2*x**(9/2)*(2*A*b*c + B*b**2)/9","A",0
153,1,80,0,1.573215," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**(1/2),x)","\frac{2 A b^{2} x^{\frac{5}{2}}}{5} + \frac{4 A b c x^{\frac{7}{2}}}{7} + \frac{2 A c^{2} x^{\frac{9}{2}}}{9} + \frac{2 B b^{2} x^{\frac{7}{2}}}{7} + \frac{4 B b c x^{\frac{9}{2}}}{9} + \frac{2 B c^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*A*b**2*x**(5/2)/5 + 4*A*b*c*x**(7/2)/7 + 2*A*c**2*x**(9/2)/9 + 2*B*b**2*x**(7/2)/7 + 4*B*b*c*x**(9/2)/9 + 2*B*c**2*x**(11/2)/11","A",0
154,1,80,0,1.502582," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**(3/2),x)","\frac{2 A b^{2} x^{\frac{3}{2}}}{3} + \frac{4 A b c x^{\frac{5}{2}}}{5} + \frac{2 A c^{2} x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} x^{\frac{5}{2}}}{5} + \frac{4 B b c x^{\frac{7}{2}}}{7} + \frac{2 B c^{2} x^{\frac{9}{2}}}{9}"," ",0,"2*A*b**2*x**(3/2)/3 + 4*A*b*c*x**(5/2)/5 + 2*A*c**2*x**(7/2)/7 + 2*B*b**2*x**(5/2)/5 + 4*B*b*c*x**(7/2)/7 + 2*B*c**2*x**(9/2)/9","A",0
155,1,78,0,1.838101," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**(5/2),x)","2 A b^{2} \sqrt{x} + \frac{4 A b c x^{\frac{3}{2}}}{3} + \frac{2 A c^{2} x^{\frac{5}{2}}}{5} + \frac{2 B b^{2} x^{\frac{3}{2}}}{3} + \frac{4 B b c x^{\frac{5}{2}}}{5} + \frac{2 B c^{2} x^{\frac{7}{2}}}{7}"," ",0,"2*A*b**2*sqrt(x) + 4*A*b*c*x**(3/2)/3 + 2*A*c**2*x**(5/2)/5 + 2*B*b**2*x**(3/2)/3 + 4*B*b*c*x**(5/2)/5 + 2*B*c**2*x**(7/2)/7","A",0
156,1,75,0,2.899089," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**(7/2),x)","- \frac{2 A b^{2}}{\sqrt{x}} + 4 A b c \sqrt{x} + \frac{2 A c^{2} x^{\frac{3}{2}}}{3} + 2 B b^{2} \sqrt{x} + \frac{4 B b c x^{\frac{3}{2}}}{3} + \frac{2 B c^{2} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*b**2/sqrt(x) + 4*A*b*c*sqrt(x) + 2*A*c**2*x**(3/2)/3 + 2*B*b**2*sqrt(x) + 4*B*b*c*x**(3/2)/3 + 2*B*c**2*x**(5/2)/5","A",0
157,1,73,0,3.957500," ","integrate((B*x+A)*(c*x**2+b*x)**2/x**(9/2),x)","- \frac{2 A b^{2}}{3 x^{\frac{3}{2}}} - \frac{4 A b c}{\sqrt{x}} + 2 A c^{2} \sqrt{x} - \frac{2 B b^{2}}{\sqrt{x}} + 4 B b c \sqrt{x} + \frac{2 B c^{2} x^{\frac{3}{2}}}{3}"," ",0,"-2*A*b**2/(3*x**(3/2)) - 4*A*b*c/sqrt(x) + 2*A*c**2*sqrt(x) - 2*B*b**2/sqrt(x) + 4*B*b*c*sqrt(x) + 2*B*c**2*x**(3/2)/3","A",0
158,1,114,0,26.590289," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x)**3,x)","\frac{2 A b^{3} x^{\frac{15}{2}}}{15} + \frac{6 A b^{2} c x^{\frac{17}{2}}}{17} + \frac{6 A b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 A c^{3} x^{\frac{21}{2}}}{21} + \frac{2 B b^{3} x^{\frac{17}{2}}}{17} + \frac{6 B b^{2} c x^{\frac{19}{2}}}{19} + \frac{2 B b c^{2} x^{\frac{21}{2}}}{7} + \frac{2 B c^{3} x^{\frac{23}{2}}}{23}"," ",0,"2*A*b**3*x**(15/2)/15 + 6*A*b**2*c*x**(17/2)/17 + 6*A*b*c**2*x**(19/2)/19 + 2*A*c**3*x**(21/2)/21 + 2*B*b**3*x**(17/2)/17 + 6*B*b**2*c*x**(19/2)/19 + 2*B*b*c**2*x**(21/2)/7 + 2*B*c**3*x**(23/2)/23","A",0
159,1,114,0,15.917321," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x)**3,x)","\frac{2 A b^{3} x^{\frac{13}{2}}}{13} + \frac{2 A b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 A b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A c^{3} x^{\frac{19}{2}}}{19} + \frac{2 B b^{3} x^{\frac{15}{2}}}{15} + \frac{6 B b^{2} c x^{\frac{17}{2}}}{17} + \frac{6 B b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B c^{3} x^{\frac{21}{2}}}{21}"," ",0,"2*A*b**3*x**(13/2)/13 + 2*A*b**2*c*x**(15/2)/5 + 6*A*b*c**2*x**(17/2)/17 + 2*A*c**3*x**(19/2)/19 + 2*B*b**3*x**(15/2)/15 + 6*B*b**2*c*x**(17/2)/17 + 6*B*b*c**2*x**(19/2)/19 + 2*B*c**3*x**(21/2)/21","A",0
160,1,114,0,8.270210," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**3,x)","\frac{2 A b^{3} x^{\frac{11}{2}}}{11} + \frac{6 A b^{2} c x^{\frac{13}{2}}}{13} + \frac{2 A b c^{2} x^{\frac{15}{2}}}{5} + \frac{2 A c^{3} x^{\frac{17}{2}}}{17} + \frac{2 B b^{3} x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 B b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B c^{3} x^{\frac{19}{2}}}{19}"," ",0,"2*A*b**3*x**(11/2)/11 + 6*A*b**2*c*x**(13/2)/13 + 2*A*b*c**2*x**(15/2)/5 + 2*A*c**3*x**(17/2)/17 + 2*B*b**3*x**(13/2)/13 + 2*B*b**2*c*x**(15/2)/5 + 6*B*b*c**2*x**(17/2)/17 + 2*B*c**3*x**(19/2)/19","A",0
161,1,95,0,3.763334," ","integrate((B*x+A)*(c*x**2+b*x)**3*x**(1/2),x)","\frac{2 A b^{3} x^{\frac{9}{2}}}{9} + \frac{2 B c^{3} x^{\frac{17}{2}}}{17} + \frac{2 x^{\frac{15}{2}} \left(A c^{3} + 3 B b c^{2}\right)}{15} + \frac{2 x^{\frac{13}{2}} \left(3 A b c^{2} + 3 B b^{2} c\right)}{13} + \frac{2 x^{\frac{11}{2}} \left(3 A b^{2} c + B b^{3}\right)}{11}"," ",0,"2*A*b**3*x**(9/2)/9 + 2*B*c**3*x**(17/2)/17 + 2*x**(15/2)*(A*c**3 + 3*B*b*c**2)/15 + 2*x**(13/2)*(3*A*b*c**2 + 3*B*b**2*c)/13 + 2*x**(11/2)*(3*A*b**2*c + B*b**3)/11","A",0
162,1,114,0,3.513055," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**(1/2),x)","\frac{2 A b^{3} x^{\frac{7}{2}}}{7} + \frac{2 A b^{2} c x^{\frac{9}{2}}}{3} + \frac{6 A b c^{2} x^{\frac{11}{2}}}{11} + \frac{2 A c^{3} x^{\frac{13}{2}}}{13} + \frac{2 B b^{3} x^{\frac{9}{2}}}{9} + \frac{6 B b^{2} c x^{\frac{11}{2}}}{11} + \frac{6 B b c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B c^{3} x^{\frac{15}{2}}}{15}"," ",0,"2*A*b**3*x**(7/2)/7 + 2*A*b**2*c*x**(9/2)/3 + 6*A*b*c**2*x**(11/2)/11 + 2*A*c**3*x**(13/2)/13 + 2*B*b**3*x**(9/2)/9 + 6*B*b**2*c*x**(11/2)/11 + 6*B*b*c**2*x**(13/2)/13 + 2*B*c**3*x**(15/2)/15","A",0
163,1,114,0,3.725578," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**(3/2),x)","\frac{2 A b^{3} x^{\frac{5}{2}}}{5} + \frac{6 A b^{2} c x^{\frac{7}{2}}}{7} + \frac{2 A b c^{2} x^{\frac{9}{2}}}{3} + \frac{2 A c^{3} x^{\frac{11}{2}}}{11} + \frac{2 B b^{3} x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} c x^{\frac{9}{2}}}{3} + \frac{6 B b c^{2} x^{\frac{11}{2}}}{11} + \frac{2 B c^{3} x^{\frac{13}{2}}}{13}"," ",0,"2*A*b**3*x**(5/2)/5 + 6*A*b**2*c*x**(7/2)/7 + 2*A*b*c**2*x**(9/2)/3 + 2*A*c**3*x**(11/2)/11 + 2*B*b**3*x**(7/2)/7 + 2*B*b**2*c*x**(9/2)/3 + 6*B*b*c**2*x**(11/2)/11 + 2*B*c**3*x**(13/2)/13","A",0
164,1,114,0,4.351801," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**(5/2),x)","\frac{2 A b^{3} x^{\frac{3}{2}}}{3} + \frac{6 A b^{2} c x^{\frac{5}{2}}}{5} + \frac{6 A b c^{2} x^{\frac{7}{2}}}{7} + \frac{2 A c^{3} x^{\frac{9}{2}}}{9} + \frac{2 B b^{3} x^{\frac{5}{2}}}{5} + \frac{6 B b^{2} c x^{\frac{7}{2}}}{7} + \frac{2 B b c^{2} x^{\frac{9}{2}}}{3} + \frac{2 B c^{3} x^{\frac{11}{2}}}{11}"," ",0,"2*A*b**3*x**(3/2)/3 + 6*A*b**2*c*x**(5/2)/5 + 6*A*b*c**2*x**(7/2)/7 + 2*A*c**3*x**(9/2)/9 + 2*B*b**3*x**(5/2)/5 + 6*B*b**2*c*x**(7/2)/7 + 2*B*b*c**2*x**(9/2)/3 + 2*B*c**3*x**(11/2)/11","A",0
165,1,110,0,5.972371," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**(7/2),x)","2 A b^{3} \sqrt{x} + 2 A b^{2} c x^{\frac{3}{2}} + \frac{6 A b c^{2} x^{\frac{5}{2}}}{5} + \frac{2 A c^{3} x^{\frac{7}{2}}}{7} + \frac{2 B b^{3} x^{\frac{3}{2}}}{3} + \frac{6 B b^{2} c x^{\frac{5}{2}}}{5} + \frac{6 B b c^{2} x^{\frac{7}{2}}}{7} + \frac{2 B c^{3} x^{\frac{9}{2}}}{9}"," ",0,"2*A*b**3*sqrt(x) + 2*A*b**2*c*x**(3/2) + 6*A*b*c**2*x**(5/2)/5 + 2*A*c**3*x**(7/2)/7 + 2*B*b**3*x**(3/2)/3 + 6*B*b**2*c*x**(5/2)/5 + 6*B*b*c**2*x**(7/2)/7 + 2*B*c**3*x**(9/2)/9","A",0
166,1,105,0,7.852220," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**(9/2),x)","- \frac{2 A b^{3}}{\sqrt{x}} + 6 A b^{2} c \sqrt{x} + 2 A b c^{2} x^{\frac{3}{2}} + \frac{2 A c^{3} x^{\frac{5}{2}}}{5} + 2 B b^{3} \sqrt{x} + 2 B b^{2} c x^{\frac{3}{2}} + \frac{6 B b c^{2} x^{\frac{5}{2}}}{5} + \frac{2 B c^{3} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*b**3/sqrt(x) + 6*A*b**2*c*sqrt(x) + 2*A*b*c**2*x**(3/2) + 2*A*c**3*x**(5/2)/5 + 2*B*b**3*sqrt(x) + 2*B*b**2*c*x**(3/2) + 6*B*b*c**2*x**(5/2)/5 + 2*B*c**3*x**(7/2)/7","A",0
167,1,105,0,10.336954," ","integrate((B*x+A)*(c*x**2+b*x)**3/x**(11/2),x)","- \frac{2 A b^{3}}{3 x^{\frac{3}{2}}} - \frac{6 A b^{2} c}{\sqrt{x}} + 6 A b c^{2} \sqrt{x} + \frac{2 A c^{3} x^{\frac{3}{2}}}{3} - \frac{2 B b^{3}}{\sqrt{x}} + 6 B b^{2} c \sqrt{x} + 2 B b c^{2} x^{\frac{3}{2}} + \frac{2 B c^{3} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*b**3/(3*x**(3/2)) - 6*A*b**2*c/sqrt(x) + 6*A*b*c**2*sqrt(x) + 2*A*c**3*x**(3/2)/3 - 2*B*b**3/sqrt(x) + 6*B*b**2*c*sqrt(x) + 2*B*b*c**2*x**(3/2) + 2*B*c**3*x**(5/2)/5","A",0
168,1,279,0,45.393601," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x),x)","\begin{cases} \frac{i A b^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{4} \sqrt{\frac{1}{c}}} - \frac{i A b^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{4} \sqrt{\frac{1}{c}}} + \frac{2 A b^{2} \sqrt{x}}{c^{3}} - \frac{2 A b x^{\frac{3}{2}}}{3 c^{2}} + \frac{2 A x^{\frac{5}{2}}}{5 c} - \frac{i B b^{\frac{7}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{5} \sqrt{\frac{1}{c}}} + \frac{i B b^{\frac{7}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{5} \sqrt{\frac{1}{c}}} - \frac{2 B b^{3} \sqrt{x}}{c^{4}} + \frac{2 B b^{2} x^{\frac{3}{2}}}{3 c^{3}} - \frac{2 B b x^{\frac{5}{2}}}{5 c^{2}} + \frac{2 B x^{\frac{7}{2}}}{7 c} & \text{for}\: c \neq 0 \\\frac{\frac{2 A x^{\frac{7}{2}}}{7} + \frac{2 B x^{\frac{9}{2}}}{9}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*A*b**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**4*sqrt(1/c)) - I*A*b**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**4*sqrt(1/c)) + 2*A*b**2*sqrt(x)/c**3 - 2*A*b*x**(3/2)/(3*c**2) + 2*A*x**(5/2)/(5*c) - I*B*b**(7/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**5*sqrt(1/c)) + I*B*b**(7/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**5*sqrt(1/c)) - 2*B*b**3*sqrt(x)/c**4 + 2*B*b**2*x**(3/2)/(3*c**3) - 2*B*b*x**(5/2)/(5*c**2) + 2*B*x**(7/2)/(7*c), Ne(c, 0)), ((2*A*x**(7/2)/7 + 2*B*x**(9/2)/9)/b, True))","A",0
169,1,245,0,16.350315," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x),x)","\begin{cases} - \frac{i A b^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{3} \sqrt{\frac{1}{c}}} + \frac{i A b^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{3} \sqrt{\frac{1}{c}}} - \frac{2 A b \sqrt{x}}{c^{2}} + \frac{2 A x^{\frac{3}{2}}}{3 c} + \frac{i B b^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{4} \sqrt{\frac{1}{c}}} - \frac{i B b^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{4} \sqrt{\frac{1}{c}}} + \frac{2 B b^{2} \sqrt{x}}{c^{3}} - \frac{2 B b x^{\frac{3}{2}}}{3 c^{2}} + \frac{2 B x^{\frac{5}{2}}}{5 c} & \text{for}\: c \neq 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*A*b**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**3*sqrt(1/c)) + I*A*b**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**3*sqrt(1/c)) - 2*A*b*sqrt(x)/c**2 + 2*A*x**(3/2)/(3*c) + I*B*b**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**4*sqrt(1/c)) - I*B*b**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**4*sqrt(1/c)) + 2*B*b**2*sqrt(x)/c**3 - 2*B*b*x**(3/2)/(3*c**2) + 2*B*x**(5/2)/(5*c), Ne(c, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(7/2)/7)/b, True))","A",0
170,1,212,0,6.703471," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x),x)","\begin{cases} \frac{i A \sqrt{b} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{2} \sqrt{\frac{1}{c}}} - \frac{i A \sqrt{b} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{2} \sqrt{\frac{1}{c}}} + \frac{2 A \sqrt{x}}{c} - \frac{i B b^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{3} \sqrt{\frac{1}{c}}} + \frac{i B b^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{3} \sqrt{\frac{1}{c}}} - \frac{2 B b \sqrt{x}}{c^{2}} + \frac{2 B x^{\frac{3}{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*A*sqrt(b)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**2*sqrt(1/c)) - I*A*sqrt(b)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**2*sqrt(1/c)) + 2*A*sqrt(x)/c - I*B*b**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**3*sqrt(1/c)) + I*B*b**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**3*sqrt(1/c)) - 2*B*b*sqrt(x)/c**2 + 2*B*x**(3/2)/(3*c), Ne(c, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/b, True))","A",0
171,1,218,0,2.193459," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{c} & \text{for}\: b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{b} & \text{for}\: c = 0 \\- \frac{i A \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} + \frac{i A \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} + \frac{i B \sqrt{b} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{2} \sqrt{\frac{1}{c}}} - \frac{i B \sqrt{b} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{2} \sqrt{\frac{1}{c}}} + \frac{2 B \sqrt{x}}{c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*sqrt(x)), Eq(b, 0) & Eq(c, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/c, Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/b, Eq(c, 0)), (-I*A*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)) + I*A*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)) + I*B*sqrt(b)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**2*sqrt(1/c)) - I*B*sqrt(b)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**2*sqrt(1/c)) + 2*B*sqrt(x)/c, True))","A",0
172,1,216,0,3.398807," ","integrate((B*x+A)/(c*x**2+b*x)/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{c} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{b} & \text{for}\: c = 0 \\- \frac{2 A}{b \sqrt{x}} + \frac{i A \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{i A \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{i B \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} + \frac{i B \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) - 2*B/sqrt(x)), Eq(b, 0) & Eq(c, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/c, Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/b, Eq(c, 0)), (-2*A/(b*sqrt(x)) + I*A*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(3/2)*sqrt(1/c)) - I*A*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(3/2)*sqrt(1/c)) - I*B*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)) + I*B*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)), True))","A",0
173,1,248,0,7.005151," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{b} & \text{for}\: c = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{c} & \text{for}\: b = 0 \\- \frac{2 A}{3 b x^{\frac{3}{2}}} + \frac{2 A c}{b^{2} \sqrt{x}} - \frac{i A c \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{i A c \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{2 B}{b \sqrt{x}} + \frac{i B \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{i B \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/b, Eq(c, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/c, Eq(b, 0)), (-2*A/(3*b*x**(3/2)) + 2*A*c/(b**2*sqrt(x)) - I*A*c*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(5/2)*sqrt(1/c)) + I*A*c*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(5/2)*sqrt(1/c)) - 2*B/(b*sqrt(x)) + I*B*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(3/2)*sqrt(1/c)) - I*B*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(3/2)*sqrt(1/c)), True))","A",0
174,1,289,0,18.367377," ","integrate((B*x+A)/x**(5/2)/(c*x**2+b*x),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{c} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{b} & \text{for}\: c = 0 \\- \frac{2 A}{5 b x^{\frac{5}{2}}} + \frac{2 A c}{3 b^{2} x^{\frac{3}{2}}} - \frac{2 A c^{2}}{b^{3} \sqrt{x}} + \frac{i A c^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{i A c^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{2 B}{3 b x^{\frac{3}{2}}} + \frac{2 B c}{b^{2} \sqrt{x}} - \frac{i B c \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{i B c \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{5}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/c, Eq(b, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/b, Eq(c, 0)), (-2*A/(5*b*x**(5/2)) + 2*A*c/(3*b**2*x**(3/2)) - 2*A*c**2/(b**3*sqrt(x)) + I*A*c**2*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(7/2)*sqrt(1/c)) - I*A*c**2*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(7/2)*sqrt(1/c)) - 2*B/(3*b*x**(3/2)) + 2*B*c/(b**2*sqrt(x)) - I*B*c*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(5/2)*sqrt(1/c)) + I*B*c*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(5/2)*sqrt(1/c)), True))","A",0
175,1,326,0,52.048179," ","integrate((B*x+A)/x**(7/2)/(c*x**2+b*x),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{b} & \text{for}\: c = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{c} & \text{for}\: b = 0 \\- \frac{2 A}{7 b x^{\frac{7}{2}}} + \frac{2 A c}{5 b^{2} x^{\frac{5}{2}}} - \frac{2 A c^{2}}{3 b^{3} x^{\frac{3}{2}}} + \frac{2 A c^{3}}{b^{4} \sqrt{x}} - \frac{i A c^{3} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{9}{2}} \sqrt{\frac{1}{c}}} + \frac{i A c^{3} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{9}{2}} \sqrt{\frac{1}{c}}} - \frac{2 B}{5 b x^{\frac{5}{2}}} + \frac{2 B c}{3 b^{2} x^{\frac{3}{2}}} - \frac{2 B c^{2}}{b^{3} \sqrt{x}} + \frac{i B c^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{i B c^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{7}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/b, Eq(c, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/c, Eq(b, 0)), (-2*A/(7*b*x**(7/2)) + 2*A*c/(5*b**2*x**(5/2)) - 2*A*c**2/(3*b**3*x**(3/2)) + 2*A*c**3/(b**4*sqrt(x)) - I*A*c**3*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(9/2)*sqrt(1/c)) + I*A*c**3*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(9/2)*sqrt(1/c)) - 2*B/(5*b*x**(5/2)) + 2*B*c/(3*b**2*x**(3/2)) - 2*B*c**2/(b**3*sqrt(x)) + I*B*c**2*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(7/2)*sqrt(1/c)) - I*B*c**2*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(7/2)*sqrt(1/c)), True))","A",0
176,1,360,0,126.307014," ","integrate((B*x+A)/x**(9/2)/(c*x**2+b*x),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{11 x^{\frac{11}{2}}} - \frac{2 B}{9 x^{\frac{9}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{11 x^{\frac{11}{2}}} - \frac{2 B}{9 x^{\frac{9}{2}}}}{c} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{b} & \text{for}\: c = 0 \\- \frac{2 A}{9 b x^{\frac{9}{2}}} + \frac{2 A c}{7 b^{2} x^{\frac{7}{2}}} - \frac{2 A c^{2}}{5 b^{3} x^{\frac{5}{2}}} + \frac{2 A c^{3}}{3 b^{4} x^{\frac{3}{2}}} - \frac{2 A c^{4}}{b^{5} \sqrt{x}} + \frac{i A c^{4} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{11}{2}} \sqrt{\frac{1}{c}}} - \frac{i A c^{4} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{11}{2}} \sqrt{\frac{1}{c}}} - \frac{2 B}{7 b x^{\frac{7}{2}}} + \frac{2 B c}{5 b^{2} x^{\frac{5}{2}}} - \frac{2 B c^{2}}{3 b^{3} x^{\frac{3}{2}}} + \frac{2 B c^{3}}{b^{4} \sqrt{x}} - \frac{i B c^{3} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{9}{2}} \sqrt{\frac{1}{c}}} + \frac{i B c^{3} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{9}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(11*x**(11/2)) - 2*B/(9*x**(9/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(11*x**(11/2)) - 2*B/(9*x**(9/2)))/c, Eq(b, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/b, Eq(c, 0)), (-2*A/(9*b*x**(9/2)) + 2*A*c/(7*b**2*x**(7/2)) - 2*A*c**2/(5*b**3*x**(5/2)) + 2*A*c**3/(3*b**4*x**(3/2)) - 2*A*c**4/(b**5*sqrt(x)) + I*A*c**4*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(11/2)*sqrt(1/c)) - I*A*c**4*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(11/2)*sqrt(1/c)) - 2*B/(7*b*x**(7/2)) + 2*B*c/(5*b**2*x**(5/2)) - 2*B*c**2/(3*b**3*x**(3/2)) + 2*B*c**3/(b**4*sqrt(x)) - I*B*c**3*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(9/2)*sqrt(1/c)) + I*B*c**3*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(9/2)*sqrt(1/c)), True))","A",0
177,-1,0,0,0.000000," ","integrate(x**(9/2)*(B*x+A)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,1,782,0,107.253948," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{c^{2}} & \text{for}\: b = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{b^{2}} & \text{for}\: c = 0 \\- \frac{2 i A \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{1}{c}}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} + \frac{A b c \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} - \frac{A b c \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} + \frac{A c^{2} x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} - \frac{A c^{2} x \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} + \frac{6 i B b^{\frac{3}{2}} c \sqrt{x} \sqrt{\frac{1}{c}}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} + \frac{4 i B \sqrt{b} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} - \frac{3 B b^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} + \frac{3 B b^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} - \frac{3 B b c x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} + \frac{3 B b c x \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{c}} + 2 i \sqrt{b} c^{4} x \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*sqrt(x)), Eq(b, 0) & Eq(c, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/c**2, Eq(b, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/b**2, Eq(c, 0)), (-2*I*A*sqrt(b)*c**2*sqrt(x)*sqrt(1/c)/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) + A*b*c*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) - A*b*c*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) + A*c**2*x*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) - A*c**2*x*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) + 6*I*B*b**(3/2)*c*sqrt(x)*sqrt(1/c)/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) + 4*I*B*sqrt(b)*c**2*x**(3/2)*sqrt(1/c)/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) - 3*B*b**2*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) + 3*B*b**2*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) - 3*B*b*c*x*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)) + 3*B*b*c*x*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(3/2)*c**3*sqrt(1/c) + 2*I*sqrt(b)*c**4*x*sqrt(1/c)), True))","A",0
180,1,716,0,55.268171," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{c^{2}} & \text{for}\: b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{b^{2}} & \text{for}\: c = 0 \\\frac{2 i A \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{1}{c}}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} + \frac{A b c \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} - \frac{A b c \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} + \frac{A c^{2} x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} - \frac{A c^{2} x \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} - \frac{2 i B b^{\frac{3}{2}} c \sqrt{x} \sqrt{\frac{1}{c}}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} + \frac{B b^{2} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} - \frac{B b^{2} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} + \frac{B b c x \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} - \frac{B b c x \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c^{2} \sqrt{\frac{1}{c}} + 2 i b^{\frac{3}{2}} c^{3} x \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) - 2*B/sqrt(x)), Eq(b, 0) & Eq(c, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/c**2, Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/b**2, Eq(c, 0)), (2*I*A*sqrt(b)*c**2*sqrt(x)*sqrt(1/c)/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) + A*b*c*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) - A*b*c*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) + A*c**2*x*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) - A*c**2*x*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) - 2*I*B*b**(3/2)*c*sqrt(x)*sqrt(1/c)/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) + B*b**2*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) - B*b**2*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) + B*b*c*x*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)) - B*b*c*x*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(5/2)*c**2*sqrt(1/c) + 2*I*b**(3/2)*c**3*x*sqrt(1/c)), True))","A",0
181,1,884,0,33.157831," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{c^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{b^{2}} & \text{for}\: c = 0 \\- \frac{4 i A b^{\frac{3}{2}} c \sqrt{\frac{1}{c}}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{6 i A \sqrt{b} c^{2} x \sqrt{\frac{1}{c}}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{3 A b c \sqrt{x} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} + \frac{3 A b c \sqrt{x} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{3 A c^{2} x^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} + \frac{3 A c^{2} x^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} + \frac{2 i B b^{\frac{3}{2}} c x \sqrt{\frac{1}{c}}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} + \frac{B b^{2} \sqrt{x} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{B b^{2} \sqrt{x} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} + \frac{B b c x^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{B b c x^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{2 i b^{\frac{7}{2}} c \sqrt{x} \sqrt{\frac{1}{c}} + 2 i b^{\frac{5}{2}} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/c**2, Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/b**2, Eq(c, 0)), (-4*I*A*b**(3/2)*c*sqrt(1/c)/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) - 6*I*A*sqrt(b)*c**2*x*sqrt(1/c)/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) - 3*A*b*c*sqrt(x)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) + 3*A*b*c*sqrt(x)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) - 3*A*c**2*x**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) + 3*A*c**2*x**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) + 2*I*B*b**(3/2)*c*x*sqrt(1/c)/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) + B*b**2*sqrt(x)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) - B*b**2*sqrt(x)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) + B*b*c*x**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)) - B*b*c*x**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(2*I*b**(7/2)*c*sqrt(x)*sqrt(1/c) + 2*I*b**(5/2)*c**2*x**(3/2)*sqrt(1/c)), True))","A",0
182,1,983,0,42.917234," ","integrate((B*x+A)/(c*x**2+b*x)**2/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{c^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{b^{2}} & \text{for}\: c = 0 \\- \frac{4 i A b^{\frac{5}{2}} \sqrt{\frac{1}{c}}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{20 i A b^{\frac{3}{2}} c x \sqrt{\frac{1}{c}}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{30 i A \sqrt{b} c^{2} x^{2} \sqrt{\frac{1}{c}}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{15 A b c x^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{15 A b c x^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{15 A c^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{15 A c^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{12 i B b^{\frac{5}{2}} x \sqrt{\frac{1}{c}}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{18 i B b^{\frac{3}{2}} c x^{2} \sqrt{\frac{1}{c}}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{9 B b^{2} x^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{9 B b^{2} x^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} - \frac{9 B b c x^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} + \frac{9 B b c x^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{6 i b^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 6 i b^{\frac{7}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/c**2, Eq(b, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/b**2, Eq(c, 0)), (-4*I*A*b**(5/2)*sqrt(1/c)/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) + 20*I*A*b**(3/2)*c*x*sqrt(1/c)/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) + 30*I*A*sqrt(b)*c**2*x**2*sqrt(1/c)/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) + 15*A*b*c*x**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) - 15*A*b*c*x**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) + 15*A*c**2*x**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) - 15*A*c**2*x**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) - 12*I*B*b**(5/2)*x*sqrt(1/c)/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) - 18*I*B*b**(3/2)*c*x**2*sqrt(1/c)/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) - 9*B*b**2*x**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) + 9*B*b**2*x**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) - 9*B*b*c*x**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)) + 9*B*b*c*x**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(6*I*b**(9/2)*x**(3/2)*sqrt(1/c) + 6*I*b**(7/2)*c*x**(5/2)*sqrt(1/c)), True))","A",0
183,1,1127,0,81.927887," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{c^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{b^{2}} & \text{for}\: c = 0 \\- \frac{12 i A b^{\frac{7}{2}} \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{28 i A b^{\frac{5}{2}} c x \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{140 i A b^{\frac{3}{2}} c^{2} x^{2} \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{210 i A \sqrt{b} c^{3} x^{3} \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{105 A b c^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{105 A b c^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{105 A c^{3} x^{\frac{7}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{105 A c^{3} x^{\frac{7}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{20 i B b^{\frac{7}{2}} x \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{100 i B b^{\frac{5}{2}} c x^{2} \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{150 i B b^{\frac{3}{2}} c^{2} x^{3} \sqrt{\frac{1}{c}}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{75 B b^{2} c x^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{75 B b^{2} c x^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{75 B b c^{2} x^{\frac{7}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{75 B b c^{2} x^{\frac{7}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{30 i b^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 30 i b^{\frac{9}{2}} c x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/c**2, Eq(b, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/b**2, Eq(c, 0)), (-12*I*A*b**(7/2)*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 28*I*A*b**(5/2)*c*x*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 140*I*A*b**(3/2)*c**2*x**2*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 210*I*A*sqrt(b)*c**3*x**3*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 105*A*b*c**2*x**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 105*A*b*c**2*x**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 105*A*c**3*x**(7/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 105*A*c**3*x**(7/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 20*I*B*b**(7/2)*x*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 100*I*B*b**(5/2)*c*x**2*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 150*I*B*b**(3/2)*c**2*x**3*sqrt(1/c)/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 75*B*b**2*c*x**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 75*B*b**2*c*x**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) + 75*B*b*c**2*x**(7/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)) - 75*B*b*c**2*x**(7/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(30*I*b**(11/2)*x**(5/2)*sqrt(1/c) + 30*I*b**(9/2)*c*x**(7/2)*sqrt(1/c)), True))","A",0
184,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate(x**(13/2)*(B*x+A)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate(x**(11/2)*(B*x+A)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate(x**(9/2)*(B*x+A)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,1,1880,0,165.440815," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x)**3,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{c^{3}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{b^{3}} & \text{for}\: c = 0 \\- \frac{16 i A b^{\frac{7}{2}} \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{112 i A b^{\frac{5}{2}} c x \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{350 i A b^{\frac{3}{2}} c^{2} x^{2} \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{210 i A \sqrt{b} c^{3} x^{3} \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{105 A b^{2} c x^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{105 A b^{2} c x^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{210 A b c^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{210 A b c^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{105 A c^{3} x^{\frac{7}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{105 A c^{3} x^{\frac{7}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{48 i B b^{\frac{7}{2}} x \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{150 i B b^{\frac{5}{2}} c x^{2} \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{90 i B b^{\frac{3}{2}} c^{2} x^{3} \sqrt{\frac{1}{c}}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{45 B b^{3} x^{\frac{3}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{45 B b^{3} x^{\frac{3}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{90 B b^{2} c x^{\frac{5}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{90 B b^{2} c x^{\frac{5}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} - \frac{45 B b c^{2} x^{\frac{7}{2}} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} + \frac{45 B b c^{2} x^{\frac{7}{2}} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{24 i b^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{c}} + 48 i b^{\frac{11}{2}} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} + 24 i b^{\frac{9}{2}} c^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(b, 0) & Eq(c, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/c**3, Eq(b, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/b**3, Eq(c, 0)), (-16*I*A*b**(7/2)*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 112*I*A*b**(5/2)*c*x*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 350*I*A*b**(3/2)*c**2*x**2*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 210*I*A*sqrt(b)*c**3*x**3*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 105*A*b**2*c*x**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 105*A*b**2*c*x**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 210*A*b*c**2*x**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 210*A*b*c**2*x**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 105*A*c**3*x**(7/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 105*A*c**3*x**(7/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 48*I*B*b**(7/2)*x*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 150*I*B*b**(5/2)*c*x**2*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 90*I*B*b**(3/2)*c**2*x**3*sqrt(1/c)/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 45*B*b**3*x**(3/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 45*B*b**3*x**(3/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 90*B*b**2*c*x**(5/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 90*B*b**2*c*x**(5/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) - 45*B*b*c**2*x**(7/2)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)) + 45*B*b*c**2*x**(7/2)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(24*I*b**(13/2)*x**(3/2)*sqrt(1/c) + 48*I*b**(11/2)*c*x**(5/2)*sqrt(1/c) + 24*I*b**(9/2)*c**2*x**(7/2)*sqrt(1/c)), True))","A",0
192,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x)**(1/2),x)","\int x^{\frac{7}{2}} \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(x**(7/2)*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
195,0,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x)**(1/2),x)","\int x^{\frac{5}{2}} \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(x**(5/2)*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
196,0,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**(1/2),x)","\int x^{\frac{3}{2}} \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(x**(3/2)*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
197,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x} \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(sqrt(x)*sqrt(x*(b + c*x))*(A + B*x), x)","F",0
198,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**(1/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\sqrt{x}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/sqrt(x), x)","F",0
199,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**(3/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**(3/2), x)","F",0
200,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**(5/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**(5/2), x)","F",0
201,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**(7/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**(7/2), x)","F",0
202,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/x**(9/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/x**(9/2), x)","F",0
203,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,0,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**(3/2),x)","\int x^{\frac{3}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(x**(3/2)*(x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
205,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)*x**(1/2),x)","\int \sqrt{x} \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(sqrt(x)*(x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
206,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(1/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\sqrt{x}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/sqrt(x), x)","F",0
207,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**(3/2), x)","F",0
208,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**(5/2), x)","F",0
209,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(7/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**(7/2), x)","F",0
210,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(9/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**(9/2), x)","F",0
211,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(11/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{x^{\frac{11}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/x**(11/2), x)","F",0
212,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)*x**(1/2),x)","\int \sqrt{x} \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)\, dx"," ",0,"Integral(sqrt(x)*(x*(b + c*x))**(5/2)*(A + B*x), x)","F",0
216,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(1/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{\sqrt{x}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/sqrt(x), x)","F",0
217,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**(3/2), x)","F",0
218,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(7/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**(7/2), x)","F",0
220,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(9/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**(9/2), x)","F",0
221,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(11/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{x^{\frac{11}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/x**(11/2), x)","F",0
222,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/x**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,0,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{\frac{7}{2}} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**(7/2)*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
226,0,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{\frac{5}{2}} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**(5/2)*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
227,0,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{x^{\frac{3}{2}} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(x**(3/2)*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
228,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\sqrt{x} \left(A + B x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)/sqrt(x*(b + c*x)), x)","F",0
229,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{e x} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(e*x)*sqrt(x*(b + c*x))), x)","F",0
230,0,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{\frac{3}{2}} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**(3/2)*sqrt(x*(b + c*x))), x)","F",0
231,0,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{\frac{5}{2}} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**(5/2)*sqrt(x*(b + c*x))), x)","F",0
232,0,0,0,0.000000," ","integrate((B*x+A)/x**(7/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{x^{\frac{7}{2}} \sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/(x**(7/2)*sqrt(x*(b + c*x))), x)","F",0
233,-1,0,0,0.000000," ","integrate(x**(9/2)*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,0,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{5}{2}} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(5/2)*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
236,0,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{x^{\frac{3}{2}} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(3/2)*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
237,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{\sqrt{x} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
238,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(3/2)/x**(1/2),x)","\int \frac{A + B x}{\sqrt{x} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x)*(x*(b + c*x))**(3/2)), x)","F",0
239,0,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{x^{\frac{3}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**(3/2)*(x*(b + c*x))**(3/2)), x)","F",0
240,0,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{x^{\frac{5}{2}} \left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**(5/2)*(x*(b + c*x))**(3/2)), x)","F",0
241,-1,0,0,0.000000," ","integrate((B*x+A)/x**(7/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate(x**(11/2)*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate(x**(9/2)*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,0,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x^{\frac{5}{2}} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**(5/2)*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
246,0,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{x^{\frac{3}{2}} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**(3/2)*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
247,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x)**(5/2),x)","\int \frac{\sqrt{x} \left(A + B x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
248,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(5/2)/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,1,56,0,43.344257," ","integrate(x**(1+p)*(3*c*x+2*b)*(c*x**2+b*x)**p,x)","\begin{cases} \frac{b x^{2} x^{p} \left(b x + c x^{2}\right)^{p}}{p + 1} + \frac{c x^{3} x^{p} \left(b x + c x^{2}\right)^{p}}{p + 1} & \text{for}\: p \neq -1 \\2 \log{\left(x \right)} + \log{\left(\frac{b}{c} + x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b*x**2*x**p*(b*x + c*x**2)**p/(p + 1) + c*x**3*x**p*(b*x + c*x**2)**p/(p + 1), Ne(p, -1)), (2*log(x) + log(b/c + x), True))","A",0
251,1,32,0,0.068269," ","integrate(x**3*(B*x+A)*(c*x**2+a),x)","\frac{A a x^{4}}{4} + \frac{A c x^{6}}{6} + \frac{B a x^{5}}{5} + \frac{B c x^{7}}{7}"," ",0,"A*a*x**4/4 + A*c*x**6/6 + B*a*x**5/5 + B*c*x**7/7","A",0
252,1,32,0,0.067817," ","integrate(x**2*(B*x+A)*(c*x**2+a),x)","\frac{A a x^{3}}{3} + \frac{A c x^{5}}{5} + \frac{B a x^{4}}{4} + \frac{B c x^{6}}{6}"," ",0,"A*a*x**3/3 + A*c*x**5/5 + B*a*x**4/4 + B*c*x**6/6","A",0
253,1,32,0,0.071574," ","integrate(x*(B*x+A)*(c*x**2+a),x)","\frac{A a x^{2}}{2} + \frac{A c x^{4}}{4} + \frac{B a x^{3}}{3} + \frac{B c x^{5}}{5}"," ",0,"A*a*x**2/2 + A*c*x**4/4 + B*a*x**3/3 + B*c*x**5/5","A",0
254,1,29,0,0.065564," ","integrate((B*x+A)*(c*x**2+a),x)","A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4}"," ",0,"A*a*x + A*c*x**3/3 + B*a*x**2/2 + B*c*x**4/4","A",0
255,1,27,0,0.114166," ","integrate((B*x+A)*(c*x**2+a)/x,x)","A a \log{\left(x \right)} + \frac{A c x^{2}}{2} + B a x + \frac{B c x^{3}}{3}"," ",0,"A*a*log(x) + A*c*x**2/2 + B*a*x + B*c*x**3/3","A",0
256,1,24,0,0.135700," ","integrate((B*x+A)*(c*x**2+a)/x**2,x)","- \frac{A a}{x} + A c x + B a \log{\left(x \right)} + \frac{B c x^{2}}{2}"," ",0,"-A*a/x + A*c*x + B*a*log(x) + B*c*x**2/2","A",0
257,1,27,0,0.214818," ","integrate((B*x+A)*(c*x**2+a)/x**3,x)","A c \log{\left(x \right)} + B c x + \frac{- A a - 2 B a x}{2 x^{2}}"," ",0,"A*c*log(x) + B*c*x + (-A*a - 2*B*a*x)/(2*x**2)","A",0
258,1,61,0,0.076180," ","integrate(x**3*(B*x+A)*(c*x**2+a)**2,x)","\frac{A a^{2} x^{4}}{4} + \frac{A a c x^{6}}{3} + \frac{A c^{2} x^{8}}{8} + \frac{B a^{2} x^{5}}{5} + \frac{2 B a c x^{7}}{7} + \frac{B c^{2} x^{9}}{9}"," ",0,"A*a**2*x**4/4 + A*a*c*x**6/3 + A*c**2*x**8/8 + B*a**2*x**5/5 + 2*B*a*c*x**7/7 + B*c**2*x**9/9","A",0
259,1,61,0,0.076366," ","integrate(x**2*(B*x+A)*(c*x**2+a)**2,x)","\frac{A a^{2} x^{3}}{3} + \frac{2 A a c x^{5}}{5} + \frac{A c^{2} x^{7}}{7} + \frac{B a^{2} x^{4}}{4} + \frac{B a c x^{6}}{3} + \frac{B c^{2} x^{8}}{8}"," ",0,"A*a**2*x**3/3 + 2*A*a*c*x**5/5 + A*c**2*x**7/7 + B*a**2*x**4/4 + B*a*c*x**6/3 + B*c**2*x**8/8","A",0
260,1,61,0,0.074722," ","integrate(x*(B*x+A)*(c*x**2+a)**2,x)","\frac{A a^{2} x^{2}}{2} + \frac{A a c x^{4}}{2} + \frac{A c^{2} x^{6}}{6} + \frac{B a^{2} x^{3}}{3} + \frac{2 B a c x^{5}}{5} + \frac{B c^{2} x^{7}}{7}"," ",0,"A*a**2*x**2/2 + A*a*c*x**4/2 + A*c**2*x**6/6 + B*a**2*x**3/3 + 2*B*a*c*x**5/5 + B*c**2*x**7/7","A",0
261,1,58,0,0.075522," ","integrate((B*x+A)*(c*x**2+a)**2,x)","A a^{2} x + \frac{2 A a c x^{3}}{3} + \frac{A c^{2} x^{5}}{5} + \frac{B a^{2} x^{2}}{2} + \frac{B a c x^{4}}{2} + \frac{B c^{2} x^{6}}{6}"," ",0,"A*a**2*x + 2*A*a*c*x**3/3 + A*c**2*x**5/5 + B*a**2*x**2/2 + B*a*c*x**4/2 + B*c**2*x**6/6","A",0
262,1,54,0,0.146700," ","integrate((B*x+A)*(c*x**2+a)**2/x,x)","A a^{2} \log{\left(x \right)} + A a c x^{2} + \frac{A c^{2} x^{4}}{4} + B a^{2} x + \frac{2 B a c x^{3}}{3} + \frac{B c^{2} x^{5}}{5}"," ",0,"A*a**2*log(x) + A*a*c*x**2 + A*c**2*x**4/4 + B*a**2*x + 2*B*a*c*x**3/3 + B*c**2*x**5/5","A",0
263,1,51,0,0.167568," ","integrate((B*x+A)*(c*x**2+a)**2/x**2,x)","- \frac{A a^{2}}{x} + 2 A a c x + \frac{A c^{2} x^{3}}{3} + B a^{2} \log{\left(x \right)} + B a c x^{2} + \frac{B c^{2} x^{4}}{4}"," ",0,"-A*a**2/x + 2*A*a*c*x + A*c**2*x**3/3 + B*a**2*log(x) + B*a*c*x**2 + B*c**2*x**4/4","A",0
264,1,58,0,0.248954," ","integrate((B*x+A)*(c*x**2+a)**2/x**3,x)","2 A a c \log{\left(x \right)} + \frac{A c^{2} x^{2}}{2} + 2 B a c x + \frac{B c^{2} x^{3}}{3} + \frac{- A a^{2} - 2 B a^{2} x}{2 x^{2}}"," ",0,"2*A*a*c*log(x) + A*c**2*x**2/2 + 2*B*a*c*x + B*c**2*x**3/3 + (-A*a**2 - 2*B*a**2*x)/(2*x**2)","A",0
265,1,90,0,0.081254," ","integrate(x**3*(B*x+A)*(c*x**2+a)**3,x)","\frac{A a^{3} x^{4}}{4} + \frac{A a^{2} c x^{6}}{2} + \frac{3 A a c^{2} x^{8}}{8} + \frac{A c^{3} x^{10}}{10} + \frac{B a^{3} x^{5}}{5} + \frac{3 B a^{2} c x^{7}}{7} + \frac{B a c^{2} x^{9}}{3} + \frac{B c^{3} x^{11}}{11}"," ",0,"A*a**3*x**4/4 + A*a**2*c*x**6/2 + 3*A*a*c**2*x**8/8 + A*c**3*x**10/10 + B*a**3*x**5/5 + 3*B*a**2*c*x**7/7 + B*a*c**2*x**9/3 + B*c**3*x**11/11","A",0
266,1,92,0,0.082612," ","integrate(x**2*(B*x+A)*(c*x**2+a)**3,x)","\frac{A a^{3} x^{3}}{3} + \frac{3 A a^{2} c x^{5}}{5} + \frac{3 A a c^{2} x^{7}}{7} + \frac{A c^{3} x^{9}}{9} + \frac{B a^{3} x^{4}}{4} + \frac{B a^{2} c x^{6}}{2} + \frac{3 B a c^{2} x^{8}}{8} + \frac{B c^{3} x^{10}}{10}"," ",0,"A*a**3*x**3/3 + 3*A*a**2*c*x**5/5 + 3*A*a*c**2*x**7/7 + A*c**3*x**9/9 + B*a**3*x**4/4 + B*a**2*c*x**6/2 + 3*B*a*c**2*x**8/8 + B*c**3*x**10/10","A",0
267,1,92,0,0.081917," ","integrate(x*(B*x+A)*(c*x**2+a)**3,x)","\frac{A a^{3} x^{2}}{2} + \frac{3 A a^{2} c x^{4}}{4} + \frac{A a c^{2} x^{6}}{2} + \frac{A c^{3} x^{8}}{8} + \frac{B a^{3} x^{3}}{3} + \frac{3 B a^{2} c x^{5}}{5} + \frac{3 B a c^{2} x^{7}}{7} + \frac{B c^{3} x^{9}}{9}"," ",0,"A*a**3*x**2/2 + 3*A*a**2*c*x**4/4 + A*a*c**2*x**6/2 + A*c**3*x**8/8 + B*a**3*x**3/3 + 3*B*a**2*c*x**5/5 + 3*B*a*c**2*x**7/7 + B*c**3*x**9/9","A",0
268,1,85,0,0.082428," ","integrate((B*x+A)*(c*x**2+a)**3,x)","A a^{3} x + A a^{2} c x^{3} + \frac{3 A a c^{2} x^{5}}{5} + \frac{A c^{3} x^{7}}{7} + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} c x^{4}}{4} + \frac{B a c^{2} x^{6}}{2} + \frac{B c^{3} x^{8}}{8}"," ",0,"A*a**3*x + A*a**2*c*x**3 + 3*A*a*c**2*x**5/5 + A*c**3*x**7/7 + B*a**3*x**2/2 + 3*B*a**2*c*x**4/4 + B*a*c**2*x**6/2 + B*c**3*x**8/8","A",0
269,1,85,0,0.180090," ","integrate((B*x+A)*(c*x**2+a)**3/x,x)","A a^{3} \log{\left(x \right)} + \frac{3 A a^{2} c x^{2}}{2} + \frac{3 A a c^{2} x^{4}}{4} + \frac{A c^{3} x^{6}}{6} + B a^{3} x + B a^{2} c x^{3} + \frac{3 B a c^{2} x^{5}}{5} + \frac{B c^{3} x^{7}}{7}"," ",0,"A*a**3*log(x) + 3*A*a**2*c*x**2/2 + 3*A*a*c**2*x**4/4 + A*c**3*x**6/6 + B*a**3*x + B*a**2*c*x**3 + 3*B*a*c**2*x**5/5 + B*c**3*x**7/7","A",0
270,1,82,0,0.202565," ","integrate((B*x+A)*(c*x**2+a)**3/x**2,x)","- \frac{A a^{3}}{x} + 3 A a^{2} c x + A a c^{2} x^{3} + \frac{A c^{3} x^{5}}{5} + B a^{3} \log{\left(x \right)} + \frac{3 B a^{2} c x^{2}}{2} + \frac{3 B a c^{2} x^{4}}{4} + \frac{B c^{3} x^{6}}{6}"," ",0,"-A*a**3/x + 3*A*a**2*c*x + A*a*c**2*x**3 + A*c**3*x**5/5 + B*a**3*log(x) + 3*B*a**2*c*x**2/2 + 3*B*a*c**2*x**4/4 + B*c**3*x**6/6","A",0
271,1,85,0,0.293693," ","integrate((B*x+A)*(c*x**2+a)**3/x**3,x)","3 A a^{2} c \log{\left(x \right)} + \frac{3 A a c^{2} x^{2}}{2} + \frac{A c^{3} x^{4}}{4} + 3 B a^{2} c x + B a c^{2} x^{3} + \frac{B c^{3} x^{5}}{5} + \frac{- A a^{3} - 2 B a^{3} x}{2 x^{2}}"," ",0,"3*A*a**2*c*log(x) + 3*A*a*c**2*x**2/2 + A*c**3*x**4/4 + 3*B*a**2*c*x + B*a*c**2*x**3 + B*c**3*x**5/5 + (-A*a**3 - 2*B*a**3*x)/(2*x**2)","A",0
272,1,124,0,0.089980," ","integrate(x**3*(B*x+A)*(c*x**2+a)**4,x)","\frac{A a^{4} x^{4}}{4} + \frac{2 A a^{3} c x^{6}}{3} + \frac{3 A a^{2} c^{2} x^{8}}{4} + \frac{2 A a c^{3} x^{10}}{5} + \frac{A c^{4} x^{12}}{12} + \frac{B a^{4} x^{5}}{5} + \frac{4 B a^{3} c x^{7}}{7} + \frac{2 B a^{2} c^{2} x^{9}}{3} + \frac{4 B a c^{3} x^{11}}{11} + \frac{B c^{4} x^{13}}{13}"," ",0,"A*a**4*x**4/4 + 2*A*a**3*c*x**6/3 + 3*A*a**2*c**2*x**8/4 + 2*A*a*c**3*x**10/5 + A*c**4*x**12/12 + B*a**4*x**5/5 + 4*B*a**3*c*x**7/7 + 2*B*a**2*c**2*x**9/3 + 4*B*a*c**3*x**11/11 + B*c**4*x**13/13","A",0
273,1,124,0,0.089387," ","integrate(x**2*(B*x+A)*(c*x**2+a)**4,x)","\frac{A a^{4} x^{3}}{3} + \frac{4 A a^{3} c x^{5}}{5} + \frac{6 A a^{2} c^{2} x^{7}}{7} + \frac{4 A a c^{3} x^{9}}{9} + \frac{A c^{4} x^{11}}{11} + \frac{B a^{4} x^{4}}{4} + \frac{2 B a^{3} c x^{6}}{3} + \frac{3 B a^{2} c^{2} x^{8}}{4} + \frac{2 B a c^{3} x^{10}}{5} + \frac{B c^{4} x^{12}}{12}"," ",0,"A*a**4*x**3/3 + 4*A*a**3*c*x**5/5 + 6*A*a**2*c**2*x**7/7 + 4*A*a*c**3*x**9/9 + A*c**4*x**11/11 + B*a**4*x**4/4 + 2*B*a**3*c*x**6/3 + 3*B*a**2*c**2*x**8/4 + 2*B*a*c**3*x**10/5 + B*c**4*x**12/12","A",0
274,1,116,0,0.090551," ","integrate(x*(B*x+A)*(c*x**2+a)**4,x)","\frac{A a^{4} x^{2}}{2} + A a^{3} c x^{4} + A a^{2} c^{2} x^{6} + \frac{A a c^{3} x^{8}}{2} + \frac{A c^{4} x^{10}}{10} + \frac{B a^{4} x^{3}}{3} + \frac{4 B a^{3} c x^{5}}{5} + \frac{6 B a^{2} c^{2} x^{7}}{7} + \frac{4 B a c^{3} x^{9}}{9} + \frac{B c^{4} x^{11}}{11}"," ",0,"A*a**4*x**2/2 + A*a**3*c*x**4 + A*a**2*c**2*x**6 + A*a*c**3*x**8/2 + A*c**4*x**10/10 + B*a**4*x**3/3 + 4*B*a**3*c*x**5/5 + 6*B*a**2*c**2*x**7/7 + 4*B*a*c**3*x**9/9 + B*c**4*x**11/11","A",0
275,1,112,0,0.088479," ","integrate((B*x+A)*(c*x**2+a)**4,x)","A a^{4} x + \frac{4 A a^{3} c x^{3}}{3} + \frac{6 A a^{2} c^{2} x^{5}}{5} + \frac{4 A a c^{3} x^{7}}{7} + \frac{A c^{4} x^{9}}{9} + \frac{B a^{4} x^{2}}{2} + B a^{3} c x^{4} + B a^{2} c^{2} x^{6} + \frac{B a c^{3} x^{8}}{2} + \frac{B c^{4} x^{10}}{10}"," ",0,"A*a**4*x + 4*A*a**3*c*x**3/3 + 6*A*a**2*c**2*x**5/5 + 4*A*a*c**3*x**7/7 + A*c**4*x**9/9 + B*a**4*x**2/2 + B*a**3*c*x**4 + B*a**2*c**2*x**6 + B*a*c**3*x**8/2 + B*c**4*x**10/10","A",0
276,1,117,0,0.218754," ","integrate((B*x+A)*(c*x**2+a)**4/x,x)","A a^{4} \log{\left(x \right)} + 2 A a^{3} c x^{2} + \frac{3 A a^{2} c^{2} x^{4}}{2} + \frac{2 A a c^{3} x^{6}}{3} + \frac{A c^{4} x^{8}}{8} + B a^{4} x + \frac{4 B a^{3} c x^{3}}{3} + \frac{6 B a^{2} c^{2} x^{5}}{5} + \frac{4 B a c^{3} x^{7}}{7} + \frac{B c^{4} x^{9}}{9}"," ",0,"A*a**4*log(x) + 2*A*a**3*c*x**2 + 3*A*a**2*c**2*x**4/2 + 2*A*a*c**3*x**6/3 + A*c**4*x**8/8 + B*a**4*x + 4*B*a**3*c*x**3/3 + 6*B*a**2*c**2*x**5/5 + 4*B*a*c**3*x**7/7 + B*c**4*x**9/9","A",0
277,1,112,0,0.252815," ","integrate((B*x+A)*(c*x**2+a)**4/x**2,x)","- \frac{A a^{4}}{x} + 4 A a^{3} c x + 2 A a^{2} c^{2} x^{3} + \frac{4 A a c^{3} x^{5}}{5} + \frac{A c^{4} x^{7}}{7} + B a^{4} \log{\left(x \right)} + 2 B a^{3} c x^{2} + \frac{3 B a^{2} c^{2} x^{4}}{2} + \frac{2 B a c^{3} x^{6}}{3} + \frac{B c^{4} x^{8}}{8}"," ",0,"-A*a**4/x + 4*A*a**3*c*x + 2*A*a**2*c**2*x**3 + 4*A*a*c**3*x**5/5 + A*c**4*x**7/7 + B*a**4*log(x) + 2*B*a**3*c*x**2 + 3*B*a**2*c**2*x**4/2 + 2*B*a*c**3*x**6/3 + B*c**4*x**8/8","A",0
278,1,112,0,0.328649," ","integrate((B*x+A)*(c*x**2+a)**4/x**3,x)","4 A a^{3} c \log{\left(x \right)} + 3 A a^{2} c^{2} x^{2} + A a c^{3} x^{4} + \frac{A c^{4} x^{6}}{6} + 4 B a^{3} c x + 2 B a^{2} c^{2} x^{3} + \frac{4 B a c^{3} x^{5}}{5} + \frac{B c^{4} x^{7}}{7} + \frac{- A a^{4} - 2 B a^{4} x}{2 x^{2}}"," ",0,"4*A*a**3*c*log(x) + 3*A*a**2*c**2*x**2 + A*a*c**3*x**4 + A*c**4*x**6/6 + 4*B*a**3*c*x + 2*B*a**2*c**2*x**3 + 4*B*a*c**3*x**5/5 + B*c**4*x**7/7 + (-A*a**4 - 2*B*a**4*x)/(2*x**2)","A",0
279,1,189,0,0.383252," ","integrate(x**4*(e*x+d)/(c*x**2+a),x)","- \frac{a d x}{c^{2}} - \frac{a e x^{2}}{2 c^{2}} + \left(\frac{a^{2} e}{2 c^{3}} - \frac{d \sqrt{- a^{3} c^{7}}}{2 c^{6}}\right) \log{\left(x + \frac{- a^{2} e + 2 c^{3} \left(\frac{a^{2} e}{2 c^{3}} - \frac{d \sqrt{- a^{3} c^{7}}}{2 c^{6}}\right)}{a c d} \right)} + \left(\frac{a^{2} e}{2 c^{3}} + \frac{d \sqrt{- a^{3} c^{7}}}{2 c^{6}}\right) \log{\left(x + \frac{- a^{2} e + 2 c^{3} \left(\frac{a^{2} e}{2 c^{3}} + \frac{d \sqrt{- a^{3} c^{7}}}{2 c^{6}}\right)}{a c d} \right)} + \frac{d x^{3}}{3 c} + \frac{e x^{4}}{4 c}"," ",0,"-a*d*x/c**2 - a*e*x**2/(2*c**2) + (a**2*e/(2*c**3) - d*sqrt(-a**3*c**7)/(2*c**6))*log(x + (-a**2*e + 2*c**3*(a**2*e/(2*c**3) - d*sqrt(-a**3*c**7)/(2*c**6)))/(a*c*d)) + (a**2*e/(2*c**3) + d*sqrt(-a**3*c**7)/(2*c**6))*log(x + (-a**2*e + 2*c**3*(a**2*e/(2*c**3) + d*sqrt(-a**3*c**7)/(2*c**6)))/(a*c*d)) + d*x**3/(3*c) + e*x**4/(4*c)","B",0
280,1,167,0,0.359408," ","integrate(x**3*(e*x+d)/(c*x**2+a),x)","- \frac{a e x}{c^{2}} + \left(- \frac{a d}{2 c^{2}} - \frac{e \sqrt{- a^{3} c^{5}}}{2 c^{5}}\right) \log{\left(x + \frac{a d + 2 c^{2} \left(- \frac{a d}{2 c^{2}} - \frac{e \sqrt{- a^{3} c^{5}}}{2 c^{5}}\right)}{a e} \right)} + \left(- \frac{a d}{2 c^{2}} + \frac{e \sqrt{- a^{3} c^{5}}}{2 c^{5}}\right) \log{\left(x + \frac{a d + 2 c^{2} \left(- \frac{a d}{2 c^{2}} + \frac{e \sqrt{- a^{3} c^{5}}}{2 c^{5}}\right)}{a e} \right)} + \frac{d x^{2}}{2 c} + \frac{e x^{3}}{3 c}"," ",0,"-a*e*x/c**2 + (-a*d/(2*c**2) - e*sqrt(-a**3*c**5)/(2*c**5))*log(x + (a*d + 2*c**2*(-a*d/(2*c**2) - e*sqrt(-a**3*c**5)/(2*c**5)))/(a*e)) + (-a*d/(2*c**2) + e*sqrt(-a**3*c**5)/(2*c**5))*log(x + (a*d + 2*c**2*(-a*d/(2*c**2) + e*sqrt(-a**3*c**5)/(2*c**5)))/(a*e)) + d*x**2/(2*c) + e*x**3/(3*c)","B",0
281,1,151,0,0.446716," ","integrate(x**2*(e*x+d)/(c*x**2+a),x)","\left(- \frac{a e}{2 c^{2}} - \frac{d \sqrt{- a c^{5}}}{2 c^{4}}\right) \log{\left(x + \frac{- a e - 2 c^{2} \left(- \frac{a e}{2 c^{2}} - \frac{d \sqrt{- a c^{5}}}{2 c^{4}}\right)}{c d} \right)} + \left(- \frac{a e}{2 c^{2}} + \frac{d \sqrt{- a c^{5}}}{2 c^{4}}\right) \log{\left(x + \frac{- a e - 2 c^{2} \left(- \frac{a e}{2 c^{2}} + \frac{d \sqrt{- a c^{5}}}{2 c^{4}}\right)}{c d} \right)} + \frac{d x}{c} + \frac{e x^{2}}{2 c}"," ",0,"(-a*e/(2*c**2) - d*sqrt(-a*c**5)/(2*c**4))*log(x + (-a*e - 2*c**2*(-a*e/(2*c**2) - d*sqrt(-a*c**5)/(2*c**4)))/(c*d)) + (-a*e/(2*c**2) + d*sqrt(-a*c**5)/(2*c**4))*log(x + (-a*e - 2*c**2*(-a*e/(2*c**2) + d*sqrt(-a*c**5)/(2*c**4)))/(c*d)) + d*x/c + e*x**2/(2*c)","B",0
282,1,112,0,0.301905," ","integrate(x*(e*x+d)/(c*x**2+a),x)","\left(\frac{d}{2 c} - \frac{e \sqrt{- a c^{3}}}{2 c^{3}}\right) \log{\left(x + \frac{- 2 c \left(\frac{d}{2 c} - \frac{e \sqrt{- a c^{3}}}{2 c^{3}}\right) + d}{e} \right)} + \left(\frac{d}{2 c} + \frac{e \sqrt{- a c^{3}}}{2 c^{3}}\right) \log{\left(x + \frac{- 2 c \left(\frac{d}{2 c} + \frac{e \sqrt{- a c^{3}}}{2 c^{3}}\right) + d}{e} \right)} + \frac{e x}{c}"," ",0,"(d/(2*c) - e*sqrt(-a*c**3)/(2*c**3))*log(x + (-2*c*(d/(2*c) - e*sqrt(-a*c**3)/(2*c**3)) + d)/e) + (d/(2*c) + e*sqrt(-a*c**3)/(2*c**3))*log(x + (-2*c*(d/(2*c) + e*sqrt(-a*c**3)/(2*c**3)) + d)/e) + e*x/c","B",0
283,1,124,0,0.272511," ","integrate((e*x+d)/(c*x**2+a),x)","\left(\frac{e}{2 c} - \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) \log{\left(x + \frac{2 a c \left(\frac{e}{2 c} - \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) - a e}{c d} \right)} + \left(\frac{e}{2 c} + \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) \log{\left(x + \frac{2 a c \left(\frac{e}{2 c} + \frac{d \sqrt{- a c^{3}}}{2 a c^{2}}\right) - a e}{c d} \right)}"," ",0,"(e/(2*c) - d*sqrt(-a*c**3)/(2*a*c**2))*log(x + (2*a*c*(e/(2*c) - d*sqrt(-a*c**3)/(2*a*c**2)) - a*e)/(c*d)) + (e/(2*c) + d*sqrt(-a*c**3)/(2*a*c**2))*log(x + (2*a*c*(e/(2*c) + d*sqrt(-a*c**3)/(2*a*c**2)) - a*e)/(c*d))","B",0
284,1,321,0,1.470362," ","integrate((e*x+d)/x/(c*x**2+a),x)","\left(- \frac{d}{2 a} - \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right) \log{\left(x + \frac{- 12 a^{2} c d \left(- \frac{d}{2 a} - \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right)^{2} + 2 a^{2} e^{2} \left(- \frac{d}{2 a} - \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right) + 6 a c d^{2} \left(- \frac{d}{2 a} - \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right) - 2 a d e^{2} + 6 c d^{3}}{a e^{3} + 9 c d^{2} e} \right)} + \left(- \frac{d}{2 a} + \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right) \log{\left(x + \frac{- 12 a^{2} c d \left(- \frac{d}{2 a} + \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right)^{2} + 2 a^{2} e^{2} \left(- \frac{d}{2 a} + \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right) + 6 a c d^{2} \left(- \frac{d}{2 a} + \frac{e \sqrt{- a^{3} c}}{2 a^{2} c}\right) - 2 a d e^{2} + 6 c d^{3}}{a e^{3} + 9 c d^{2} e} \right)} + \frac{d \log{\left(x \right)}}{a}"," ",0,"(-d/(2*a) - e*sqrt(-a**3*c)/(2*a**2*c))*log(x + (-12*a**2*c*d*(-d/(2*a) - e*sqrt(-a**3*c)/(2*a**2*c))**2 + 2*a**2*e**2*(-d/(2*a) - e*sqrt(-a**3*c)/(2*a**2*c)) + 6*a*c*d**2*(-d/(2*a) - e*sqrt(-a**3*c)/(2*a**2*c)) - 2*a*d*e**2 + 6*c*d**3)/(a*e**3 + 9*c*d**2*e)) + (-d/(2*a) + e*sqrt(-a**3*c)/(2*a**2*c))*log(x + (-12*a**2*c*d*(-d/(2*a) + e*sqrt(-a**3*c)/(2*a**2*c))**2 + 2*a**2*e**2*(-d/(2*a) + e*sqrt(-a**3*c)/(2*a**2*c)) + 6*a*c*d**2*(-d/(2*a) + e*sqrt(-a**3*c)/(2*a**2*c)) - 2*a*d*e**2 + 6*c*d**3)/(a*e**3 + 9*c*d**2*e)) + d*log(x)/a","B",0
285,1,326,0,1.621235," ","integrate((e*x+d)/x**2/(c*x**2+a),x)","\left(- \frac{e}{2 a} - \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right) \log{\left(x + \frac{12 a^{4} e \left(- \frac{e}{2 a} - \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right)^{2} - 6 a^{3} e^{2} \left(- \frac{e}{2 a} - \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right) - 2 a^{2} c d^{2} \left(- \frac{e}{2 a} - \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right) - 6 a^{2} e^{3} + 2 a c d^{2} e}{9 a c d e^{2} + c^{2} d^{3}} \right)} + \left(- \frac{e}{2 a} + \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right) \log{\left(x + \frac{12 a^{4} e \left(- \frac{e}{2 a} + \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right)^{2} - 6 a^{3} e^{2} \left(- \frac{e}{2 a} + \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right) - 2 a^{2} c d^{2} \left(- \frac{e}{2 a} + \frac{d \sqrt{- a^{3} c}}{2 a^{3}}\right) - 6 a^{2} e^{3} + 2 a c d^{2} e}{9 a c d e^{2} + c^{2} d^{3}} \right)} - \frac{d}{a x} + \frac{e \log{\left(x \right)}}{a}"," ",0,"(-e/(2*a) - d*sqrt(-a**3*c)/(2*a**3))*log(x + (12*a**4*e*(-e/(2*a) - d*sqrt(-a**3*c)/(2*a**3))**2 - 6*a**3*e**2*(-e/(2*a) - d*sqrt(-a**3*c)/(2*a**3)) - 2*a**2*c*d**2*(-e/(2*a) - d*sqrt(-a**3*c)/(2*a**3)) - 6*a**2*e**3 + 2*a*c*d**2*e)/(9*a*c*d*e**2 + c**2*d**3)) + (-e/(2*a) + d*sqrt(-a**3*c)/(2*a**3))*log(x + (12*a**4*e*(-e/(2*a) + d*sqrt(-a**3*c)/(2*a**3))**2 - 6*a**3*e**2*(-e/(2*a) + d*sqrt(-a**3*c)/(2*a**3)) - 2*a**2*c*d**2*(-e/(2*a) + d*sqrt(-a**3*c)/(2*a**3)) - 6*a**2*e**3 + 2*a*c*d**2*e)/(9*a*c*d*e**2 + c**2*d**3)) - d/(a*x) + e*log(x)/a","B",0
286,1,360,0,1.703208," ","integrate((e*x+d)/x**3/(c*x**2+a),x)","\left(\frac{c d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right) \log{\left(x + \frac{- 12 a^{4} d \left(\frac{c d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right)^{2} - 2 a^{3} e^{2} \left(\frac{c d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right) - 6 a^{2} c d^{2} \left(\frac{c d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right) - 2 a c d e^{2} + 6 c^{2} d^{3}}{a c e^{3} + 9 c^{2} d^{2} e} \right)} + \left(\frac{c d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right) \log{\left(x + \frac{- 12 a^{4} d \left(\frac{c d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right)^{2} - 2 a^{3} e^{2} \left(\frac{c d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right) - 6 a^{2} c d^{2} \left(\frac{c d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{2 a^{4}}\right) - 2 a c d e^{2} + 6 c^{2} d^{3}}{a c e^{3} + 9 c^{2} d^{2} e} \right)} + \frac{- d - 2 e x}{2 a x^{2}} - \frac{c d \log{\left(x \right)}}{a^{2}}"," ",0,"(c*d/(2*a**2) - e*sqrt(-a**5*c)/(2*a**4))*log(x + (-12*a**4*d*(c*d/(2*a**2) - e*sqrt(-a**5*c)/(2*a**4))**2 - 2*a**3*e**2*(c*d/(2*a**2) - e*sqrt(-a**5*c)/(2*a**4)) - 6*a**2*c*d**2*(c*d/(2*a**2) - e*sqrt(-a**5*c)/(2*a**4)) - 2*a*c*d*e**2 + 6*c**2*d**3)/(a*c*e**3 + 9*c**2*d**2*e)) + (c*d/(2*a**2) + e*sqrt(-a**5*c)/(2*a**4))*log(x + (-12*a**4*d*(c*d/(2*a**2) + e*sqrt(-a**5*c)/(2*a**4))**2 - 2*a**3*e**2*(c*d/(2*a**2) + e*sqrt(-a**5*c)/(2*a**4)) - 6*a**2*c*d**2*(c*d/(2*a**2) + e*sqrt(-a**5*c)/(2*a**4)) - 2*a*c*d*e**2 + 6*c**2*d**3)/(a*c*e**3 + 9*c**2*d**2*e)) + (-d - 2*e*x)/(2*a*x**2) - c*d*log(x)/a**2","B",0
287,1,408,0,1.771793," ","integrate((e*x+d)/x**4/(c*x**2+a),x)","\left(\frac{c e}{2 a^{2}} - \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right) \log{\left(x + \frac{12 a^{6} e \left(\frac{c e}{2 a^{2}} - \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right)^{2} + 6 a^{4} c e^{2} \left(\frac{c e}{2 a^{2}} - \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right) + 2 a^{3} c^{2} d^{2} \left(\frac{c e}{2 a^{2}} - \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right) - 6 a^{2} c^{2} e^{3} + 2 a c^{3} d^{2} e}{9 a c^{3} d e^{2} + c^{4} d^{3}} \right)} + \left(\frac{c e}{2 a^{2}} + \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right) \log{\left(x + \frac{12 a^{6} e \left(\frac{c e}{2 a^{2}} + \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right)^{2} + 6 a^{4} c e^{2} \left(\frac{c e}{2 a^{2}} + \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right) + 2 a^{3} c^{2} d^{2} \left(\frac{c e}{2 a^{2}} + \frac{d \sqrt{- a^{5} c^{3}}}{2 a^{5}}\right) - 6 a^{2} c^{2} e^{3} + 2 a c^{3} d^{2} e}{9 a c^{3} d e^{2} + c^{4} d^{3}} \right)} - \frac{c e \log{\left(x \right)}}{a^{2}} + \frac{- 2 a d - 3 a e x + 6 c d x^{2}}{6 a^{2} x^{3}}"," ",0,"(c*e/(2*a**2) - d*sqrt(-a**5*c**3)/(2*a**5))*log(x + (12*a**6*e*(c*e/(2*a**2) - d*sqrt(-a**5*c**3)/(2*a**5))**2 + 6*a**4*c*e**2*(c*e/(2*a**2) - d*sqrt(-a**5*c**3)/(2*a**5)) + 2*a**3*c**2*d**2*(c*e/(2*a**2) - d*sqrt(-a**5*c**3)/(2*a**5)) - 6*a**2*c**2*e**3 + 2*a*c**3*d**2*e)/(9*a*c**3*d*e**2 + c**4*d**3)) + (c*e/(2*a**2) + d*sqrt(-a**5*c**3)/(2*a**5))*log(x + (12*a**6*e*(c*e/(2*a**2) + d*sqrt(-a**5*c**3)/(2*a**5))**2 + 6*a**4*c*e**2*(c*e/(2*a**2) + d*sqrt(-a**5*c**3)/(2*a**5)) + 2*a**3*c**2*d**2*(c*e/(2*a**2) + d*sqrt(-a**5*c**3)/(2*a**5)) - 6*a**2*c**2*e**3 + 2*a*c**3*d**2*e)/(9*a*c**3*d*e**2 + c**4*d**3)) - c*e*log(x)/a**2 + (-2*a*d - 3*a*e*x + 6*c*d*x**2)/(6*a**2*x**3)","B",0
288,1,119,0,0.283439," ","integrate((e*x+d)/(-c*x**2+a),x)","- \left(\frac{e}{2 c} - \frac{d \sqrt{a c^{3}}}{2 a c^{2}}\right) \log{\left(x + \frac{- 2 a c \left(\frac{e}{2 c} - \frac{d \sqrt{a c^{3}}}{2 a c^{2}}\right) + a e}{c d} \right)} - \left(\frac{e}{2 c} + \frac{d \sqrt{a c^{3}}}{2 a c^{2}}\right) \log{\left(x + \frac{- 2 a c \left(\frac{e}{2 c} + \frac{d \sqrt{a c^{3}}}{2 a c^{2}}\right) + a e}{c d} \right)}"," ",0,"-(e/(2*c) - d*sqrt(a*c**3)/(2*a*c**2))*log(x + (-2*a*c*(e/(2*c) - d*sqrt(a*c**3)/(2*a*c**2)) + a*e)/(c*d)) - (e/(2*c) + d*sqrt(a*c**3)/(2*a*c**2))*log(x + (-2*a*c*(e/(2*c) + d*sqrt(a*c**3)/(2*a*c**2)) + a*e)/(c*d))","B",0
289,1,189,0,0.722085," ","integrate(x**4*(e*x+d)/(c*x**2+a)**2,x)","\left(- \frac{a e}{c^{3}} - \frac{3 d \sqrt{- a c^{7}}}{4 c^{6}}\right) \log{\left(x + \frac{- 4 a e - 4 c^{3} \left(- \frac{a e}{c^{3}} - \frac{3 d \sqrt{- a c^{7}}}{4 c^{6}}\right)}{3 c d} \right)} + \left(- \frac{a e}{c^{3}} + \frac{3 d \sqrt{- a c^{7}}}{4 c^{6}}\right) \log{\left(x + \frac{- 4 a e - 4 c^{3} \left(- \frac{a e}{c^{3}} + \frac{3 d \sqrt{- a c^{7}}}{4 c^{6}}\right)}{3 c d} \right)} + \frac{- a^{2} e + a c d x}{2 a c^{3} + 2 c^{4} x^{2}} + \frac{d x}{c^{2}} + \frac{e x^{2}}{2 c^{2}}"," ",0,"(-a*e/c**3 - 3*d*sqrt(-a*c**7)/(4*c**6))*log(x + (-4*a*e - 4*c**3*(-a*e/c**3 - 3*d*sqrt(-a*c**7)/(4*c**6)))/(3*c*d)) + (-a*e/c**3 + 3*d*sqrt(-a*c**7)/(4*c**6))*log(x + (-4*a*e - 4*c**3*(-a*e/c**3 + 3*d*sqrt(-a*c**7)/(4*c**6)))/(3*c*d)) + (-a**2*e + a*c*d*x)/(2*a*c**3 + 2*c**4*x**2) + d*x/c**2 + e*x**2/(2*c**2)","B",0
290,1,162,0,0.671709," ","integrate(x**3*(e*x+d)/(c*x**2+a)**2,x)","\left(\frac{d}{2 c^{2}} - \frac{3 e \sqrt{- a c^{5}}}{4 c^{5}}\right) \log{\left(x + \frac{- 4 c^{2} \left(\frac{d}{2 c^{2}} - \frac{3 e \sqrt{- a c^{5}}}{4 c^{5}}\right) + 2 d}{3 e} \right)} + \left(\frac{d}{2 c^{2}} + \frac{3 e \sqrt{- a c^{5}}}{4 c^{5}}\right) \log{\left(x + \frac{- 4 c^{2} \left(\frac{d}{2 c^{2}} + \frac{3 e \sqrt{- a c^{5}}}{4 c^{5}}\right) + 2 d}{3 e} \right)} + \frac{a d + a e x}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{e x}{c^{2}}"," ",0,"(d/(2*c**2) - 3*e*sqrt(-a*c**5)/(4*c**5))*log(x + (-4*c**2*(d/(2*c**2) - 3*e*sqrt(-a*c**5)/(4*c**5)) + 2*d)/(3*e)) + (d/(2*c**2) + 3*e*sqrt(-a*c**5)/(4*c**5))*log(x + (-4*c**2*(d/(2*c**2) + 3*e*sqrt(-a*c**5)/(4*c**5)) + 2*d)/(3*e)) + (a*d + a*e*x)/(2*a*c**2 + 2*c**3*x**2) + e*x/c**2","B",0
291,1,162,0,0.575095," ","integrate(x**2*(e*x+d)/(c*x**2+a)**2,x)","\left(\frac{e}{2 c^{2}} - \frac{d \sqrt{- a c^{5}}}{4 a c^{4}}\right) \log{\left(x + \frac{4 a c^{2} \left(\frac{e}{2 c^{2}} - \frac{d \sqrt{- a c^{5}}}{4 a c^{4}}\right) - 2 a e}{c d} \right)} + \left(\frac{e}{2 c^{2}} + \frac{d \sqrt{- a c^{5}}}{4 a c^{4}}\right) \log{\left(x + \frac{4 a c^{2} \left(\frac{e}{2 c^{2}} + \frac{d \sqrt{- a c^{5}}}{4 a c^{4}}\right) - 2 a e}{c d} \right)} + \frac{a e - c d x}{2 a c^{2} + 2 c^{3} x^{2}}"," ",0,"(e/(2*c**2) - d*sqrt(-a*c**5)/(4*a*c**4))*log(x + (4*a*c**2*(e/(2*c**2) - d*sqrt(-a*c**5)/(4*a*c**4)) - 2*a*e)/(c*d)) + (e/(2*c**2) + d*sqrt(-a*c**5)/(4*a*c**4))*log(x + (4*a*c**2*(e/(2*c**2) + d*sqrt(-a*c**5)/(4*a*c**4)) - 2*a*e)/(c*d)) + (a*e - c*d*x)/(2*a*c**2 + 2*c**3*x**2)","B",0
292,1,85,0,0.357328," ","integrate(x*(e*x+d)/(c*x**2+a)**2,x)","e \left(- \frac{\sqrt{- \frac{1}{a c^{3}}} \log{\left(- a c \sqrt{- \frac{1}{a c^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a c^{3}}} \log{\left(a c \sqrt{- \frac{1}{a c^{3}}} + x \right)}}{4}\right) + \frac{- d - e x}{2 a c + 2 c^{2} x^{2}}"," ",0,"e*(-sqrt(-1/(a*c**3))*log(-a*c*sqrt(-1/(a*c**3)) + x)/4 + sqrt(-1/(a*c**3))*log(a*c*sqrt(-1/(a*c**3)) + x)/4) + (-d - e*x)/(2*a*c + 2*c**2*x**2)","A",0
293,1,90,0,0.361265," ","integrate((e*x+d)/(c*x**2+a)**2,x)","d \left(- \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} c}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} c}} + x \right)}}{4}\right) + \frac{- a e + c d x}{2 a^{2} c + 2 a c^{2} x^{2}}"," ",0,"d*(-sqrt(-1/(a**3*c))*log(-a**2*sqrt(-1/(a**3*c)) + x)/4 + sqrt(-1/(a**3*c))*log(a**2*sqrt(-1/(a**3*c)) + x)/4) + (-a*e + c*d*x)/(2*a**2*c + 2*a*c**2*x**2)","A",0
294,1,359,0,1.712095," ","integrate((e*x+d)/x/(c*x**2+a)**2,x)","\left(- \frac{d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right) \log{\left(x + \frac{- 96 a^{4} c d \left(- \frac{d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right)^{2} + 4 a^{3} e^{2} \left(- \frac{d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right) + 48 a^{2} c d^{2} \left(- \frac{d}{2 a^{2}} - \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right) - 4 a d e^{2} + 48 c d^{3}}{a e^{3} + 36 c d^{2} e} \right)} + \left(- \frac{d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right) \log{\left(x + \frac{- 96 a^{4} c d \left(- \frac{d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right)^{2} + 4 a^{3} e^{2} \left(- \frac{d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right) + 48 a^{2} c d^{2} \left(- \frac{d}{2 a^{2}} + \frac{e \sqrt{- a^{5} c}}{4 a^{4} c}\right) - 4 a d e^{2} + 48 c d^{3}}{a e^{3} + 36 c d^{2} e} \right)} + \frac{d + e x}{2 a^{2} + 2 a c x^{2}} + \frac{d \log{\left(x \right)}}{a^{2}}"," ",0,"(-d/(2*a**2) - e*sqrt(-a**5*c)/(4*a**4*c))*log(x + (-96*a**4*c*d*(-d/(2*a**2) - e*sqrt(-a**5*c)/(4*a**4*c))**2 + 4*a**3*e**2*(-d/(2*a**2) - e*sqrt(-a**5*c)/(4*a**4*c)) + 48*a**2*c*d**2*(-d/(2*a**2) - e*sqrt(-a**5*c)/(4*a**4*c)) - 4*a*d*e**2 + 48*c*d**3)/(a*e**3 + 36*c*d**2*e)) + (-d/(2*a**2) + e*sqrt(-a**5*c)/(4*a**4*c))*log(x + (-96*a**4*c*d*(-d/(2*a**2) + e*sqrt(-a**5*c)/(4*a**4*c))**2 + 4*a**3*e**2*(-d/(2*a**2) + e*sqrt(-a**5*c)/(4*a**4*c)) + 48*a**2*c*d**2*(-d/(2*a**2) + e*sqrt(-a**5*c)/(4*a**4*c)) - 4*a*d*e**2 + 48*c*d**3)/(a*e**3 + 36*c*d**2*e)) + (d + e*x)/(2*a**2 + 2*a*c*x**2) + d*log(x)/a**2","B",0
295,1,389,0,1.810052," ","integrate((e*x+d)/x**2/(c*x**2+a)**2,x)","\left(- \frac{e}{2 a^{2}} - \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right) \log{\left(x + \frac{32 a^{6} e \left(- \frac{e}{2 a^{2}} - \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right)^{2} - 16 a^{4} e^{2} \left(- \frac{e}{2 a^{2}} - \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right) - 12 a^{3} c d^{2} \left(- \frac{e}{2 a^{2}} - \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right) - 16 a^{2} e^{3} + 12 a c d^{2} e}{36 a c d e^{2} + 9 c^{2} d^{3}} \right)} + \left(- \frac{e}{2 a^{2}} + \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right) \log{\left(x + \frac{32 a^{6} e \left(- \frac{e}{2 a^{2}} + \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right)^{2} - 16 a^{4} e^{2} \left(- \frac{e}{2 a^{2}} + \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right) - 12 a^{3} c d^{2} \left(- \frac{e}{2 a^{2}} + \frac{3 d \sqrt{- a^{5} c}}{4 a^{5}}\right) - 16 a^{2} e^{3} + 12 a c d^{2} e}{36 a c d e^{2} + 9 c^{2} d^{3}} \right)} + \frac{- 2 a d + a e x - 3 c d x^{2}}{2 a^{3} x + 2 a^{2} c x^{3}} + \frac{e \log{\left(x \right)}}{a^{2}}"," ",0,"(-e/(2*a**2) - 3*d*sqrt(-a**5*c)/(4*a**5))*log(x + (32*a**6*e*(-e/(2*a**2) - 3*d*sqrt(-a**5*c)/(4*a**5))**2 - 16*a**4*e**2*(-e/(2*a**2) - 3*d*sqrt(-a**5*c)/(4*a**5)) - 12*a**3*c*d**2*(-e/(2*a**2) - 3*d*sqrt(-a**5*c)/(4*a**5)) - 16*a**2*e**3 + 12*a*c*d**2*e)/(36*a*c*d*e**2 + 9*c**2*d**3)) + (-e/(2*a**2) + 3*d*sqrt(-a**5*c)/(4*a**5))*log(x + (32*a**6*e*(-e/(2*a**2) + 3*d*sqrt(-a**5*c)/(4*a**5))**2 - 16*a**4*e**2*(-e/(2*a**2) + 3*d*sqrt(-a**5*c)/(4*a**5)) - 12*a**3*c*d**2*(-e/(2*a**2) + 3*d*sqrt(-a**5*c)/(4*a**5)) - 16*a**2*e**3 + 12*a*c*d**2*e)/(36*a*c*d*e**2 + 9*c**2*d**3)) + (-2*a*d + a*e*x - 3*c*d*x**2)/(2*a**3*x + 2*a**2*c*x**3) + e*log(x)/a**2","B",0
296,1,398,0,2.035172," ","integrate((e*x+d)/x**3/(c*x**2+a)**2,x)","\left(\frac{c d}{a^{3}} - \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right) \log{\left(x + \frac{- 64 a^{6} d \left(\frac{c d}{a^{3}} - \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right)^{2} - 12 a^{4} e^{2} \left(\frac{c d}{a^{3}} - \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right) - 64 a^{3} c d^{2} \left(\frac{c d}{a^{3}} - \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right) - 24 a c d e^{2} + 128 c^{2} d^{3}}{9 a c e^{3} + 144 c^{2} d^{2} e} \right)} + \left(\frac{c d}{a^{3}} + \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right) \log{\left(x + \frac{- 64 a^{6} d \left(\frac{c d}{a^{3}} + \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right)^{2} - 12 a^{4} e^{2} \left(\frac{c d}{a^{3}} + \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right) - 64 a^{3} c d^{2} \left(\frac{c d}{a^{3}} + \frac{3 e \sqrt{- a^{7} c}}{4 a^{6}}\right) - 24 a c d e^{2} + 128 c^{2} d^{3}}{9 a c e^{3} + 144 c^{2} d^{2} e} \right)} + \frac{- a d - 2 a e x - 2 c d x^{2} - 3 c e x^{3}}{2 a^{3} x^{2} + 2 a^{2} c x^{4}} - \frac{2 c d \log{\left(x \right)}}{a^{3}}"," ",0,"(c*d/a**3 - 3*e*sqrt(-a**7*c)/(4*a**6))*log(x + (-64*a**6*d*(c*d/a**3 - 3*e*sqrt(-a**7*c)/(4*a**6))**2 - 12*a**4*e**2*(c*d/a**3 - 3*e*sqrt(-a**7*c)/(4*a**6)) - 64*a**3*c*d**2*(c*d/a**3 - 3*e*sqrt(-a**7*c)/(4*a**6)) - 24*a*c*d*e**2 + 128*c**2*d**3)/(9*a*c*e**3 + 144*c**2*d**2*e)) + (c*d/a**3 + 3*e*sqrt(-a**7*c)/(4*a**6))*log(x + (-64*a**6*d*(c*d/a**3 + 3*e*sqrt(-a**7*c)/(4*a**6))**2 - 12*a**4*e**2*(c*d/a**3 + 3*e*sqrt(-a**7*c)/(4*a**6)) - 64*a**3*c*d**2*(c*d/a**3 + 3*e*sqrt(-a**7*c)/(4*a**6)) - 24*a*c*d*e**2 + 128*c**2*d**3)/(9*a*c*e**3 + 144*c**2*d**2*e)) + (-a*d - 2*a*e*x - 2*c*d*x**2 - 3*c*e*x**3)/(2*a**3*x**2 + 2*a**2*c*x**4) - 2*c*d*log(x)/a**3","B",0
297,1,129,0,0.473059," ","integrate(x**4*(e*x+d)/(-c**2*x**2+a**2),x)","- \frac{a^{3} \left(a e - c d\right) \log{\left(x + \frac{a^{4} e - a^{3} \left(a e - c d\right)}{a^{2} c^{2} d} \right)}}{2 c^{6}} - \frac{a^{3} \left(a e + c d\right) \log{\left(x + \frac{a^{4} e - a^{3} \left(a e + c d\right)}{a^{2} c^{2} d} \right)}}{2 c^{6}} - \frac{a^{2} d x}{c^{4}} - \frac{a^{2} e x^{2}}{2 c^{4}} - \frac{d x^{3}}{3 c^{2}} - \frac{e x^{4}}{4 c^{2}}"," ",0,"-a**3*(a*e - c*d)*log(x + (a**4*e - a**3*(a*e - c*d))/(a**2*c**2*d))/(2*c**6) - a**3*(a*e + c*d)*log(x + (a**4*e - a**3*(a*e + c*d))/(a**2*c**2*d))/(2*c**6) - a**2*d*x/c**4 - a**2*e*x**2/(2*c**4) - d*x**3/(3*c**2) - e*x**4/(4*c**2)","A",0
298,1,110,0,0.442809," ","integrate(x**3*(e*x+d)/(-c**2*x**2+a**2),x)","- \frac{a^{2} e x}{c^{4}} + \frac{a^{2} \left(a e - c d\right) \log{\left(x + \frac{a^{2} d + \frac{a^{2} \left(a e - c d\right)}{c}}{a^{2} e} \right)}}{2 c^{5}} - \frac{a^{2} \left(a e + c d\right) \log{\left(x + \frac{a^{2} d - \frac{a^{2} \left(a e + c d\right)}{c}}{a^{2} e} \right)}}{2 c^{5}} - \frac{d x^{2}}{2 c^{2}} - \frac{e x^{3}}{3 c^{2}}"," ",0,"-a**2*e*x/c**4 + a**2*(a*e - c*d)*log(x + (a**2*d + a**2*(a*e - c*d)/c)/(a**2*e))/(2*c**5) - a**2*(a*e + c*d)*log(x + (a**2*d - a**2*(a*e + c*d)/c)/(a**2*e))/(2*c**5) - d*x**2/(2*c**2) - e*x**3/(3*c**2)","A",0
299,1,88,0,0.466158," ","integrate(x**2*(e*x+d)/(-c**2*x**2+a**2),x)","- \frac{a \left(a e - c d\right) \log{\left(x + \frac{a^{2} e - a \left(a e - c d\right)}{c^{2} d} \right)}}{2 c^{4}} - \frac{a \left(a e + c d\right) \log{\left(x + \frac{a^{2} e - a \left(a e + c d\right)}{c^{2} d} \right)}}{2 c^{4}} - \frac{d x}{c^{2}} - \frac{e x^{2}}{2 c^{2}}"," ",0,"-a*(a*e - c*d)*log(x + (a**2*e - a*(a*e - c*d))/(c**2*d))/(2*c**4) - a*(a*e + c*d)*log(x + (a**2*e - a*(a*e + c*d))/(c**2*d))/(2*c**4) - d*x/c**2 - e*x**2/(2*c**2)","A",0
300,1,60,0,0.353032," ","integrate(x*(e*x+d)/(-c**2*x**2+a**2),x)","- \frac{e x}{c^{2}} + \frac{\left(a e - c d\right) \log{\left(x + \frac{d + \frac{a e - c d}{c}}{e} \right)}}{2 c^{3}} - \frac{\left(a e + c d\right) \log{\left(x + \frac{d - \frac{a e + c d}{c}}{e} \right)}}{2 c^{3}}"," ",0,"-e*x/c**2 + (a*e - c*d)*log(x + (d + (a*e - c*d)/c)/e)/(2*c**3) - (a*e + c*d)*log(x + (d - (a*e + c*d)/c)/e)/(2*c**3)","A",0
301,1,71,0,0.332465," ","integrate((e*x+d)/(-c**2*x**2+a**2),x)","- \frac{\left(a e - c d\right) \log{\left(x + \frac{a^{2} e - a \left(a e - c d\right)}{c^{2} d} \right)}}{2 a c^{2}} - \frac{\left(a e + c d\right) \log{\left(x + \frac{a^{2} e - a \left(a e + c d\right)}{c^{2} d} \right)}}{2 a c^{2}}"," ",0,"-(a*e - c*d)*log(x + (a**2*e - a*(a*e - c*d))/(c**2*d))/(2*a*c**2) - (a*e + c*d)*log(x + (a**2*e - a*(a*e + c*d))/(c**2*d))/(2*a*c**2)","A",0
302,1,194,0,1.594221," ","integrate((e*x+d)/x/(-c**2*x**2+a**2),x)","\frac{d \log{\left(x \right)}}{a^{2}} + \frac{\left(a e - c d\right) \log{\left(x + \frac{- 2 a^{2} d e^{2} + \frac{a^{2} e^{2} \left(a e - c d\right)}{c} - 6 c^{2} d^{3} - 3 c d^{2} \left(a e - c d\right) + 3 d \left(a e - c d\right)^{2}}{a^{2} e^{3} - 9 c^{2} d^{2} e} \right)}}{2 a^{2} c} - \frac{\left(a e + c d\right) \log{\left(x + \frac{- 2 a^{2} d e^{2} - \frac{a^{2} e^{2} \left(a e + c d\right)}{c} - 6 c^{2} d^{3} + 3 c d^{2} \left(a e + c d\right) + 3 d \left(a e + c d\right)^{2}}{a^{2} e^{3} - 9 c^{2} d^{2} e} \right)}}{2 a^{2} c}"," ",0,"d*log(x)/a**2 + (a*e - c*d)*log(x + (-2*a**2*d*e**2 + a**2*e**2*(a*e - c*d)/c - 6*c**2*d**3 - 3*c*d**2*(a*e - c*d) + 3*d*(a*e - c*d)**2)/(a**2*e**3 - 9*c**2*d**2*e))/(2*a**2*c) - (a*e + c*d)*log(x + (-2*a**2*d*e**2 - a**2*e**2*(a*e + c*d)/c - 6*c**2*d**3 + 3*c*d**2*(a*e + c*d) + 3*d*(a*e + c*d)**2)/(a**2*e**3 - 9*c**2*d**2*e))/(2*a**2*c)","B",0
303,1,221,0,1.695718," ","integrate((e*x+d)/x**2/(-c**2*x**2+a**2),x)","- \frac{d}{a^{2} x} + \frac{e \log{\left(x \right)}}{a^{2}} - \frac{\left(a e - c d\right) \log{\left(x + \frac{6 a^{4} e^{3} - 3 a^{3} e^{2} \left(a e - c d\right) + 2 a^{2} c^{2} d^{2} e - 3 a^{2} e \left(a e - c d\right)^{2} + a c^{2} d^{2} \left(a e - c d\right)}{9 a^{2} c^{2} d e^{2} - c^{4} d^{3}} \right)}}{2 a^{3}} - \frac{\left(a e + c d\right) \log{\left(x + \frac{6 a^{4} e^{3} - 3 a^{3} e^{2} \left(a e + c d\right) + 2 a^{2} c^{2} d^{2} e - 3 a^{2} e \left(a e + c d\right)^{2} + a c^{2} d^{2} \left(a e + c d\right)}{9 a^{2} c^{2} d e^{2} - c^{4} d^{3}} \right)}}{2 a^{3}}"," ",0,"-d/(a**2*x) + e*log(x)/a**2 - (a*e - c*d)*log(x + (6*a**4*e**3 - 3*a**3*e**2*(a*e - c*d) + 2*a**2*c**2*d**2*e - 3*a**2*e*(a*e - c*d)**2 + a*c**2*d**2*(a*e - c*d))/(9*a**2*c**2*d*e**2 - c**4*d**3))/(2*a**3) - (a*e + c*d)*log(x + (6*a**4*e**3 - 3*a**3*e**2*(a*e + c*d) + 2*a**2*c**2*d**2*e - 3*a**2*e*(a*e + c*d)**2 + a*c**2*d**2*(a*e + c*d))/(9*a**2*c**2*d*e**2 - c**4*d**3))/(2*a**3)","B",0
304,1,236,0,1.862937," ","integrate((e*x+d)/x**3/(-c**2*x**2+a**2),x)","- \frac{d + 2 e x}{2 a^{2} x^{2}} + \frac{c^{2} d \log{\left(x \right)}}{a^{4}} + \frac{c \left(a e - c d\right) \log{\left(x + \frac{- 2 a^{2} c^{2} d e^{2} + a^{2} c e^{2} \left(a e - c d\right) - 6 c^{4} d^{3} - 3 c^{3} d^{2} \left(a e - c d\right) + 3 c^{2} d \left(a e - c d\right)^{2}}{a^{2} c^{2} e^{3} - 9 c^{4} d^{2} e} \right)}}{2 a^{4}} - \frac{c \left(a e + c d\right) \log{\left(x + \frac{- 2 a^{2} c^{2} d e^{2} - a^{2} c e^{2} \left(a e + c d\right) - 6 c^{4} d^{3} + 3 c^{3} d^{2} \left(a e + c d\right) + 3 c^{2} d \left(a e + c d\right)^{2}}{a^{2} c^{2} e^{3} - 9 c^{4} d^{2} e} \right)}}{2 a^{4}}"," ",0,"-(d + 2*e*x)/(2*a**2*x**2) + c**2*d*log(x)/a**4 + c*(a*e - c*d)*log(x + (-2*a**2*c**2*d*e**2 + a**2*c*e**2*(a*e - c*d) - 6*c**4*d**3 - 3*c**3*d**2*(a*e - c*d) + 3*c**2*d*(a*e - c*d)**2)/(a**2*c**2*e**3 - 9*c**4*d**2*e))/(2*a**4) - c*(a*e + c*d)*log(x + (-2*a**2*c**2*d*e**2 - a**2*c*e**2*(a*e + c*d) - 6*c**4*d**3 + 3*c**3*d**2*(a*e + c*d) + 3*c**2*d*(a*e + c*d)**2)/(a**2*c**2*e**3 - 9*c**4*d**2*e))/(2*a**4)","B",0
305,1,279,0,1.996360," ","integrate((e*x+d)/x**4/(-c**2*x**2+a**2),x)","\frac{c^{2} e \log{\left(x \right)}}{a^{4}} - \frac{2 a^{2} d + 3 a^{2} e x + 6 c^{2} d x^{2}}{6 a^{4} x^{3}} - \frac{c^{2} \left(a e - c d\right) \log{\left(x + \frac{6 a^{4} c^{4} e^{3} - 3 a^{3} c^{4} e^{2} \left(a e - c d\right) + 2 a^{2} c^{6} d^{2} e - 3 a^{2} c^{4} e \left(a e - c d\right)^{2} + a c^{6} d^{2} \left(a e - c d\right)}{9 a^{2} c^{6} d e^{2} - c^{8} d^{3}} \right)}}{2 a^{5}} - \frac{c^{2} \left(a e + c d\right) \log{\left(x + \frac{6 a^{4} c^{4} e^{3} - 3 a^{3} c^{4} e^{2} \left(a e + c d\right) + 2 a^{2} c^{6} d^{2} e - 3 a^{2} c^{4} e \left(a e + c d\right)^{2} + a c^{6} d^{2} \left(a e + c d\right)}{9 a^{2} c^{6} d e^{2} - c^{8} d^{3}} \right)}}{2 a^{5}}"," ",0,"c**2*e*log(x)/a**4 - (2*a**2*d + 3*a**2*e*x + 6*c**2*d*x**2)/(6*a**4*x**3) - c**2*(a*e - c*d)*log(x + (6*a**4*c**4*e**3 - 3*a**3*c**4*e**2*(a*e - c*d) + 2*a**2*c**6*d**2*e - 3*a**2*c**4*e*(a*e - c*d)**2 + a*c**6*d**2*(a*e - c*d))/(9*a**2*c**6*d*e**2 - c**8*d**3))/(2*a**5) - c**2*(a*e + c*d)*log(x + (6*a**4*c**4*e**3 - 3*a**3*c**4*e**2*(a*e + c*d) + 2*a**2*c**6*d**2*e - 3*a**2*c**4*e*(a*e + c*d)**2 + a*c**6*d**2*(a*e + c*d))/(9*a**2*c**6*d*e**2 - c**8*d**3))/(2*a**5)","B",0
306,1,141,0,0.804626," ","integrate(x**4*(e*x+d)/(-c**2*x**2+a**2)**2,x)","\frac{a \left(4 a e - 3 c d\right) \log{\left(x + \frac{4 a^{2} e - a \left(4 a e - 3 c d\right)}{3 c^{2} d} \right)}}{4 c^{6}} + \frac{a \left(4 a e + 3 c d\right) \log{\left(x + \frac{4 a^{2} e - a \left(4 a e + 3 c d\right)}{3 c^{2} d} \right)}}{4 c^{6}} + \frac{- a^{4} e - a^{2} c^{2} d x}{- 2 a^{2} c^{6} + 2 c^{8} x^{2}} + \frac{d x}{c^{4}} + \frac{e x^{2}}{2 c^{4}}"," ",0,"a*(4*a*e - 3*c*d)*log(x + (4*a**2*e - a*(4*a*e - 3*c*d))/(3*c**2*d))/(4*c**6) + a*(4*a*e + 3*c*d)*log(x + (4*a**2*e - a*(4*a*e + 3*c*d))/(3*c**2*d))/(4*c**6) + (-a**4*e - a**2*c**2*d*x)/(-2*a**2*c**6 + 2*c**8*x**2) + d*x/c**4 + e*x**2/(2*c**4)","A",0
307,1,110,0,0.736270," ","integrate(x**3*(e*x+d)/(-c**2*x**2+a**2)**2,x)","\frac{- a^{2} d - a^{2} e x}{- 2 a^{2} c^{4} + 2 c^{6} x^{2}} + \frac{e x}{c^{4}} - \frac{\left(3 a e - 2 c d\right) \log{\left(x + \frac{2 d + \frac{3 a e - 2 c d}{c}}{3 e} \right)}}{4 c^{5}} + \frac{\left(3 a e + 2 c d\right) \log{\left(x + \frac{2 d - \frac{3 a e + 2 c d}{c}}{3 e} \right)}}{4 c^{5}}"," ",0,"(-a**2*d - a**2*e*x)/(-2*a**2*c**4 + 2*c**6*x**2) + e*x/c**4 - (3*a*e - 2*c*d)*log(x + (2*d + (3*a*e - 2*c*d)/c)/(3*e))/(4*c**5) + (3*a*e + 2*c*d)*log(x + (2*d - (3*a*e + 2*c*d)/c)/(3*e))/(4*c**5)","A",0
308,1,110,0,0.625488," ","integrate(x**2*(e*x+d)/(-c**2*x**2+a**2)**2,x)","\frac{- a^{2} e - c^{2} d x}{- 2 a^{2} c^{4} + 2 c^{6} x^{2}} + \frac{\left(2 a e - c d\right) \log{\left(x + \frac{2 a^{2} e - a \left(2 a e - c d\right)}{c^{2} d} \right)}}{4 a c^{4}} + \frac{\left(2 a e + c d\right) \log{\left(x + \frac{2 a^{2} e - a \left(2 a e + c d\right)}{c^{2} d} \right)}}{4 a c^{4}}"," ",0,"(-a**2*e - c**2*d*x)/(-2*a**2*c**4 + 2*c**6*x**2) + (2*a*e - c*d)*log(x + (2*a**2*e - a*(2*a*e - c*d))/(c**2*d))/(4*a*c**4) + (2*a*e + c*d)*log(x + (2*a**2*e - a*(2*a*e + c*d))/(c**2*d))/(4*a*c**4)","A",0
309,1,46,0,0.363062," ","integrate(x*(e*x+d)/(-c**2*x**2+a**2)**2,x)","\frac{- d - e x}{- 2 a^{2} c^{2} + 2 c^{4} x^{2}} + \frac{e \left(\frac{\log{\left(- \frac{a}{c} + x \right)}}{4} - \frac{\log{\left(\frac{a}{c} + x \right)}}{4}\right)}{a c^{3}}"," ",0,"(-d - e*x)/(-2*a**2*c**2 + 2*c**4*x**2) + e*(log(-a/c + x)/4 - log(a/c + x)/4)/(a*c**3)","A",0
310,1,56,0,0.326496," ","integrate((e*x+d)/(-c**2*x**2+a**2)**2,x)","\frac{- a^{2} e - c^{2} d x}{- 2 a^{4} c^{2} + 2 a^{2} c^{4} x^{2}} + \frac{d \left(- \frac{\log{\left(- \frac{a}{c} + x \right)}}{4} + \frac{\log{\left(\frac{a}{c} + x \right)}}{4}\right)}{a^{3} c}"," ",0,"(-a**2*e - c**2*d*x)/(-2*a**4*c**2 + 2*a**2*c**4*x**2) + d*(-log(-a/c + x)/4 + log(a/c + x)/4)/(a**3*c)","A",0
311,1,231,0,1.827502," ","integrate((e*x+d)/x/(-c**2*x**2+a**2)**2,x)","\frac{- d - e x}{- 2 a^{4} + 2 a^{2} c^{2} x^{2}} + \frac{d \log{\left(x \right)}}{a^{4}} + \frac{\left(a e - 2 c d\right) \log{\left(x + \frac{- 4 a^{2} d e^{2} + \frac{a^{2} e^{2} \left(a e - 2 c d\right)}{c} - 48 c^{2} d^{3} - 12 c d^{2} \left(a e - 2 c d\right) + 6 d \left(a e - 2 c d\right)^{2}}{a^{2} e^{3} - 36 c^{2} d^{2} e} \right)}}{4 a^{4} c} - \frac{\left(a e + 2 c d\right) \log{\left(x + \frac{- 4 a^{2} d e^{2} - \frac{a^{2} e^{2} \left(a e + 2 c d\right)}{c} - 48 c^{2} d^{3} + 12 c d^{2} \left(a e + 2 c d\right) + 6 d \left(a e + 2 c d\right)^{2}}{a^{2} e^{3} - 36 c^{2} d^{2} e} \right)}}{4 a^{4} c}"," ",0,"(-d - e*x)/(-2*a**4 + 2*a**2*c**2*x**2) + d*log(x)/a**4 + (a*e - 2*c*d)*log(x + (-4*a**2*d*e**2 + a**2*e**2*(a*e - 2*c*d)/c - 48*c**2*d**3 - 12*c*d**2*(a*e - 2*c*d) + 6*d*(a*e - 2*c*d)**2)/(a**2*e**3 - 36*c**2*d**2*e))/(4*a**4*c) - (a*e + 2*c*d)*log(x + (-4*a**2*d*e**2 - a**2*e**2*(a*e + 2*c*d)/c - 48*c**2*d**3 + 12*c*d**2*(a*e + 2*c*d) + 6*d*(a*e + 2*c*d)**2)/(a**2*e**3 - 36*c**2*d**2*e))/(4*a**4*c)","B",0
312,1,291,0,1.946221," ","integrate((e*x+d)/x**2/(-c**2*x**2+a**2)**2,x)","\frac{2 a^{2} d - a^{2} e x - 3 c^{2} d x^{2}}{- 2 a^{6} x + 2 a^{4} c^{2} x^{3}} + \frac{e \log{\left(x \right)}}{a^{4}} - \frac{\left(2 a e - 3 c d\right) \log{\left(x + \frac{16 a^{4} e^{3} - 4 a^{3} e^{2} \left(2 a e - 3 c d\right) + 12 a^{2} c^{2} d^{2} e - 2 a^{2} e \left(2 a e - 3 c d\right)^{2} + 3 a c^{2} d^{2} \left(2 a e - 3 c d\right)}{36 a^{2} c^{2} d e^{2} - 9 c^{4} d^{3}} \right)}}{4 a^{5}} - \frac{\left(2 a e + 3 c d\right) \log{\left(x + \frac{16 a^{4} e^{3} - 4 a^{3} e^{2} \left(2 a e + 3 c d\right) + 12 a^{2} c^{2} d^{2} e - 2 a^{2} e \left(2 a e + 3 c d\right)^{2} + 3 a c^{2} d^{2} \left(2 a e + 3 c d\right)}{36 a^{2} c^{2} d e^{2} - 9 c^{4} d^{3}} \right)}}{4 a^{5}}"," ",0,"(2*a**2*d - a**2*e*x - 3*c**2*d*x**2)/(-2*a**6*x + 2*a**4*c**2*x**3) + e*log(x)/a**4 - (2*a*e - 3*c*d)*log(x + (16*a**4*e**3 - 4*a**3*e**2*(2*a*e - 3*c*d) + 12*a**2*c**2*d**2*e - 2*a**2*e*(2*a*e - 3*c*d)**2 + 3*a*c**2*d**2*(2*a*e - 3*c*d))/(36*a**2*c**2*d*e**2 - 9*c**4*d**3))/(4*a**5) - (2*a*e + 3*c*d)*log(x + (16*a**4*e**3 - 4*a**3*e**2*(2*a*e + 3*c*d) + 12*a**2*c**2*d**2*e - 2*a**2*e*(2*a*e + 3*c*d)**2 + 3*a*c**2*d**2*(2*a*e + 3*c*d))/(36*a**2*c**2*d*e**2 - 9*c**4*d**3))/(4*a**5)","B",0
313,1,311,0,2.297606," ","integrate((e*x+d)/x**3/(-c**2*x**2+a**2)**2,x)","\frac{a^{2} d + 2 a^{2} e x - 2 c^{2} d x^{2} - 3 c^{2} e x^{3}}{- 2 a^{6} x^{2} + 2 a^{4} c^{2} x^{4}} + \frac{2 c^{2} d \log{\left(x \right)}}{a^{6}} + \frac{c \left(3 a e - 4 c d\right) \log{\left(x + \frac{- 24 a^{2} c^{2} d e^{2} + 3 a^{2} c e^{2} \left(3 a e - 4 c d\right) - 128 c^{4} d^{3} - 16 c^{3} d^{2} \left(3 a e - 4 c d\right) + 4 c^{2} d \left(3 a e - 4 c d\right)^{2}}{9 a^{2} c^{2} e^{3} - 144 c^{4} d^{2} e} \right)}}{4 a^{6}} - \frac{c \left(3 a e + 4 c d\right) \log{\left(x + \frac{- 24 a^{2} c^{2} d e^{2} - 3 a^{2} c e^{2} \left(3 a e + 4 c d\right) - 128 c^{4} d^{3} + 16 c^{3} d^{2} \left(3 a e + 4 c d\right) + 4 c^{2} d \left(3 a e + 4 c d\right)^{2}}{9 a^{2} c^{2} e^{3} - 144 c^{4} d^{2} e} \right)}}{4 a^{6}}"," ",0,"(a**2*d + 2*a**2*e*x - 2*c**2*d*x**2 - 3*c**2*e*x**3)/(-2*a**6*x**2 + 2*a**4*c**2*x**4) + 2*c**2*d*log(x)/a**6 + c*(3*a*e - 4*c*d)*log(x + (-24*a**2*c**2*d*e**2 + 3*a**2*c*e**2*(3*a*e - 4*c*d) - 128*c**4*d**3 - 16*c**3*d**2*(3*a*e - 4*c*d) + 4*c**2*d*(3*a*e - 4*c*d)**2)/(9*a**2*c**2*e**3 - 144*c**4*d**2*e))/(4*a**6) - c*(3*a*e + 4*c*d)*log(x + (-24*a**2*c**2*d*e**2 - 3*a**2*c*e**2*(3*a*e + 4*c*d) - 128*c**4*d**3 + 16*c**3*d**2*(3*a*e + 4*c*d) + 4*c**2*d*(3*a*e + 4*c*d)**2)/(9*a**2*c**2*e**3 - 144*c**4*d**2*e))/(4*a**6)","B",0
314,1,216,0,8.364283," ","integrate(x**4*(B*x+A)*(c*x**2+a)**(1/2),x)","- \frac{A a^{\frac{5}{2}} x}{16 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{\frac{3}{2}} x^{3}}{48 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 A \sqrt{a} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{5}{2}}} + \frac{A c x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"-A*a**(5/2)*x/(16*c**2*sqrt(1 + c*x**2/a)) - A*a**(3/2)*x**3/(48*c*sqrt(1 + c*x**2/a)) + 5*A*sqrt(a)*x**5/(24*sqrt(1 + c*x**2/a)) + A*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*c**(5/2)) + A*c*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + B*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True))","A",0
315,1,192,0,7.859183," ","integrate(x**3*(B*x+A)*(c*x**2+a)**(1/2),x)","A \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) - \frac{B a^{\frac{5}{2}} x}{16 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{\frac{3}{2}} x^{3}}{48 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 B \sqrt{a} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{5}{2}}} + \frac{B c x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) - B*a**(5/2)*x/(16*c**2*sqrt(1 + c*x**2/a)) - B*a**(3/2)*x**3/(48*c*sqrt(1 + c*x**2/a)) + 5*B*sqrt(a)*x**5/(24*sqrt(1 + c*x**2/a)) + B*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*c**(5/2)) + B*c*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
316,1,165,0,5.460118," ","integrate(x**2*(B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A a^{\frac{3}{2}} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A \sqrt{a} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{A c x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"A*a**(3/2)*x/(8*c*sqrt(1 + c*x**2/a)) + 3*A*sqrt(a)*x**3/(8*sqrt(1 + c*x**2/a)) - A*a**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + A*c*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + B*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True))","A",0
317,1,124,0,5.406986," ","integrate(x*(B*x+A)*(c*x**2+a)**(1/2),x)","A \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + \frac{B a^{\frac{3}{2}} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B \sqrt{a} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{B c x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + B*a**(3/2)*x/(8*c*sqrt(1 + c*x**2/a)) + 3*B*sqrt(a)*x**3/(8*sqrt(1 + c*x**2/a)) - B*a**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + B*c*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
318,1,70,0,3.383513," ","integrate((B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{A a \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + B \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)"," ",0,"A*sqrt(a)*x*sqrt(1 + c*x**2/a)/2 + A*a*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + B*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True))","A",0
319,1,107,0,6.742374," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x,x)","- A \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)} + \frac{A a}{\sqrt{c} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A \sqrt{c} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B \sqrt{a} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{B a \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}}"," ",0,"-A*sqrt(a)*asinh(sqrt(a)/(sqrt(c)*x)) + A*a/(sqrt(c)*x*sqrt(a/(c*x**2) + 1)) + A*sqrt(c)*x/sqrt(a/(c*x**2) + 1) + B*sqrt(a)*x*sqrt(1 + c*x**2/a)/2 + B*a*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c))","A",0
320,1,124,0,4.555964," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x**2,x)","- \frac{A \sqrt{a}}{x \sqrt{1 + \frac{c x^{2}}{a}}} + A \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)} - \frac{A c x}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} - B \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)} + \frac{B a}{\sqrt{c} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B \sqrt{c} x}{\sqrt{\frac{a}{c x^{2}} + 1}}"," ",0,"-A*sqrt(a)/(x*sqrt(1 + c*x**2/a)) + A*sqrt(c)*asinh(sqrt(c)*x/sqrt(a)) - A*c*x/(sqrt(a)*sqrt(1 + c*x**2/a)) - B*sqrt(a)*asinh(sqrt(a)/(sqrt(c)*x)) + B*a/(sqrt(c)*x*sqrt(a/(c*x**2) + 1)) + B*sqrt(c)*x/sqrt(a/(c*x**2) + 1)","A",0
321,1,107,0,4.842858," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x**3,x)","- \frac{A \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} - \frac{A c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2 \sqrt{a}} - \frac{B \sqrt{a}}{x \sqrt{1 + \frac{c x^{2}}{a}}} + B \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)} - \frac{B c x}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-A*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*x) - A*c*asinh(sqrt(a)/(sqrt(c)*x))/(2*sqrt(a)) - B*sqrt(a)/(x*sqrt(1 + c*x**2/a)) + B*sqrt(c)*asinh(sqrt(c)*x/sqrt(a)) - B*c*x/(sqrt(a)*sqrt(1 + c*x**2/a))","A",0
322,1,92,0,4.211983," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x**4,x)","- \frac{A \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 x^{2}} - \frac{A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a} - \frac{B \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} - \frac{B c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2 \sqrt{a}}"," ",0,"-A*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*x**2) - A*c**(3/2)*sqrt(a/(c*x**2) + 1)/(3*a) - B*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*x) - B*c*asinh(sqrt(a)/(sqrt(c)*x))/(2*sqrt(a))","A",0
323,1,144,0,5.940938," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x**5,x)","- \frac{A a}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 A \sqrt{c}}{8 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{A c^{\frac{3}{2}}}{8 a x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8 a^{\frac{3}{2}}} - \frac{B \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 x^{2}} - \frac{B c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a}"," ",0,"-A*a/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) - 3*A*sqrt(c)/(8*x**3*sqrt(a/(c*x**2) + 1)) - A*c**(3/2)/(8*a*x*sqrt(a/(c*x**2) + 1)) + A*c**2*asinh(sqrt(a)/(sqrt(c)*x))/(8*a**(3/2)) - B*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*x**2) - B*c**(3/2)*sqrt(a/(c*x**2) + 1)/(3*a)","A",0
324,1,173,0,6.248967," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x**6,x)","- \frac{A \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a x^{2}} + \frac{2 A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{2}} - \frac{B a}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 B \sqrt{c}}{8 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{B c^{\frac{3}{2}}}{8 a x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8 a^{\frac{3}{2}}}"," ",0,"-A*sqrt(c)*sqrt(a/(c*x**2) + 1)/(5*x**4) - A*c**(3/2)*sqrt(a/(c*x**2) + 1)/(15*a*x**2) + 2*A*c**(5/2)*sqrt(a/(c*x**2) + 1)/(15*a**2) - B*a/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) - 3*B*sqrt(c)/(8*x**3*sqrt(a/(c*x**2) + 1)) - B*c**(3/2)/(8*a*x*sqrt(a/(c*x**2) + 1)) + B*c**2*asinh(sqrt(a)/(sqrt(c)*x))/(8*a**(3/2))","A",0
325,1,201,0,8.567616," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/x**7,x)","- \frac{A a}{6 \sqrt{c} x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{5 A \sqrt{c}}{24 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A c^{\frac{3}{2}}}{48 a x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A c^{\frac{5}{2}}}{16 a^{2} x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{A c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{16 a^{\frac{5}{2}}} - \frac{B \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{B c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a x^{2}} + \frac{2 B c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{2}}"," ",0,"-A*a/(6*sqrt(c)*x**7*sqrt(a/(c*x**2) + 1)) - 5*A*sqrt(c)/(24*x**5*sqrt(a/(c*x**2) + 1)) + A*c**(3/2)/(48*a*x**3*sqrt(a/(c*x**2) + 1)) + A*c**(5/2)/(16*a**2*x*sqrt(a/(c*x**2) + 1)) - A*c**3*asinh(sqrt(a)/(sqrt(c)*x))/(16*a**(5/2)) - B*sqrt(c)*sqrt(a/(c*x**2) + 1)/(5*x**4) - B*c**(3/2)*sqrt(a/(c*x**2) + 1)/(15*a*x**2) + 2*B*c**(5/2)*sqrt(a/(c*x**2) + 1)/(15*a**2)","A",0
326,1,366,0,19.240107," ","integrate(x**4*(B*x+A)*(c*x**2+a)**(3/2),x)","- \frac{3 A a^{\frac{7}{2}} x}{128 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{\frac{5}{2}} x^{3}}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{13 A a^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 A \sqrt{a} c x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A a^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{5}{2}}} + \frac{A c^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + B c \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"-3*A*a**(7/2)*x/(128*c**2*sqrt(1 + c*x**2/a)) - A*a**(5/2)*x**3/(128*c*sqrt(1 + c*x**2/a)) + 13*A*a**(3/2)*x**5/(64*sqrt(1 + c*x**2/a)) + 5*A*sqrt(a)*c*x**7/(16*sqrt(1 + c*x**2/a)) + 3*A*a**4*asinh(sqrt(c)*x/sqrt(a))/(128*c**(5/2)) + A*c**2*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + B*c*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True))","A",0
327,1,318,0,18.139913," ","integrate(x**3*(B*x+A)*(c*x**2+a)**(3/2),x)","A a \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + A c \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) - \frac{3 B a^{\frac{7}{2}} x}{128 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{\frac{5}{2}} x^{3}}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{13 B a^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 B \sqrt{a} c x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B a^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{5}{2}}} + \frac{B c^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*a*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + A*c*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) - 3*B*a**(7/2)*x/(128*c**2*sqrt(1 + c*x**2/a)) - B*a**(5/2)*x**3/(128*c*sqrt(1 + c*x**2/a)) + 13*B*a**(3/2)*x**5/(64*sqrt(1 + c*x**2/a)) + 5*B*sqrt(a)*c*x**7/(16*sqrt(1 + c*x**2/a)) + 3*B*a**4*asinh(sqrt(c)*x/sqrt(a))/(128*c**(5/2)) + B*c**2*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
328,1,287,0,12.446949," ","integrate(x**2*(B*x+A)*(c*x**2+a)**(3/2),x)","\frac{A a^{\frac{5}{2}} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 A a^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 A \sqrt{a} c x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{A c^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + B c \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"A*a**(5/2)*x/(16*c*sqrt(1 + c*x**2/a)) + 17*A*a**(3/2)*x**3/(48*sqrt(1 + c*x**2/a)) + 11*A*sqrt(a)*c*x**5/(24*sqrt(1 + c*x**2/a)) - A*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + A*c**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + B*c*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True))","A",0
329,1,223,0,12.113729," ","integrate(x*(B*x+A)*(c*x**2+a)**(3/2),x)","A a \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + A c \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{B a^{\frac{5}{2}} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 B a^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 B \sqrt{a} c x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{B c^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*a*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + A*c*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + B*a**(5/2)*x/(16*c*sqrt(1 + c*x**2/a)) + 17*B*a**(3/2)*x**3/(48*sqrt(1 + c*x**2/a)) + 11*B*sqrt(a)*c*x**5/(24*sqrt(1 + c*x**2/a)) - B*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + B*c**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
330,1,219,0,7.618205," ","integrate((B*x+A)*(c*x**2+a)**(3/2),x)","\frac{A a^{\frac{3}{2}} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{A a^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A \sqrt{a} c x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + \frac{A c^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + B c \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"A*a**(3/2)*x*sqrt(1 + c*x**2/a)/2 + A*a**(3/2)*x/(8*sqrt(1 + c*x**2/a)) + 3*A*sqrt(a)*c*x**3/(8*sqrt(1 + c*x**2/a)) + 3*A*a**2*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + A*c**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + B*c*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True))","A",0
331,1,218,0,17.916626," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x,x)","- A a^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)} + \frac{A a^{2}}{\sqrt{c} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A a \sqrt{c} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + A c \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + \frac{B a^{\frac{3}{2}} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{B a^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B \sqrt{a} c x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + \frac{B c^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-A*a**(3/2)*asinh(sqrt(a)/(sqrt(c)*x)) + A*a**2/(sqrt(c)*x*sqrt(a/(c*x**2) + 1)) + A*a*sqrt(c)*x/sqrt(a/(c*x**2) + 1) + A*c*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + B*a**(3/2)*x*sqrt(1 + c*x**2/a)/2 + B*a**(3/2)*x/(8*sqrt(1 + c*x**2/a)) + 3*B*sqrt(a)*c*x**3/(8*sqrt(1 + c*x**2/a)) + 3*B*a**2*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + B*c**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
332,1,184,0,7.071268," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**2,x)","- \frac{A a^{\frac{3}{2}}}{x \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{A \sqrt{a} c x \sqrt{1 + \frac{c x^{2}}{a}}}{2} - \frac{A \sqrt{a} c x}{\sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A a \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2} - B a^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)} + \frac{B a^{2}}{\sqrt{c} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B a \sqrt{c} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + B c \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)"," ",0,"-A*a**(3/2)/(x*sqrt(1 + c*x**2/a)) + A*sqrt(a)*c*x*sqrt(1 + c*x**2/a)/2 - A*sqrt(a)*c*x/sqrt(1 + c*x**2/a) + 3*A*a*sqrt(c)*asinh(sqrt(c)*x/sqrt(a))/2 - B*a**(3/2)*asinh(sqrt(a)/(sqrt(c)*x)) + B*a**2/(sqrt(c)*x*sqrt(a/(c*x**2) + 1)) + B*a*sqrt(c)*x/sqrt(a/(c*x**2) + 1) + B*c*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True))","A",0
333,1,182,0,8.187738," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**3,x)","- \frac{3 A \sqrt{a} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2} - \frac{A a \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} + \frac{A a \sqrt{c}}{x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A c^{\frac{3}{2}} x}{\sqrt{\frac{a}{c x^{2}} + 1}} - \frac{B a^{\frac{3}{2}}}{x \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{B \sqrt{a} c x \sqrt{1 + \frac{c x^{2}}{a}}}{2} - \frac{B \sqrt{a} c x}{\sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B a \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2}"," ",0,"-3*A*sqrt(a)*c*asinh(sqrt(a)/(sqrt(c)*x))/2 - A*a*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*x) + A*a*sqrt(c)/(x*sqrt(a/(c*x**2) + 1)) + A*c**(3/2)*x/sqrt(a/(c*x**2) + 1) - B*a**(3/2)/(x*sqrt(1 + c*x**2/a)) + B*sqrt(a)*c*x*sqrt(1 + c*x**2/a)/2 - B*sqrt(a)*c*x/sqrt(1 + c*x**2/a) + 3*B*a*sqrt(c)*asinh(sqrt(c)*x/sqrt(a))/2","A",0
334,1,202,0,7.327529," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**4,x)","- \frac{A \sqrt{a} c}{x \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 x^{2}} - \frac{A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3} + A c^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)} - \frac{A c^{2} x}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 B \sqrt{a} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2} - \frac{B a \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} + \frac{B a \sqrt{c}}{x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B c^{\frac{3}{2}} x}{\sqrt{\frac{a}{c x^{2}} + 1}}"," ",0,"-A*sqrt(a)*c/(x*sqrt(1 + c*x**2/a)) - A*a*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*x**2) - A*c**(3/2)*sqrt(a/(c*x**2) + 1)/3 + A*c**(3/2)*asinh(sqrt(c)*x/sqrt(a)) - A*c**2*x/(sqrt(a)*sqrt(1 + c*x**2/a)) - 3*B*sqrt(a)*c*asinh(sqrt(a)/(sqrt(c)*x))/2 - B*a*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*x) + B*a*sqrt(c)/(x*sqrt(a/(c*x**2) + 1)) + B*c**(3/2)*x/sqrt(a/(c*x**2) + 1)","B",0
335,1,236,0,9.337245," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**5,x)","- \frac{A a^{2}}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 A a \sqrt{c}}{8 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} - \frac{A c^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 A c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8 \sqrt{a}} - \frac{B \sqrt{a} c}{x \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 x^{2}} - \frac{B c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3} + B c^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)} - \frac{B c^{2} x}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-A*a**2/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) - 3*A*a*sqrt(c)/(8*x**3*sqrt(a/(c*x**2) + 1)) - A*c**(3/2)*sqrt(a/(c*x**2) + 1)/(2*x) - A*c**(3/2)/(8*x*sqrt(a/(c*x**2) + 1)) - 3*A*c**2*asinh(sqrt(a)/(sqrt(c)*x))/(8*sqrt(a)) - B*sqrt(a)*c/(x*sqrt(1 + c*x**2/a)) - B*a*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*x**2) - B*c**(3/2)*sqrt(a/(c*x**2) + 1)/3 + B*c**(3/2)*asinh(sqrt(c)*x/sqrt(a)) - B*c**2*x/(sqrt(a)*sqrt(1 + c*x**2/a))","B",0
336,1,199,0,8.952438," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**6,x)","- \frac{A a \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{2 A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{2}} - \frac{A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 a} - \frac{B a^{2}}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 B a \sqrt{c}}{8 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{B c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} - \frac{B c^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 B c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8 \sqrt{a}}"," ",0,"-A*a*sqrt(c)*sqrt(a/(c*x**2) + 1)/(5*x**4) - 2*A*c**(3/2)*sqrt(a/(c*x**2) + 1)/(5*x**2) - A*c**(5/2)*sqrt(a/(c*x**2) + 1)/(5*a) - B*a**2/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) - 3*B*a*sqrt(c)/(8*x**3*sqrt(a/(c*x**2) + 1)) - B*c**(3/2)*sqrt(a/(c*x**2) + 1)/(2*x) - B*c**(3/2)/(8*x*sqrt(a/(c*x**2) + 1)) - 3*B*c**2*asinh(sqrt(a)/(sqrt(c)*x))/(8*sqrt(a))","B",0
337,1,201,0,13.387289," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**7,x)","- \frac{A a^{2}}{6 \sqrt{c} x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{11 A a \sqrt{c}}{24 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{17 A c^{\frac{3}{2}}}{48 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{A c^{\frac{5}{2}}}{16 a x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{16 a^{\frac{3}{2}}} - \frac{B a \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{2 B c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{2}} - \frac{B c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 a}"," ",0,"-A*a**2/(6*sqrt(c)*x**7*sqrt(a/(c*x**2) + 1)) - 11*A*a*sqrt(c)/(24*x**5*sqrt(a/(c*x**2) + 1)) - 17*A*c**(3/2)/(48*x**3*sqrt(a/(c*x**2) + 1)) - A*c**(5/2)/(16*a*x*sqrt(a/(c*x**2) + 1)) + A*c**3*asinh(sqrt(a)/(sqrt(c)*x))/(16*a**(3/2)) - B*a*sqrt(c)*sqrt(a/(c*x**2) + 1)/(5*x**4) - 2*B*c**(3/2)*sqrt(a/(c*x**2) + 1)/(5*x**2) - B*c**(5/2)*sqrt(a/(c*x**2) + 1)/(5*a)","A",0
338,1,575,0,13.985051," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/x**8,x)","- \frac{15 A a^{6} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{33 A a^{5} c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{17 A a^{4} c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{3 A a^{3} c^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{12 A a^{2} c^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{8 A a c^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a x^{2}} + \frac{2 A c^{\frac{7}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{2}} - \frac{B a^{2}}{6 \sqrt{c} x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{11 B a \sqrt{c}}{24 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{17 B c^{\frac{3}{2}}}{48 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{B c^{\frac{5}{2}}}{16 a x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{16 a^{\frac{3}{2}}}"," ",0,"-15*A*a**6*c**(9/2)*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 33*A*a**5*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 17*A*a**4*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 3*A*a**3*c**(15/2)*x**6*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 12*A*a**2*c**(17/2)*x**8*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 8*A*a*c**(19/2)*x**10*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - A*c**(3/2)*sqrt(a/(c*x**2) + 1)/(5*x**4) - A*c**(5/2)*sqrt(a/(c*x**2) + 1)/(15*a*x**2) + 2*A*c**(7/2)*sqrt(a/(c*x**2) + 1)/(15*a**2) - B*a**2/(6*sqrt(c)*x**7*sqrt(a/(c*x**2) + 1)) - 11*B*a*sqrt(c)/(24*x**5*sqrt(a/(c*x**2) + 1)) - 17*B*c**(3/2)/(48*x**3*sqrt(a/(c*x**2) + 1)) - B*c**(5/2)/(16*a*x*sqrt(a/(c*x**2) + 1)) + B*c**3*asinh(sqrt(a)/(sqrt(c)*x))/(16*a**(3/2))","B",0
339,1,541,0,37.228968," ","integrate(x**4*(B*x+A)*(c*x**2+a)**(5/2),x)","- \frac{3 A a^{\frac{9}{2}} x}{256 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{\frac{7}{2}} x^{3}}{256 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{129 A a^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{73 A a^{\frac{3}{2}} c x^{7}}{160 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{29 A \sqrt{a} c^{2} x^{9}}{80 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A a^{5} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{256 c^{\frac{5}{2}}} + \frac{A c^{3} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 2 B a c \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + B c^{2} \left(\begin{cases} \frac{128 a^{5} \sqrt{a + c x^{2}}}{3465 c^{5}} - \frac{64 a^{4} x^{2} \sqrt{a + c x^{2}}}{3465 c^{4}} + \frac{16 a^{3} x^{4} \sqrt{a + c x^{2}}}{1155 c^{3}} - \frac{8 a^{2} x^{6} \sqrt{a + c x^{2}}}{693 c^{2}} + \frac{a x^{8} \sqrt{a + c x^{2}}}{99 c} + \frac{x^{10} \sqrt{a + c x^{2}}}{11} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{10}}{10} & \text{otherwise} \end{cases}\right)"," ",0,"-3*A*a**(9/2)*x/(256*c**2*sqrt(1 + c*x**2/a)) - A*a**(7/2)*x**3/(256*c*sqrt(1 + c*x**2/a)) + 129*A*a**(5/2)*x**5/(640*sqrt(1 + c*x**2/a)) + 73*A*a**(3/2)*c*x**7/(160*sqrt(1 + c*x**2/a)) + 29*A*sqrt(a)*c**2*x**9/(80*sqrt(1 + c*x**2/a)) + 3*A*a**5*asinh(sqrt(c)*x/sqrt(a))/(256*c**(5/2)) + A*c**3*x**11/(10*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a**2*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 2*B*a*c*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True)) + B*c**2*Piecewise((128*a**5*sqrt(a + c*x**2)/(3465*c**5) - 64*a**4*x**2*sqrt(a + c*x**2)/(3465*c**4) + 16*a**3*x**4*sqrt(a + c*x**2)/(1155*c**3) - 8*a**2*x**6*sqrt(a + c*x**2)/(693*c**2) + a*x**8*sqrt(a + c*x**2)/(99*c) + x**10*sqrt(a + c*x**2)/11, Ne(c, 0)), (sqrt(a)*x**10/10, True))","A",0
340,1,469,0,34.716075," ","integrate(x**3*(B*x+A)*(c*x**2+a)**(5/2),x)","A a^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 A a c \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + A c^{2} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) - \frac{3 B a^{\frac{9}{2}} x}{256 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{\frac{7}{2}} x^{3}}{256 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{129 B a^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{73 B a^{\frac{3}{2}} c x^{7}}{160 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{29 B \sqrt{a} c^{2} x^{9}}{80 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B a^{5} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{256 c^{\frac{5}{2}}} + \frac{B c^{3} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*a**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*A*a*c*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + A*c**2*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True)) - 3*B*a**(9/2)*x/(256*c**2*sqrt(1 + c*x**2/a)) - B*a**(7/2)*x**3/(256*c*sqrt(1 + c*x**2/a)) + 129*B*a**(5/2)*x**5/(640*sqrt(1 + c*x**2/a)) + 73*B*a**(3/2)*c*x**7/(160*sqrt(1 + c*x**2/a)) + 29*B*sqrt(a)*c**2*x**9/(80*sqrt(1 + c*x**2/a)) + 3*B*a**5*asinh(sqrt(c)*x/sqrt(a))/(256*c**(5/2)) + B*c**3*x**11/(10*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
341,1,442,0,24.057968," ","integrate(x**2*(B*x+A)*(c*x**2+a)**(5/2),x)","\frac{5 A a^{\frac{7}{2}} x}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{133 A a^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{127 A a^{\frac{3}{2}} c x^{5}}{192 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{23 A \sqrt{a} c^{2} x^{7}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{5 A a^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{3}{2}}} + \frac{A c^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 B a c \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + B c^{2} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"5*A*a**(7/2)*x/(128*c*sqrt(1 + c*x**2/a)) + 133*A*a**(5/2)*x**3/(384*sqrt(1 + c*x**2/a)) + 127*A*a**(3/2)*c*x**5/(192*sqrt(1 + c*x**2/a)) + 23*A*sqrt(a)*c**2*x**7/(48*sqrt(1 + c*x**2/a)) - 5*A*a**4*asinh(sqrt(c)*x/sqrt(a))/(128*c**(3/2)) + A*c**3*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*B*a*c*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + B*c**2*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True))","A",0
342,1,354,0,22.220685," ","integrate(x*(B*x+A)*(c*x**2+a)**(5/2),x)","A a^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 2 A a c \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + A c^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{5 B a^{\frac{7}{2}} x}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{133 B a^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{127 B a^{\frac{3}{2}} c x^{5}}{192 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{23 B \sqrt{a} c^{2} x^{7}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{5 B a^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{3}{2}}} + \frac{B c^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*a**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 2*A*a*c*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + A*c**2*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 5*B*a**(7/2)*x/(128*c*sqrt(1 + c*x**2/a)) + 133*B*a**(5/2)*x**3/(384*sqrt(1 + c*x**2/a)) + 127*B*a**(3/2)*c*x**5/(192*sqrt(1 + c*x**2/a)) + 23*B*sqrt(a)*c**2*x**7/(48*sqrt(1 + c*x**2/a)) - 5*B*a**4*asinh(sqrt(c)*x/sqrt(a))/(128*c**(3/2)) + B*c**3*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
343,1,348,0,14.703173," ","integrate((B*x+A)*(c*x**2+a)**(5/2),x)","\frac{A a^{\frac{5}{2}} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 A a^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 A a^{\frac{3}{2}} c x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 A \sqrt{a} c^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + \frac{A c^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 2 B a c \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + B c^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"A*a**(5/2)*x*sqrt(1 + c*x**2/a)/2 + 3*A*a**(5/2)*x/(16*sqrt(1 + c*x**2/a)) + 35*A*a**(3/2)*c*x**3/(48*sqrt(1 + c*x**2/a)) + 17*A*sqrt(a)*c**2*x**5/(24*sqrt(1 + c*x**2/a)) + 5*A*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + A*c**3*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 2*B*a*c*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + B*c**2*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True))","A",0
344,1,323,0,29.889710," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x,x)","- A a^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)} + \frac{A a^{3}}{\sqrt{c} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A a^{2} \sqrt{c} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + 2 A a c \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + A c^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{B a^{\frac{5}{2}} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 B a^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 B a^{\frac{3}{2}} c x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 B \sqrt{a} c^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + \frac{B c^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-A*a**(5/2)*asinh(sqrt(a)/(sqrt(c)*x)) + A*a**3/(sqrt(c)*x*sqrt(a/(c*x**2) + 1)) + A*a**2*sqrt(c)*x/sqrt(a/(c*x**2) + 1) + 2*A*a*c*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + A*c**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + B*a**(5/2)*x*sqrt(1 + c*x**2/a)/2 + 3*B*a**(5/2)*x/(16*sqrt(1 + c*x**2/a)) + 35*B*a**(3/2)*c*x**3/(48*sqrt(1 + c*x**2/a)) + 17*B*sqrt(a)*c**2*x**5/(24*sqrt(1 + c*x**2/a)) + 5*B*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + B*c**3*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
345,1,318,0,11.723426," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**2,x)","- \frac{A a^{\frac{5}{2}}}{x \sqrt{1 + \frac{c x^{2}}{a}}} + A a^{\frac{3}{2}} c x \sqrt{1 + \frac{c x^{2}}{a}} - \frac{7 A a^{\frac{3}{2}} c x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A \sqrt{a} c^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{15 A a^{2} \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8} + \frac{A c^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} - B a^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)} + \frac{B a^{3}}{\sqrt{c} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B a^{2} \sqrt{c} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + 2 B a c \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + B c^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"-A*a**(5/2)/(x*sqrt(1 + c*x**2/a)) + A*a**(3/2)*c*x*sqrt(1 + c*x**2/a) - 7*A*a**(3/2)*c*x/(8*sqrt(1 + c*x**2/a)) + 3*A*sqrt(a)*c**2*x**3/(8*sqrt(1 + c*x**2/a)) + 15*A*a**2*sqrt(c)*asinh(sqrt(c)*x/sqrt(a))/8 + A*c**3*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) - B*a**(5/2)*asinh(sqrt(a)/(sqrt(c)*x)) + B*a**3/(sqrt(c)*x*sqrt(a/(c*x**2) + 1)) + B*a**2*sqrt(c)*x/sqrt(a/(c*x**2) + 1) + 2*B*a*c*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + B*c**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True))","A",0
346,1,279,0,12.578585," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**3,x)","- \frac{5 A a^{\frac{3}{2}} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2} - \frac{A a^{2} \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} + \frac{2 A a^{2} \sqrt{c}}{x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{2 A a c^{\frac{3}{2}} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + A c^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) - \frac{B a^{\frac{5}{2}}}{x \sqrt{1 + \frac{c x^{2}}{a}}} + B a^{\frac{3}{2}} c x \sqrt{1 + \frac{c x^{2}}{a}} - \frac{7 B a^{\frac{3}{2}} c x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B \sqrt{a} c^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{15 B a^{2} \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8} + \frac{B c^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-5*A*a**(3/2)*c*asinh(sqrt(a)/(sqrt(c)*x))/2 - A*a**2*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*x) + 2*A*a**2*sqrt(c)/(x*sqrt(a/(c*x**2) + 1)) + 2*A*a*c**(3/2)*x/sqrt(a/(c*x**2) + 1) + A*c**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) - B*a**(5/2)/(x*sqrt(1 + c*x**2/a)) + B*a**(3/2)*c*x*sqrt(1 + c*x**2/a) - 7*B*a**(3/2)*c*x/(8*sqrt(1 + c*x**2/a)) + 3*B*sqrt(a)*c**2*x**3/(8*sqrt(1 + c*x**2/a)) + 15*B*a**2*sqrt(c)*asinh(sqrt(c)*x/sqrt(a))/8 + B*c**3*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
347,1,277,0,9.682225," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**4,x)","- \frac{2 A a^{\frac{3}{2}} c}{x \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{A \sqrt{a} c^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} - \frac{2 A \sqrt{a} c^{2} x}{\sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{2} \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 x^{2}} - \frac{A a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3} + \frac{5 A a c^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2} - \frac{5 B a^{\frac{3}{2}} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2} - \frac{B a^{2} \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} + \frac{2 B a^{2} \sqrt{c}}{x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{2 B a c^{\frac{3}{2}} x}{\sqrt{\frac{a}{c x^{2}} + 1}} + B c^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right)"," ",0,"-2*A*a**(3/2)*c/(x*sqrt(1 + c*x**2/a)) + A*sqrt(a)*c**2*x*sqrt(1 + c*x**2/a)/2 - 2*A*sqrt(a)*c**2*x/sqrt(1 + c*x**2/a) - A*a**2*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*x**2) - A*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/3 + 5*A*a*c**(3/2)*asinh(sqrt(c)*x/sqrt(a))/2 - 5*B*a**(3/2)*c*asinh(sqrt(a)/(sqrt(c)*x))/2 - B*a**2*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*x) + 2*B*a**2*sqrt(c)/(x*sqrt(a/(c*x**2) + 1)) + 2*B*a*c**(3/2)*x/sqrt(a/(c*x**2) + 1) + B*c**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True))","A",0
348,1,299,0,12.864968," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**5,x)","- \frac{15 A \sqrt{a} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8} - \frac{A a^{3}}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 A a^{2} \sqrt{c}}{8 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{A a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{x} + \frac{7 A a c^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A c^{\frac{5}{2}} x}{\sqrt{\frac{a}{c x^{2}} + 1}} - \frac{2 B a^{\frac{3}{2}} c}{x \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{B \sqrt{a} c^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} - \frac{2 B \sqrt{a} c^{2} x}{\sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{2} \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 x^{2}} - \frac{B a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3} + \frac{5 B a c^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2}"," ",0,"-15*A*sqrt(a)*c**2*asinh(sqrt(a)/(sqrt(c)*x))/8 - A*a**3/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) - 3*A*a**2*sqrt(c)/(8*x**3*sqrt(a/(c*x**2) + 1)) - A*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/x + 7*A*a*c**(3/2)/(8*x*sqrt(a/(c*x**2) + 1)) + A*c**(5/2)*x/sqrt(a/(c*x**2) + 1) - 2*B*a**(3/2)*c/(x*sqrt(1 + c*x**2/a)) + B*sqrt(a)*c**2*x*sqrt(1 + c*x**2/a)/2 - 2*B*sqrt(a)*c**2*x/sqrt(1 + c*x**2/a) - B*a**2*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*x**2) - B*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/3 + 5*B*a*c**(3/2)*asinh(sqrt(c)*x/sqrt(a))/2","B",0
349,1,294,0,12.215535," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**6,x)","- \frac{A \sqrt{a} c^{2}}{x \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A a^{2} \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{11 A a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 x^{2}} - \frac{8 A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15} + A c^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)} - \frac{A c^{3} x}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{15 B \sqrt{a} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8} - \frac{B a^{3}}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 B a^{2} \sqrt{c}}{8 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{B a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{x} + \frac{7 B a c^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B c^{\frac{5}{2}} x}{\sqrt{\frac{a}{c x^{2}} + 1}}"," ",0,"-A*sqrt(a)*c**2/(x*sqrt(1 + c*x**2/a)) - A*a**2*sqrt(c)*sqrt(a/(c*x**2) + 1)/(5*x**4) - 11*A*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/(15*x**2) - 8*A*c**(5/2)*sqrt(a/(c*x**2) + 1)/15 + A*c**(5/2)*asinh(sqrt(c)*x/sqrt(a)) - A*c**3*x/(sqrt(a)*sqrt(1 + c*x**2/a)) - 15*B*sqrt(a)*c**2*asinh(sqrt(a)/(sqrt(c)*x))/8 - B*a**3/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) - 3*B*a**2*sqrt(c)/(8*x**3*sqrt(a/(c*x**2) + 1)) - B*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/x + 7*B*a*c**(3/2)/(8*x*sqrt(a/(c*x**2) + 1)) + B*c**(5/2)*x/sqrt(a/(c*x**2) + 1)","B",0
350,1,299,0,17.158594," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**7,x)","- \frac{A a^{3}}{6 \sqrt{c} x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{17 A a^{2} \sqrt{c}}{24 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{35 A a c^{\frac{3}{2}}}{48 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} - \frac{3 A c^{\frac{5}{2}}}{16 x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{5 A c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{16 \sqrt{a}} - \frac{B \sqrt{a} c^{2}}{x \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B a^{2} \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{11 B a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 x^{2}} - \frac{8 B c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15} + B c^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)} - \frac{B c^{3} x}{\sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-A*a**3/(6*sqrt(c)*x**7*sqrt(a/(c*x**2) + 1)) - 17*A*a**2*sqrt(c)/(24*x**5*sqrt(a/(c*x**2) + 1)) - 35*A*a*c**(3/2)/(48*x**3*sqrt(a/(c*x**2) + 1)) - A*c**(5/2)*sqrt(a/(c*x**2) + 1)/(2*x) - 3*A*c**(5/2)/(16*x*sqrt(a/(c*x**2) + 1)) - 5*A*c**3*asinh(sqrt(a)/(sqrt(c)*x))/(16*sqrt(a)) - B*sqrt(a)*c**2/(x*sqrt(1 + c*x**2/a)) - B*a**2*sqrt(c)*sqrt(a/(c*x**2) + 1)/(5*x**4) - 11*B*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/(15*x**2) - 8*B*c**(5/2)*sqrt(a/(c*x**2) + 1)/15 + B*c**(5/2)*asinh(sqrt(c)*x/sqrt(a)) - B*c**3*x/(sqrt(a)*sqrt(1 + c*x**2/a))","B",0
351,1,605,0,16.819709," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**8,x)","- \frac{15 A a^{7} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{33 A a^{6} c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{17 A a^{5} c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{3 A a^{4} c^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{12 A a^{3} c^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{8 A a^{2} c^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{2 A a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{7 A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 x^{2}} - \frac{A c^{\frac{7}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a} - \frac{B a^{3}}{6 \sqrt{c} x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{17 B a^{2} \sqrt{c}}{24 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{35 B a c^{\frac{3}{2}}}{48 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{B c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{2 x} - \frac{3 B c^{\frac{5}{2}}}{16 x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{5 B c^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{16 \sqrt{a}}"," ",0,"-15*A*a**7*c**(9/2)*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 33*A*a**6*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 17*A*a**5*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 3*A*a**4*c**(15/2)*x**6*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 12*A*a**3*c**(17/2)*x**8*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 8*A*a**2*c**(19/2)*x**10*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 2*A*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/(5*x**4) - 7*A*c**(5/2)*sqrt(a/(c*x**2) + 1)/(15*x**2) - A*c**(7/2)*sqrt(a/(c*x**2) + 1)/(15*a) - B*a**3/(6*sqrt(c)*x**7*sqrt(a/(c*x**2) + 1)) - 17*B*a**2*sqrt(c)/(24*x**5*sqrt(a/(c*x**2) + 1)) - 35*B*a*c**(3/2)/(48*x**3*sqrt(a/(c*x**2) + 1)) - B*c**(5/2)*sqrt(a/(c*x**2) + 1)/(2*x) - 3*B*c**(5/2)/(16*x*sqrt(a/(c*x**2) + 1)) - 5*B*c**3*asinh(sqrt(a)/(sqrt(c)*x))/(16*sqrt(a))","B",0
352,1,609,0,25.767798," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**9,x)","- \frac{A a^{3}}{8 \sqrt{c} x^{9} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{23 A a^{2} \sqrt{c}}{48 x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{127 A a c^{\frac{3}{2}}}{192 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{133 A c^{\frac{5}{2}}}{384 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{5 A c^{\frac{7}{2}}}{128 a x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{5 A c^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{128 a^{\frac{3}{2}}} - \frac{15 B a^{7} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{33 B a^{6} c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{17 B a^{5} c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{3 B a^{4} c^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{12 B a^{3} c^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{8 B a^{2} c^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{2 B a c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{7 B c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 x^{2}} - \frac{B c^{\frac{7}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a}"," ",0,"-A*a**3/(8*sqrt(c)*x**9*sqrt(a/(c*x**2) + 1)) - 23*A*a**2*sqrt(c)/(48*x**7*sqrt(a/(c*x**2) + 1)) - 127*A*a*c**(3/2)/(192*x**5*sqrt(a/(c*x**2) + 1)) - 133*A*c**(5/2)/(384*x**3*sqrt(a/(c*x**2) + 1)) - 5*A*c**(7/2)/(128*a*x*sqrt(a/(c*x**2) + 1)) + 5*A*c**4*asinh(sqrt(a)/(sqrt(c)*x))/(128*a**(3/2)) - 15*B*a**7*c**(9/2)*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 33*B*a**6*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 17*B*a**5*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 3*B*a**4*c**(15/2)*x**6*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 12*B*a**3*c**(17/2)*x**8*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 8*B*a**2*c**(19/2)*x**10*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 2*B*a*c**(3/2)*sqrt(a/(c*x**2) + 1)/(5*x**4) - 7*B*c**(5/2)*sqrt(a/(c*x**2) + 1)/(15*x**2) - B*c**(7/2)*sqrt(a/(c*x**2) + 1)/(15*a)","B",0
353,1,1202,0,25.671656," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/x**10,x)","- \frac{35 A a^{9} c^{\frac{19}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{110 A a^{8} c^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{114 A a^{7} c^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{40 A a^{6} c^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{30 A a^{6} c^{\frac{11}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} + \frac{5 A a^{5} c^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{66 A a^{5} c^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} + \frac{30 A a^{4} c^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{34 A a^{4} c^{\frac{15}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} + \frac{40 A a^{3} c^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{6 A a^{3} c^{\frac{17}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} + \frac{16 A a^{2} c^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{c x^{2}} + 1}}{315 a^{7} c^{9} x^{8} + 945 a^{6} c^{10} x^{10} + 945 a^{5} c^{11} x^{12} + 315 a^{4} c^{12} x^{14}} - \frac{24 A a^{2} c^{\frac{19}{2}} x^{8} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{16 A a c^{\frac{21}{2}} x^{10} \sqrt{\frac{a}{c x^{2}} + 1}}{105 a^{5} c^{4} x^{6} + 210 a^{4} c^{5} x^{8} + 105 a^{3} c^{6} x^{10}} - \frac{A c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{5 x^{4}} - \frac{A c^{\frac{7}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a x^{2}} + \frac{2 A c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{2}} - \frac{B a^{3}}{8 \sqrt{c} x^{9} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{23 B a^{2} \sqrt{c}}{48 x^{7} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{127 B a c^{\frac{3}{2}}}{192 x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{133 B c^{\frac{5}{2}}}{384 x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{5 B c^{\frac{7}{2}}}{128 a x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{5 B c^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{128 a^{\frac{3}{2}}}"," ",0,"-35*A*a**9*c**(19/2)*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 110*A*a**8*c**(21/2)*x**2*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 114*A*a**7*c**(23/2)*x**4*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 40*A*a**6*c**(25/2)*x**6*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 30*A*a**6*c**(11/2)*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) + 5*A*a**5*c**(27/2)*x**8*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 66*A*a**5*c**(13/2)*x**2*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) + 30*A*a**4*c**(29/2)*x**10*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 34*A*a**4*c**(15/2)*x**4*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) + 40*A*a**3*c**(31/2)*x**12*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 6*A*a**3*c**(17/2)*x**6*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) + 16*A*a**2*c**(33/2)*x**14*sqrt(a/(c*x**2) + 1)/(315*a**7*c**9*x**8 + 945*a**6*c**10*x**10 + 945*a**5*c**11*x**12 + 315*a**4*c**12*x**14) - 24*A*a**2*c**(19/2)*x**8*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - 16*A*a*c**(21/2)*x**10*sqrt(a/(c*x**2) + 1)/(105*a**5*c**4*x**6 + 210*a**4*c**5*x**8 + 105*a**3*c**6*x**10) - A*c**(5/2)*sqrt(a/(c*x**2) + 1)/(5*x**4) - A*c**(7/2)*sqrt(a/(c*x**2) + 1)/(15*a*x**2) + 2*A*c**(9/2)*sqrt(a/(c*x**2) + 1)/(15*a**2) - B*a**3/(8*sqrt(c)*x**9*sqrt(a/(c*x**2) + 1)) - 23*B*a**2*sqrt(c)/(48*x**7*sqrt(a/(c*x**2) + 1)) - 127*B*a*c**(3/2)/(192*x**5*sqrt(a/(c*x**2) + 1)) - 133*B*c**(5/2)/(384*x**3*sqrt(a/(c*x**2) + 1)) - 5*B*c**(7/2)/(128*a*x*sqrt(a/(c*x**2) + 1)) + 5*B*c**4*asinh(sqrt(a)/(sqrt(c)*x))/(128*a**(3/2))","B",0
354,1,173,0,6.584417," ","integrate(x**4*(B*x+A)/(c*x**2+a)**(1/2),x)","- \frac{3 A a^{\frac{3}{2}} x}{8 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{A \sqrt{a} x^{3}}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 A a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{5}{2}}} + \frac{A x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B \left(\begin{cases} \frac{8 a^{2} \sqrt{a + c x^{2}}}{15 c^{3}} - \frac{4 a x^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{x^{4} \sqrt{a + c x^{2}}}{5 c} & \text{for}\: c \neq 0 \\\frac{x^{6}}{6 \sqrt{a}} & \text{otherwise} \end{cases}\right)"," ",0,"-3*A*a**(3/2)*x/(8*c**2*sqrt(1 + c*x**2/a)) - A*sqrt(a)*x**3/(8*c*sqrt(1 + c*x**2/a)) + 3*A*a**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(5/2)) + A*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + B*Piecewise((8*a**2*sqrt(a + c*x**2)/(15*c**3) - 4*a*x**2*sqrt(a + c*x**2)/(15*c**2) + x**4*sqrt(a + c*x**2)/(5*c), Ne(c, 0)), (x**6/(6*sqrt(a)), True))","A",0
355,1,150,0,6.225127," ","integrate(x**3*(B*x+A)/(c*x**2+a)**(1/2),x)","A \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) - \frac{3 B a^{\frac{3}{2}} x}{8 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{B \sqrt{a} x^{3}}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 B a^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{5}{2}}} + \frac{B x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) - 3*B*a**(3/2)*x/(8*c**2*sqrt(1 + c*x**2/a)) - B*sqrt(a)*x**3/(8*c*sqrt(1 + c*x**2/a)) + 3*B*a**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(5/2)) + B*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
356,1,94,0,4.272382," ","integrate(x**2*(B*x+A)/(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{A a \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + B \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right)"," ",0,"A*sqrt(a)*x*sqrt(1 + c*x**2/a)/(2*c) - A*a*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + B*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True))","A",0
357,1,70,0,4.202233," ","integrate(x*(B*x+A)/(c*x**2+a)**(1/2),x)","A \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + \frac{B \sqrt{a} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{B a \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}}"," ",0,"A*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + B*sqrt(a)*x*sqrt(1 + c*x**2/a)/(2*c) - B*a*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2))","A",0
358,1,102,0,1.487433," ","integrate((B*x+A)/(c*x**2+a)**(1/2),x)","A \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + B \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right)"," ",0,"A*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + B*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True))","B",0
359,1,99,0,3.328070," ","integrate((B*x+A)/x/(c*x**2+a)**(1/2),x)","- \frac{A \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{\sqrt{a}} + B \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right)"," ",0,"-A*asinh(sqrt(a)/(sqrt(c)*x))/sqrt(a) + B*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0)))","A",0
360,1,41,0,2.639599," ","integrate((B*x+A)/x**2/(c*x**2+a)**(1/2),x)","- \frac{A \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{a} - \frac{B \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{\sqrt{a}}"," ",0,"-A*sqrt(c)*sqrt(a/(c*x**2) + 1)/a - B*asinh(sqrt(a)/(sqrt(c)*x))/sqrt(a)","A",0
361,1,66,0,3.663661," ","integrate((B*x+A)/x**3/(c*x**2+a)**(1/2),x)","- \frac{A \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 a x} + \frac{A c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2 a^{\frac{3}{2}}} - \frac{B \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{a}"," ",0,"-A*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*a*x) + A*c*asinh(sqrt(a)/(sqrt(c)*x))/(2*a**(3/2)) - B*sqrt(c)*sqrt(a/(c*x**2) + 1)/a","A",0
362,1,97,0,3.789709," ","integrate((B*x+A)/x**4/(c*x**2+a)**(1/2),x)","- \frac{A \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a x^{2}} + \frac{2 A c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{2}} - \frac{B \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{2 a x} + \frac{B c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"-A*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*a*x**2) + 2*A*c**(3/2)*sqrt(a/(c*x**2) + 1)/(3*a**2) - B*sqrt(c)*sqrt(a/(c*x**2) + 1)/(2*a*x) + B*c*asinh(sqrt(a)/(sqrt(c)*x))/(2*a**(3/2))","A",0
363,1,153,0,5.714926," ","integrate((B*x+A)/x**5/(c*x**2+a)**(1/2),x)","- \frac{A}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{A \sqrt{c}}{8 a x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{3 A c^{\frac{3}{2}}}{8 a^{2} x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 A c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8 a^{\frac{5}{2}}} - \frac{B \sqrt{c} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a x^{2}} + \frac{2 B c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{2}}"," ",0,"-A/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) + A*sqrt(c)/(8*a*x**3*sqrt(a/(c*x**2) + 1)) + 3*A*c**(3/2)/(8*a**2*x*sqrt(a/(c*x**2) + 1)) - 3*A*c**2*asinh(sqrt(a)/(sqrt(c)*x))/(8*a**(5/2)) - B*sqrt(c)*sqrt(a/(c*x**2) + 1)/(3*a*x**2) + 2*B*c**(3/2)*sqrt(a/(c*x**2) + 1)/(3*a**2)","A",0
364,1,408,0,6.462854," ","integrate((B*x+A)/x**6/(c*x**2+a)**(1/2),x)","- \frac{3 A a^{4} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{5} c^{4} x^{4} + 30 a^{4} c^{5} x^{6} + 15 a^{3} c^{6} x^{8}} - \frac{2 A a^{3} c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{5} c^{4} x^{4} + 30 a^{4} c^{5} x^{6} + 15 a^{3} c^{6} x^{8}} - \frac{3 A a^{2} c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{5} c^{4} x^{4} + 30 a^{4} c^{5} x^{6} + 15 a^{3} c^{6} x^{8}} - \frac{12 A a c^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{5} c^{4} x^{4} + 30 a^{4} c^{5} x^{6} + 15 a^{3} c^{6} x^{8}} - \frac{8 A c^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{c x^{2}} + 1}}{15 a^{5} c^{4} x^{4} + 30 a^{4} c^{5} x^{6} + 15 a^{3} c^{6} x^{8}} - \frac{B}{4 \sqrt{c} x^{5} \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{B \sqrt{c}}{8 a x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{3 B c^{\frac{3}{2}}}{8 a^{2} x \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 B c^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{8 a^{\frac{5}{2}}}"," ",0,"-3*A*a**4*c**(9/2)*sqrt(a/(c*x**2) + 1)/(15*a**5*c**4*x**4 + 30*a**4*c**5*x**6 + 15*a**3*c**6*x**8) - 2*A*a**3*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(15*a**5*c**4*x**4 + 30*a**4*c**5*x**6 + 15*a**3*c**6*x**8) - 3*A*a**2*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(15*a**5*c**4*x**4 + 30*a**4*c**5*x**6 + 15*a**3*c**6*x**8) - 12*A*a*c**(15/2)*x**6*sqrt(a/(c*x**2) + 1)/(15*a**5*c**4*x**4 + 30*a**4*c**5*x**6 + 15*a**3*c**6*x**8) - 8*A*c**(17/2)*x**8*sqrt(a/(c*x**2) + 1)/(15*a**5*c**4*x**4 + 30*a**4*c**5*x**6 + 15*a**3*c**6*x**8) - B/(4*sqrt(c)*x**5*sqrt(a/(c*x**2) + 1)) + B*sqrt(c)/(8*a*x**3*sqrt(a/(c*x**2) + 1)) + 3*B*c**(3/2)/(8*a**2*x*sqrt(a/(c*x**2) + 1)) - 3*B*c**2*asinh(sqrt(a)/(sqrt(c)*x))/(8*a**(5/2))","B",0
365,1,144,0,12.306977," ","integrate(x**4*(B*x+A)/(c*x**2+a)**(3/2),x)","A \left(\frac{3 \sqrt{a} x}{2 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{5}{2}}} + \frac{x^{3}}{2 \sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{8 a^{2}}{3 c^{3} \sqrt{a + c x^{2}}} - \frac{4 a x^{2}}{3 c^{2} \sqrt{a + c x^{2}}} + \frac{x^{4}}{3 c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*(3*sqrt(a)*x/(2*c**2*sqrt(1 + c*x**2/a)) - 3*a*asinh(sqrt(c)*x/sqrt(a))/(2*c**(5/2)) + x**3/(2*sqrt(a)*c*sqrt(1 + c*x**2/a))) + B*Piecewise((-8*a**2/(3*c**3*sqrt(a + c*x**2)) - 4*a*x**2/(3*c**2*sqrt(a + c*x**2)) + x**4/(3*c*sqrt(a + c*x**2)), Ne(c, 0)), (x**6/(6*a**(3/2)), True))","A",0
366,1,117,0,10.926322," ","integrate(x**3*(B*x+A)/(c*x**2+a)**(3/2),x)","A \left(\begin{cases} \frac{2 a}{c^{2} \sqrt{a + c x^{2}}} + \frac{x^{2}}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + B \left(\frac{3 \sqrt{a} x}{2 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{5}{2}}} + \frac{x^{3}}{2 \sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right)"," ",0,"A*Piecewise((2*a/(c**2*sqrt(a + c*x**2)) + x**2/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**4/(4*a**(3/2)), True)) + B*(3*sqrt(a)*x/(2*c**2*sqrt(1 + c*x**2/a)) - 3*a*asinh(sqrt(c)*x/sqrt(a))/(2*c**(5/2)) + x**3/(2*sqrt(a)*c*sqrt(1 + c*x**2/a)))","A",0
367,1,83,0,8.869455," ","integrate(x**2*(B*x+A)/(c*x**2+a)**(3/2),x)","A \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} - \frac{x}{\sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} \frac{2 a}{c^{2} \sqrt{a + c x^{2}}} + \frac{x^{2}}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*(asinh(sqrt(c)*x/sqrt(a))/c**(3/2) - x/(sqrt(a)*c*sqrt(1 + c*x**2/a))) + B*Piecewise((2*a/(c**2*sqrt(a + c*x**2)) + x**2/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**4/(4*a**(3/2)), True))","A",0
368,1,66,0,8.031289," ","integrate(x*(B*x+A)/(c*x**2+a)**(3/2),x)","A \left(\begin{cases} - \frac{1}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + B \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} - \frac{x}{\sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right)"," ",0,"A*Piecewise((-1/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(3/2)), True)) + B*(asinh(sqrt(c)*x/sqrt(a))/c**(3/2) - x/(sqrt(a)*c*sqrt(1 + c*x**2/a)))","A",0
369,1,46,0,7.227184," ","integrate((B*x+A)/(c*x**2+a)**(3/2),x)","\frac{A x}{a^{\frac{3}{2}} \sqrt{1 + \frac{c x^{2}}{a}}} + B \left(\begin{cases} - \frac{1}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*x/(a**(3/2)*sqrt(1 + c*x**2/a)) + B*Piecewise((-1/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(3/2)), True))","A",0
370,1,206,0,9.567776," ","integrate((B*x+A)/x/(c*x**2+a)**(3/2),x)","A \left(\frac{2 a^{3} \sqrt{1 + \frac{c x^{2}}{a}}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} + \frac{a^{3} \log{\left(\frac{c x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} + \frac{a^{2} c x^{2} \log{\left(\frac{c x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} - \frac{2 a^{2} c x^{2} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}}\right) + \frac{B x}{a^{\frac{3}{2}} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*(2*a**3*sqrt(1 + c*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) + a**3*log(c*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) - 2*a**3*log(sqrt(1 + c*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) + a**2*c*x**2*log(c*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) - 2*a**2*c*x**2*log(sqrt(1 + c*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*c*x**2)) + B*x/(a**(3/2)*sqrt(1 + c*x**2/a))","B",0
371,1,235,0,13.929754," ","integrate((B*x+A)/x**2/(c*x**2+a)**(3/2),x)","A \left(- \frac{1}{a \sqrt{c} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{2 \sqrt{c}}{a^{2} \sqrt{\frac{a}{c x^{2}} + 1}}\right) + B \left(\frac{2 a^{3} \sqrt{1 + \frac{c x^{2}}{a}}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} + \frac{a^{3} \log{\left(\frac{c x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} + \frac{a^{2} c x^{2} \log{\left(\frac{c x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}} - \frac{2 a^{2} c x^{2} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} c x^{2}}\right)"," ",0,"A*(-1/(a*sqrt(c)*x**2*sqrt(a/(c*x**2) + 1)) - 2*sqrt(c)/(a**2*sqrt(a/(c*x**2) + 1))) + B*(2*a**3*sqrt(1 + c*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) + a**3*log(c*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) - 2*a**3*log(sqrt(1 + c*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) + a**2*c*x**2*log(c*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*c*x**2) - 2*a**2*c*x**2*log(sqrt(1 + c*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*c*x**2))","B",0
372,1,124,0,10.373977," ","integrate((B*x+A)/x**3/(c*x**2+a)**(3/2),x)","A \left(- \frac{1}{2 a \sqrt{c} x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 \sqrt{c}}{2 a^{2} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{3 c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2 a^{\frac{5}{2}}}\right) + B \left(- \frac{1}{a \sqrt{c} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{2 \sqrt{c}}{a^{2} \sqrt{\frac{a}{c x^{2}} + 1}}\right)"," ",0,"A*(-1/(2*a*sqrt(c)*x**3*sqrt(a/(c*x**2) + 1)) - 3*sqrt(c)/(2*a**2*x*sqrt(a/(c*x**2) + 1)) + 3*c*asinh(sqrt(a)/(sqrt(c)*x))/(2*a**(5/2))) + B*(-1/(a*sqrt(c)*x**2*sqrt(a/(c*x**2) + 1)) - 2*sqrt(c)/(a**2*sqrt(a/(c*x**2) + 1)))","A",0
373,1,311,0,28.082957," ","integrate((B*x+A)/x**4/(c*x**2+a)**(3/2),x)","A \left(- \frac{a^{3} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} x^{2} + 6 a^{4} c^{5} x^{4} + 3 a^{3} c^{6} x^{6}} + \frac{3 a^{2} c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} x^{2} + 6 a^{4} c^{5} x^{4} + 3 a^{3} c^{6} x^{6}} + \frac{12 a c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} x^{2} + 6 a^{4} c^{5} x^{4} + 3 a^{3} c^{6} x^{6}} + \frac{8 c^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} x^{2} + 6 a^{4} c^{5} x^{4} + 3 a^{3} c^{6} x^{6}}\right) + B \left(- \frac{1}{2 a \sqrt{c} x^{3} \sqrt{\frac{a}{c x^{2}} + 1}} - \frac{3 \sqrt{c}}{2 a^{2} x \sqrt{\frac{a}{c x^{2}} + 1}} + \frac{3 c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x} \right)}}{2 a^{\frac{5}{2}}}\right)"," ",0,"A*(-a**3*c**(9/2)*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4*x**2 + 6*a**4*c**5*x**4 + 3*a**3*c**6*x**6) + 3*a**2*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4*x**2 + 6*a**4*c**5*x**4 + 3*a**3*c**6*x**6) + 12*a*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4*x**2 + 6*a**4*c**5*x**4 + 3*a**3*c**6*x**6) + 8*c**(15/2)*x**6*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4*x**2 + 6*a**4*c**5*x**4 + 3*a**3*c**6*x**6)) + B*(-1/(2*a*sqrt(c)*x**3*sqrt(a/(c*x**2) + 1)) - 3*sqrt(c)/(2*a**2*x*sqrt(a/(c*x**2) + 1)) + 3*c*asinh(sqrt(a)/(sqrt(c)*x))/(2*a**(5/2)))","B",0
374,1,445,0,29.109002," ","integrate(x**4*(B*x+A)/(c*x**2+a)**(5/2),x)","A \left(\frac{3 a^{\frac{39}{2}} c^{11} \sqrt{1 + \frac{c x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{37}{2}} c^{12} x^{2} \sqrt{1 + \frac{c x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a^{19} c^{\frac{23}{2}} x}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{4 a^{18} c^{\frac{25}{2}} x^{3}}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} \frac{8 a^{2}}{3 a c^{3} \sqrt{a + c x^{2}} + 3 c^{4} x^{2} \sqrt{a + c x^{2}}} + \frac{12 a c x^{2}}{3 a c^{3} \sqrt{a + c x^{2}} + 3 c^{4} x^{2} \sqrt{a + c x^{2}}} + \frac{3 c^{2} x^{4}}{3 a c^{3} \sqrt{a + c x^{2}} + 3 c^{4} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{6}}{6 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*(3*a**(39/2)*c**11*sqrt(1 + c*x**2/a)*asinh(sqrt(c)*x/sqrt(a))/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)) + 3*a**(37/2)*c**12*x**2*sqrt(1 + c*x**2/a)*asinh(sqrt(c)*x/sqrt(a))/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)) - 3*a**19*c**(23/2)*x/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)) - 4*a**18*c**(25/2)*x**3/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a))) + B*Piecewise((8*a**2/(3*a*c**3*sqrt(a + c*x**2) + 3*c**4*x**2*sqrt(a + c*x**2)) + 12*a*c*x**2/(3*a*c**3*sqrt(a + c*x**2) + 3*c**4*x**2*sqrt(a + c*x**2)) + 3*c**2*x**4/(3*a*c**3*sqrt(a + c*x**2) + 3*c**4*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**6/(6*a**(5/2)), True))","B",0
375,1,400,0,15.979427," ","integrate(x**3*(B*x+A)/(c*x**2+a)**(5/2),x)","A \left(\begin{cases} - \frac{2 a}{3 a c^{2} \sqrt{a + c x^{2}} + 3 c^{3} x^{2} \sqrt{a + c x^{2}}} - \frac{3 c x^{2}}{3 a c^{2} \sqrt{a + c x^{2}} + 3 c^{3} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right) + B \left(\frac{3 a^{\frac{39}{2}} c^{11} \sqrt{1 + \frac{c x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{37}{2}} c^{12} x^{2} \sqrt{1 + \frac{c x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a^{19} c^{\frac{23}{2}} x}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{4 a^{18} c^{\frac{25}{2}} x^{3}}{3 a^{\frac{39}{2}} c^{\frac{27}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{37}{2}} c^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}\right)"," ",0,"A*Piecewise((-2*a/(3*a*c**2*sqrt(a + c*x**2) + 3*c**3*x**2*sqrt(a + c*x**2)) - 3*c*x**2/(3*a*c**2*sqrt(a + c*x**2) + 3*c**3*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**4/(4*a**(5/2)), True)) + B*(3*a**(39/2)*c**11*sqrt(1 + c*x**2/a)*asinh(sqrt(c)*x/sqrt(a))/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)) + 3*a**(37/2)*c**12*x**2*sqrt(1 + c*x**2/a)*asinh(sqrt(c)*x/sqrt(a))/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)) - 3*a**19*c**(23/2)*x/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)) - 4*a**18*c**(25/2)*x**3/(3*a**(39/2)*c**(27/2)*sqrt(1 + c*x**2/a) + 3*a**(37/2)*c**(29/2)*x**2*sqrt(1 + c*x**2/a)))","A",0
376,1,141,0,13.693384," ","integrate(x**2*(B*x+A)/(c*x**2+a)**(5/2),x)","\frac{A x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{3}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + B \left(\begin{cases} - \frac{2 a}{3 a c^{2} \sqrt{a + c x^{2}} + 3 c^{3} x^{2} \sqrt{a + c x^{2}}} - \frac{3 c x^{2}}{3 a c^{2} \sqrt{a + c x^{2}} + 3 c^{3} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*x**3/(3*a**(5/2)*sqrt(1 + c*x**2/a) + 3*a**(3/2)*c*x**2*sqrt(1 + c*x**2/a)) + B*Piecewise((-2*a/(3*a*c**2*sqrt(a + c*x**2) + 3*c**3*x**2*sqrt(a + c*x**2)) - 3*c*x**2/(3*a*c**2*sqrt(a + c*x**2) + 3*c**3*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**4/(4*a**(5/2)), True))","B",0
377,1,95,0,13.254703," ","integrate(x*(B*x+A)/(c*x**2+a)**(5/2),x)","A \left(\begin{cases} - \frac{1}{3 a c \sqrt{a + c x^{2}} + 3 c^{2} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right) + \frac{B x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{3}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*Piecewise((-1/(3*a*c*sqrt(a + c*x**2) + 3*c**2*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(5/2)), True)) + B*x**3/(3*a**(5/2)*sqrt(1 + c*x**2/a) + 3*a**(3/2)*c*x**2*sqrt(1 + c*x**2/a))","A",0
378,1,146,0,12.459969," ","integrate((B*x+A)/(c*x**2+a)**(5/2),x)","A \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{2 c x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{1}{3 a c \sqrt{a + c x^{2}} + 3 c^{2} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*(3*a*x/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a)) + 2*c*x**3/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a))) + B*Piecewise((-1/(3*a*c*sqrt(a + c*x**2) + 3*c**2*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(5/2)), True))","B",0
379,1,840,0,25.672087," ","integrate((B*x+A)/x/(c*x**2+a)**(5/2),x)","A \left(\frac{8 a^{7} \sqrt{1 + \frac{c x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{3 a^{7} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{6 a^{7} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{14 a^{6} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{9 a^{6} c x^{2} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{18 a^{6} c x^{2} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{6 a^{5} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{9 a^{5} c^{2} x^{4} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{18 a^{5} c^{2} x^{4} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{3 a^{4} c^{3} x^{6} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{6 a^{4} c^{3} x^{6} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}}\right) + B \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{2 c x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}\right)"," ",0,"A*(8*a**7*sqrt(1 + c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 3*a**7*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 6*a**7*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 14*a**6*c*x**2*sqrt(1 + c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 9*a**6*c*x**2*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 18*a**6*c*x**2*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 6*a**5*c**2*x**4*sqrt(1 + c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 9*a**5*c**2*x**4*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 18*a**5*c**2*x**4*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 3*a**4*c**3*x**6*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 6*a**4*c**3*x**6*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6)) + B*(3*a*x/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a)) + 2*c*x**3/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a)))","B",0
380,1,910,0,22.255192," ","integrate((B*x+A)/x**2/(c*x**2+a)**(5/2),x)","A \left(- \frac{3 a^{2} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} + 6 a^{4} c^{5} x^{2} + 3 a^{3} c^{6} x^{4}} - \frac{12 a c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} + 6 a^{4} c^{5} x^{2} + 3 a^{3} c^{6} x^{4}} - \frac{8 c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} + 6 a^{4} c^{5} x^{2} + 3 a^{3} c^{6} x^{4}}\right) + B \left(\frac{8 a^{7} \sqrt{1 + \frac{c x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{3 a^{7} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{6 a^{7} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{14 a^{6} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{9 a^{6} c x^{2} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{18 a^{6} c x^{2} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{6 a^{5} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{9 a^{5} c^{2} x^{4} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{18 a^{5} c^{2} x^{4} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} + \frac{3 a^{4} c^{3} x^{6} \log{\left(\frac{c x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}} - \frac{6 a^{4} c^{3} x^{6} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} c x^{2} + 18 a^{\frac{15}{2}} c^{2} x^{4} + 6 a^{\frac{13}{2}} c^{3} x^{6}}\right)"," ",0,"A*(-3*a**2*c**(9/2)*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4 + 6*a**4*c**5*x**2 + 3*a**3*c**6*x**4) - 12*a*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4 + 6*a**4*c**5*x**2 + 3*a**3*c**6*x**4) - 8*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4 + 6*a**4*c**5*x**2 + 3*a**3*c**6*x**4)) + B*(8*a**7*sqrt(1 + c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 3*a**7*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 6*a**7*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 14*a**6*c*x**2*sqrt(1 + c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 9*a**6*c*x**2*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 18*a**6*c*x**2*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 6*a**5*c**2*x**4*sqrt(1 + c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 9*a**5*c**2*x**4*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 18*a**5*c**2*x**4*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) + 3*a**4*c**3*x**6*log(c*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6) - 6*a**4*c**3*x**6*log(sqrt(1 + c*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*c*x**2 + 18*a**(15/2)*c**2*x**4 + 6*a**(13/2)*c**3*x**6))","B",0
381,1,1034,0,22.821593," ","integrate((B*x+A)/x**3/(c*x**2+a)**(5/2),x)","A \left(- \frac{6 a^{17} \sqrt{1 + \frac{c x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{46 a^{16} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{15 a^{16} c x^{2} \log{\left(\frac{c x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} + \frac{30 a^{16} c x^{2} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{70 a^{15} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{45 a^{15} c^{2} x^{4} \log{\left(\frac{c x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} + \frac{90 a^{15} c^{2} x^{4} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{30 a^{14} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{45 a^{14} c^{3} x^{6} \log{\left(\frac{c x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} + \frac{90 a^{14} c^{3} x^{6} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} - \frac{15 a^{13} c^{4} x^{8} \log{\left(\frac{c x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}} + \frac{30 a^{13} c^{4} x^{8} \log{\left(\sqrt{1 + \frac{c x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} c x^{4} + 36 a^{\frac{35}{2}} c^{2} x^{6} + 12 a^{\frac{33}{2}} c^{3} x^{8}}\right) + B \left(- \frac{3 a^{2} c^{\frac{9}{2}} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} + 6 a^{4} c^{5} x^{2} + 3 a^{3} c^{6} x^{4}} - \frac{12 a c^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} + 6 a^{4} c^{5} x^{2} + 3 a^{3} c^{6} x^{4}} - \frac{8 c^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{c x^{2}} + 1}}{3 a^{5} c^{4} + 6 a^{4} c^{5} x^{2} + 3 a^{3} c^{6} x^{4}}\right)"," ",0,"A*(-6*a**17*sqrt(1 + c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 46*a**16*c*x**2*sqrt(1 + c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 15*a**16*c*x**2*log(c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) + 30*a**16*c*x**2*log(sqrt(1 + c*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 70*a**15*c**2*x**4*sqrt(1 + c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 45*a**15*c**2*x**4*log(c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) + 90*a**15*c**2*x**4*log(sqrt(1 + c*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 30*a**14*c**3*x**6*sqrt(1 + c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 45*a**14*c**3*x**6*log(c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) + 90*a**14*c**3*x**6*log(sqrt(1 + c*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) - 15*a**13*c**4*x**8*log(c*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8) + 30*a**13*c**4*x**8*log(sqrt(1 + c*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*c*x**4 + 36*a**(35/2)*c**2*x**6 + 12*a**(33/2)*c**3*x**8)) + B*(-3*a**2*c**(9/2)*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4 + 6*a**4*c**5*x**2 + 3*a**3*c**6*x**4) - 12*a*c**(11/2)*x**2*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4 + 6*a**4*c**5*x**2 + 3*a**3*c**6*x**4) - 8*c**(13/2)*x**4*sqrt(a/(c*x**2) + 1)/(3*a**5*c**4 + 6*a**4*c**5*x**2 + 3*a**3*c**6*x**4))","B",0
382,1,486,0,23.374042," ","integrate((e*x+d)/(c*x**2+a)**(7/2),x)","d \left(\frac{15 a^{5} x}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 a^{4} c x^{3}}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{28 a^{3} c^{2} x^{5}}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{8 a^{2} c^{3} x^{7}}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + e \left(\begin{cases} - \frac{1}{5 a^{2} c \sqrt{a + c x^{2}} + 10 a c^{2} x^{2} \sqrt{a + c x^{2}} + 5 c^{3} x^{4} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*(15*a**5*x/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a)) + 35*a**4*c*x**3/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a)) + 28*a**3*c**2*x**5/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a)) + 8*a**2*c**3*x**7/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a))) + e*Piecewise((-1/(5*a**2*c*sqrt(a + c*x**2) + 10*a*c**2*x**2*sqrt(a + c*x**2) + 5*c**3*x**4*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(7/2)), True))","B",0
383,1,1360,0,39.861132," ","integrate((e*x+d)/(c*x**2+a)**(9/2),x)","d \left(\frac{35 a^{14} x}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{175 a^{13} c x^{3}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{371 a^{12} c^{2} x^{5}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{429 a^{11} c^{3} x^{7}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{286 a^{10} c^{4} x^{9}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{104 a^{9} c^{5} x^{11}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{16 a^{8} c^{6} x^{13}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + e \left(\begin{cases} - \frac{1}{7 a^{3} c \sqrt{a + c x^{2}} + 21 a^{2} c^{2} x^{2} \sqrt{a + c x^{2}} + 21 a c^{3} x^{4} \sqrt{a + c x^{2}} + 7 c^{4} x^{6} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*(35*a**14*x/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 175*a**13*c*x**3/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 371*a**12*c**2*x**5/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 429*a**11*c**3*x**7/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 286*a**10*c**4*x**9/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 104*a**9*c**5*x**11/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 16*a**8*c**6*x**13/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a))) + e*Piecewise((-1/(7*a**3*c*sqrt(a + c*x**2) + 21*a**2*c**2*x**2*sqrt(a + c*x**2) + 21*a*c**3*x**4*sqrt(a + c*x**2) + 7*c**4*x**6*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(9/2)), True))","B",0
384,1,46,0,8.222719," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+a),x)","\frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A c x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{11}{2}}}{11} + \frac{2 B c x^{\frac{15}{2}}}{15}"," ",0,"2*A*a*x**(9/2)/9 + 2*A*c*x**(13/2)/13 + 2*B*a*x**(11/2)/11 + 2*B*c*x**(15/2)/15","A",0
385,1,46,0,3.764259," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+a),x)","\frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A c x^{\frac{11}{2}}}{11} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{13}{2}}}{13}"," ",0,"2*A*a*x**(7/2)/7 + 2*A*c*x**(11/2)/11 + 2*B*a*x**(9/2)/9 + 2*B*c*x**(13/2)/13","A",0
386,1,46,0,1.656977," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+a),x)","\frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 A c x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{7}{2}}}{7} + \frac{2 B c x^{\frac{11}{2}}}{11}"," ",0,"2*A*a*x**(5/2)/5 + 2*A*c*x**(9/2)/9 + 2*B*a*x**(7/2)/7 + 2*B*c*x**(11/2)/11","A",0
387,1,46,0,2.383036," ","integrate((B*x+A)*(c*x**2+a)*x**(1/2),x)","\frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 A c x^{\frac{7}{2}}}{7} + \frac{2 B a x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{9}{2}}}{9}"," ",0,"2*A*a*x**(3/2)/3 + 2*A*c*x**(7/2)/7 + 2*B*a*x**(5/2)/5 + 2*B*c*x**(9/2)/9","A",0
388,1,44,0,0.451379," ","integrate((B*x+A)*(c*x**2+a)/x**(1/2),x)","2 A a \sqrt{x} + \frac{2 A c x^{\frac{5}{2}}}{5} + \frac{2 B a x^{\frac{3}{2}}}{3} + \frac{2 B c x^{\frac{7}{2}}}{7}"," ",0,"2*A*a*sqrt(x) + 2*A*c*x**(5/2)/5 + 2*B*a*x**(3/2)/3 + 2*B*c*x**(7/2)/7","A",0
389,1,42,0,0.621986," ","integrate((B*x+A)*(c*x**2+a)/x**(3/2),x)","- \frac{2 A a}{\sqrt{x}} + \frac{2 A c x^{\frac{3}{2}}}{3} + 2 B a \sqrt{x} + \frac{2 B c x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a/sqrt(x) + 2*A*c*x**(3/2)/3 + 2*B*a*sqrt(x) + 2*B*c*x**(5/2)/5","A",0
390,1,42,0,0.845803," ","integrate((B*x+A)*(c*x**2+a)/x**(5/2),x)","- \frac{2 A a}{3 x^{\frac{3}{2}}} + 2 A c \sqrt{x} - \frac{2 B a}{\sqrt{x}} + \frac{2 B c x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a/(3*x**(3/2)) + 2*A*c*sqrt(x) - 2*B*a/sqrt(x) + 2*B*c*x**(3/2)/3","A",0
391,1,42,0,1.440947," ","integrate((B*x+A)*(c*x**2+a)/x**(7/2),x)","- \frac{2 A a}{5 x^{\frac{5}{2}}} - \frac{2 A c}{\sqrt{x}} - \frac{2 B a}{3 x^{\frac{3}{2}}} + 2 B c \sqrt{x}"," ",0,"-2*A*a/(5*x**(5/2)) - 2*A*c/sqrt(x) - 2*B*a/(3*x**(3/2)) + 2*B*c*sqrt(x)","A",0
392,1,46,0,3.155036," ","integrate((B*x+A)*(c*x**2+a)/x**(9/2),x)","- \frac{2 A a}{7 x^{\frac{7}{2}}} - \frac{2 A c}{3 x^{\frac{3}{2}}} - \frac{2 B a}{5 x^{\frac{5}{2}}} - \frac{2 B c}{\sqrt{x}}"," ",0,"-2*A*a/(7*x**(7/2)) - 2*A*c/(3*x**(3/2)) - 2*B*a/(5*x**(5/2)) - 2*B*c/sqrt(x)","A",0
393,1,80,0,16.122200," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+a)**2,x)","\frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a c x^{\frac{13}{2}}}{13} + \frac{2 A c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a c x^{\frac{15}{2}}}{15} + \frac{2 B c^{2} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**2*x**(9/2)/9 + 4*A*a*c*x**(13/2)/13 + 2*A*c**2*x**(17/2)/17 + 2*B*a**2*x**(11/2)/11 + 4*B*a*c*x**(15/2)/15 + 2*B*c**2*x**(19/2)/19","A",0
394,1,80,0,8.498378," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+a)**2,x)","\frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{4 A a c x^{\frac{11}{2}}}{11} + \frac{2 A c^{2} x^{\frac{15}{2}}}{15} + \frac{2 B a^{2} x^{\frac{9}{2}}}{9} + \frac{4 B a c x^{\frac{13}{2}}}{13} + \frac{2 B c^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*A*a**2*x**(7/2)/7 + 4*A*a*c*x**(11/2)/11 + 2*A*c**2*x**(15/2)/15 + 2*B*a**2*x**(9/2)/9 + 4*B*a*c*x**(13/2)/13 + 2*B*c**2*x**(17/2)/17","A",0
395,1,80,0,4.263692," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+a)**2,x)","\frac{2 A a^{2} x^{\frac{5}{2}}}{5} + \frac{4 A a c x^{\frac{9}{2}}}{9} + \frac{2 A c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} x^{\frac{7}{2}}}{7} + \frac{4 B a c x^{\frac{11}{2}}}{11} + \frac{2 B c^{2} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**2*x**(5/2)/5 + 4*A*a*c*x**(9/2)/9 + 2*A*c**2*x**(13/2)/13 + 2*B*a**2*x**(7/2)/7 + 4*B*a*c*x**(11/2)/11 + 2*B*c**2*x**(15/2)/15","A",0
396,1,80,0,3.076880," ","integrate((B*x+A)*(c*x**2+a)**2*x**(1/2),x)","\frac{2 A a^{2} x^{\frac{3}{2}}}{3} + \frac{4 A a c x^{\frac{7}{2}}}{7} + \frac{2 A c^{2} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} x^{\frac{5}{2}}}{5} + \frac{4 B a c x^{\frac{9}{2}}}{9} + \frac{2 B c^{2} x^{\frac{13}{2}}}{13}"," ",0,"2*A*a**2*x**(3/2)/3 + 4*A*a*c*x**(7/2)/7 + 2*A*c**2*x**(11/2)/11 + 2*B*a**2*x**(5/2)/5 + 4*B*a*c*x**(9/2)/9 + 2*B*c**2*x**(13/2)/13","A",0
397,1,78,0,1.442503," ","integrate((B*x+A)*(c*x**2+a)**2/x**(1/2),x)","2 A a^{2} \sqrt{x} + \frac{4 A a c x^{\frac{5}{2}}}{5} + \frac{2 A c^{2} x^{\frac{9}{2}}}{9} + \frac{2 B a^{2} x^{\frac{3}{2}}}{3} + \frac{4 B a c x^{\frac{7}{2}}}{7} + \frac{2 B c^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*A*a**2*sqrt(x) + 4*A*a*c*x**(5/2)/5 + 2*A*c**2*x**(9/2)/9 + 2*B*a**2*x**(3/2)/3 + 4*B*a*c*x**(7/2)/7 + 2*B*c**2*x**(11/2)/11","A",0
398,1,76,0,1.678110," ","integrate((B*x+A)*(c*x**2+a)**2/x**(3/2),x)","- \frac{2 A a^{2}}{\sqrt{x}} + \frac{4 A a c x^{\frac{3}{2}}}{3} + \frac{2 A c^{2} x^{\frac{7}{2}}}{7} + 2 B a^{2} \sqrt{x} + \frac{4 B a c x^{\frac{5}{2}}}{5} + \frac{2 B c^{2} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**2/sqrt(x) + 4*A*a*c*x**(3/2)/3 + 2*A*c**2*x**(7/2)/7 + 2*B*a**2*sqrt(x) + 4*B*a*c*x**(5/2)/5 + 2*B*c**2*x**(9/2)/9","A",0
399,1,76,0,2.119782," ","integrate((B*x+A)*(c*x**2+a)**2/x**(5/2),x)","- \frac{2 A a^{2}}{3 x^{\frac{3}{2}}} + 4 A a c \sqrt{x} + \frac{2 A c^{2} x^{\frac{5}{2}}}{5} - \frac{2 B a^{2}}{\sqrt{x}} + \frac{4 B a c x^{\frac{3}{2}}}{3} + \frac{2 B c^{2} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**2/(3*x**(3/2)) + 4*A*a*c*sqrt(x) + 2*A*c**2*x**(5/2)/5 - 2*B*a**2/sqrt(x) + 4*B*a*c*x**(3/2)/3 + 2*B*c**2*x**(7/2)/7","A",0
400,1,76,0,2.903181," ","integrate((B*x+A)*(c*x**2+a)**2/x**(7/2),x)","- \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a c}{\sqrt{x}} + \frac{2 A c^{2} x^{\frac{3}{2}}}{3} - \frac{2 B a^{2}}{3 x^{\frac{3}{2}}} + 4 B a c \sqrt{x} + \frac{2 B c^{2} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**2/(5*x**(5/2)) - 4*A*a*c/sqrt(x) + 2*A*c**2*x**(3/2)/3 - 2*B*a**2/(3*x**(3/2)) + 4*B*a*c*sqrt(x) + 2*B*c**2*x**(5/2)/5","A",0
401,1,76,0,4.020569," ","integrate((B*x+A)*(c*x**2+a)**2/x**(9/2),x)","- \frac{2 A a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 A a c}{3 x^{\frac{3}{2}}} + 2 A c^{2} \sqrt{x} - \frac{2 B a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 B a c}{\sqrt{x}} + \frac{2 B c^{2} x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a**2/(7*x**(7/2)) - 4*A*a*c/(3*x**(3/2)) + 2*A*c**2*sqrt(x) - 2*B*a**2/(5*x**(5/2)) - 4*B*a*c/sqrt(x) + 2*B*c**2*x**(3/2)/3","A",0
402,1,114,0,27.935706," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+a)**3,x)","\frac{2 A a^{3} x^{\frac{9}{2}}}{9} + \frac{6 A a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 A a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A c^{3} x^{\frac{21}{2}}}{21} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} c x^{\frac{15}{2}}}{5} + \frac{6 B a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B c^{3} x^{\frac{23}{2}}}{23}"," ",0,"2*A*a**3*x**(9/2)/9 + 6*A*a**2*c*x**(13/2)/13 + 6*A*a*c**2*x**(17/2)/17 + 2*A*c**3*x**(21/2)/21 + 2*B*a**3*x**(11/2)/11 + 2*B*a**2*c*x**(15/2)/5 + 6*B*a*c**2*x**(19/2)/19 + 2*B*c**3*x**(23/2)/23","A",0
403,1,114,0,16.450930," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+a)**3,x)","\frac{2 A a^{3} x^{\frac{7}{2}}}{7} + \frac{6 A a^{2} c x^{\frac{11}{2}}}{11} + \frac{2 A a c^{2} x^{\frac{15}{2}}}{5} + \frac{2 A c^{3} x^{\frac{19}{2}}}{19} + \frac{2 B a^{3} x^{\frac{9}{2}}}{9} + \frac{6 B a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 B a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B c^{3} x^{\frac{21}{2}}}{21}"," ",0,"2*A*a**3*x**(7/2)/7 + 6*A*a**2*c*x**(11/2)/11 + 2*A*a*c**2*x**(15/2)/5 + 2*A*c**3*x**(19/2)/19 + 2*B*a**3*x**(9/2)/9 + 6*B*a**2*c*x**(13/2)/13 + 6*B*a*c**2*x**(17/2)/17 + 2*B*c**3*x**(21/2)/21","A",0
404,1,114,0,9.819848," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+a)**3,x)","\frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{2 A a^{2} c x^{\frac{9}{2}}}{3} + \frac{6 A a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 A c^{3} x^{\frac{17}{2}}}{17} + \frac{2 B a^{3} x^{\frac{7}{2}}}{7} + \frac{6 B a^{2} c x^{\frac{11}{2}}}{11} + \frac{2 B a c^{2} x^{\frac{15}{2}}}{5} + \frac{2 B c^{3} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**3*x**(5/2)/5 + 2*A*a**2*c*x**(9/2)/3 + 6*A*a*c**2*x**(13/2)/13 + 2*A*c**3*x**(17/2)/17 + 2*B*a**3*x**(7/2)/7 + 6*B*a**2*c*x**(11/2)/11 + 2*B*a*c**2*x**(15/2)/5 + 2*B*c**3*x**(19/2)/19","A",0
405,1,114,0,4.414875," ","integrate((B*x+A)*(c*x**2+a)**3*x**(1/2),x)","\frac{2 A a^{3} x^{\frac{3}{2}}}{3} + \frac{6 A a^{2} c x^{\frac{7}{2}}}{7} + \frac{6 A a c^{2} x^{\frac{11}{2}}}{11} + \frac{2 A c^{3} x^{\frac{15}{2}}}{15} + \frac{2 B a^{3} x^{\frac{5}{2}}}{5} + \frac{2 B a^{2} c x^{\frac{9}{2}}}{3} + \frac{6 B a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B c^{3} x^{\frac{17}{2}}}{17}"," ",0,"2*A*a**3*x**(3/2)/3 + 6*A*a**2*c*x**(7/2)/7 + 6*A*a*c**2*x**(11/2)/11 + 2*A*c**3*x**(15/2)/15 + 2*B*a**3*x**(5/2)/5 + 2*B*a**2*c*x**(9/2)/3 + 6*B*a*c**2*x**(13/2)/13 + 2*B*c**3*x**(17/2)/17","A",0
406,1,112,0,3.874381," ","integrate((B*x+A)*(c*x**2+a)**3/x**(1/2),x)","2 A a^{3} \sqrt{x} + \frac{6 A a^{2} c x^{\frac{5}{2}}}{5} + \frac{2 A a c^{2} x^{\frac{9}{2}}}{3} + \frac{2 A c^{3} x^{\frac{13}{2}}}{13} + \frac{2 B a^{3} x^{\frac{3}{2}}}{3} + \frac{6 B a^{2} c x^{\frac{7}{2}}}{7} + \frac{6 B a c^{2} x^{\frac{11}{2}}}{11} + \frac{2 B c^{3} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**3*sqrt(x) + 6*A*a**2*c*x**(5/2)/5 + 2*A*a*c**2*x**(9/2)/3 + 2*A*c**3*x**(13/2)/13 + 2*B*a**3*x**(3/2)/3 + 6*B*a**2*c*x**(7/2)/7 + 6*B*a*c**2*x**(11/2)/11 + 2*B*c**3*x**(15/2)/15","A",0
407,1,109,0,4.259676," ","integrate((B*x+A)*(c*x**2+a)**3/x**(3/2),x)","- \frac{2 A a^{3}}{\sqrt{x}} + 2 A a^{2} c x^{\frac{3}{2}} + \frac{6 A a c^{2} x^{\frac{7}{2}}}{7} + \frac{2 A c^{3} x^{\frac{11}{2}}}{11} + 2 B a^{3} \sqrt{x} + \frac{6 B a^{2} c x^{\frac{5}{2}}}{5} + \frac{2 B a c^{2} x^{\frac{9}{2}}}{3} + \frac{2 B c^{3} x^{\frac{13}{2}}}{13}"," ",0,"-2*A*a**3/sqrt(x) + 2*A*a**2*c*x**(3/2) + 6*A*a*c**2*x**(7/2)/7 + 2*A*c**3*x**(11/2)/11 + 2*B*a**3*sqrt(x) + 6*B*a**2*c*x**(5/2)/5 + 2*B*a*c**2*x**(9/2)/3 + 2*B*c**3*x**(13/2)/13","A",0
408,1,109,0,4.833692," ","integrate((B*x+A)*(c*x**2+a)**3/x**(5/2),x)","- \frac{2 A a^{3}}{3 x^{\frac{3}{2}}} + 6 A a^{2} c \sqrt{x} + \frac{6 A a c^{2} x^{\frac{5}{2}}}{5} + \frac{2 A c^{3} x^{\frac{9}{2}}}{9} - \frac{2 B a^{3}}{\sqrt{x}} + 2 B a^{2} c x^{\frac{3}{2}} + \frac{6 B a c^{2} x^{\frac{7}{2}}}{7} + \frac{2 B c^{3} x^{\frac{11}{2}}}{11}"," ",0,"-2*A*a**3/(3*x**(3/2)) + 6*A*a**2*c*sqrt(x) + 6*A*a*c**2*x**(5/2)/5 + 2*A*c**3*x**(9/2)/9 - 2*B*a**3/sqrt(x) + 2*B*a**2*c*x**(3/2) + 6*B*a*c**2*x**(7/2)/7 + 2*B*c**3*x**(11/2)/11","A",0
409,1,109,0,6.485914," ","integrate((B*x+A)*(c*x**2+a)**3/x**(7/2),x)","- \frac{2 A a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 A a^{2} c}{\sqrt{x}} + 2 A a c^{2} x^{\frac{3}{2}} + \frac{2 A c^{3} x^{\frac{7}{2}}}{7} - \frac{2 B a^{3}}{3 x^{\frac{3}{2}}} + 6 B a^{2} c \sqrt{x} + \frac{6 B a c^{2} x^{\frac{5}{2}}}{5} + \frac{2 B c^{3} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**3/(5*x**(5/2)) - 6*A*a**2*c/sqrt(x) + 2*A*a*c**2*x**(3/2) + 2*A*c**3*x**(7/2)/7 - 2*B*a**3/(3*x**(3/2)) + 6*B*a**2*c*sqrt(x) + 6*B*a*c**2*x**(5/2)/5 + 2*B*c**3*x**(9/2)/9","A",0
410,1,107,0,8.606741," ","integrate((B*x+A)*(c*x**2+a)**3/x**(9/2),x)","- \frac{2 A a^{3}}{7 x^{\frac{7}{2}}} - \frac{2 A a^{2} c}{x^{\frac{3}{2}}} + 6 A a c^{2} \sqrt{x} + \frac{2 A c^{3} x^{\frac{5}{2}}}{5} - \frac{2 B a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 B a^{2} c}{\sqrt{x}} + 2 B a c^{2} x^{\frac{3}{2}} + \frac{2 B c^{3} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**3/(7*x**(7/2)) - 2*A*a**2*c/x**(3/2) + 6*A*a*c**2*sqrt(x) + 2*A*c**3*x**(5/2)/5 - 2*B*a**3/(5*x**(5/2)) - 6*B*a**2*c/sqrt(x) + 2*B*a*c**2*x**(3/2) + 2*B*c**3*x**(7/2)/7","A",0
411,1,109,0,11.241803," ","integrate((B*x+A)*(c*x**2+a)**3/x**(11/2),x)","- \frac{2 A a^{3}}{9 x^{\frac{9}{2}}} - \frac{6 A a^{2} c}{5 x^{\frac{5}{2}}} - \frac{6 A a c^{2}}{\sqrt{x}} + \frac{2 A c^{3} x^{\frac{3}{2}}}{3} - \frac{2 B a^{3}}{7 x^{\frac{7}{2}}} - \frac{2 B a^{2} c}{x^{\frac{3}{2}}} + 6 B a c^{2} \sqrt{x} + \frac{2 B c^{3} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**3/(9*x**(9/2)) - 6*A*a**2*c/(5*x**(5/2)) - 6*A*a*c**2/sqrt(x) + 2*A*c**3*x**(3/2)/3 - 2*B*a**3/(7*x**(7/2)) - 2*B*a**2*c/x**(3/2) + 6*B*a*c**2*sqrt(x) + 2*B*c**3*x**(5/2)/5","A",0
412,1,403,0,33.964342," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{\frac{2 A x^{\frac{7}{2}}}{7} + \frac{2 B x^{\frac{9}{2}}}{9}}{a} & \text{for}\: c = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{c} & \text{for}\: a = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{c^{2} \sqrt[4]{\frac{1}{c}}} + \frac{2 A x^{\frac{3}{2}}}{3 c} - \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2}} + \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2}} - \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{c^{2}} - \frac{2 B a \sqrt{x}}{c^{2}} + \frac{2 B x^{\frac{5}{2}}}{5 c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*x**(3/2)/3 + 2*B*x**(5/2)/5), Eq(a, 0) & Eq(c, 0)), ((2*A*x**(7/2)/7 + 2*B*x**(9/2)/9)/a, Eq(c, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/c, Eq(a, 0)), ((-1)**(3/4)*A*a**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2*(1/c)**(1/4)) - (-1)**(3/4)*A*a**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2*(1/c)**(1/4)) - (-1)**(3/4)*A*a**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(c**2*(1/c)**(1/4)) + 2*A*x**(3/2)/(3*c) - (-1)**(1/4)*B*a**(5/4)*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2) + (-1)**(1/4)*B*a**(5/4)*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2) - (-1)**(1/4)*B*a**(5/4)*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/c**2 - 2*B*a*sqrt(x)/c**2 + 2*B*x**(5/2)/(5*c), True))","A",0
413,1,379,0,10.060075," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}}{a} & \text{for}\: c = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{c} & \text{for}\: a = 0 \\\frac{\sqrt[4]{-1} A \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c} - \frac{\sqrt[4]{-1} A \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c} + \frac{\sqrt[4]{-1} A \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{c} + \frac{2 A \sqrt{x}}{c} + \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{c^{2} \sqrt[4]{\frac{1}{c}}} + \frac{2 B x^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*sqrt(x) + 2*B*x**(3/2)/3), Eq(a, 0) & Eq(c, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(7/2)/7)/a, Eq(c, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/c, Eq(a, 0)), ((-1)**(1/4)*A*a**(1/4)*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c) - (-1)**(1/4)*A*a**(1/4)*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c) + (-1)**(1/4)*A*a**(1/4)*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/c + 2*A*sqrt(x)/c + (-1)**(3/4)*B*a**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2*(1/c)**(1/4)) - (-1)**(3/4)*B*a**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2*(1/c)**(1/4)) - (-1)**(3/4)*B*a**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(c**2*(1/c)**(1/4)) + 2*B*x**(3/2)/(3*c), True))","A",0
414,1,359,0,6.480517," ","integrate(x**(1/2)*(B*x+A)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{c} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{a} & \text{for}\: c = 0 \\- \frac{\left(-1\right)^{\frac{3}{4}} A \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} c \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} A \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} c \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} A \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{\sqrt[4]{a} c \sqrt[4]{\frac{1}{c}}} + \frac{\sqrt[4]{-1} B \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c} - \frac{\sqrt[4]{-1} B \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c} + \frac{\sqrt[4]{-1} B \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{c} + \frac{2 B \sqrt{x}}{c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*sqrt(x)), Eq(a, 0) & Eq(c, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/c, Eq(a, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/a, Eq(c, 0)), (-(-1)**(3/4)*A*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(1/4)*c*(1/c)**(1/4)) + (-1)**(3/4)*A*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(1/4)*c*(1/c)**(1/4)) + (-1)**(3/4)*A*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(a**(1/4)*c*(1/c)**(1/4)) + (-1)**(1/4)*B*a**(1/4)*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c) - (-1)**(1/4)*B*a**(1/4)*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c) + (-1)**(1/4)*B*a**(1/4)*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/c + 2*B*sqrt(x)/c, True))","A",0
415,1,348,0,7.034116," ","integrate((B*x+A)/x**(1/2)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{c} & \text{for}\: a = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{a} & \text{for}\: c = 0 \\- \frac{\sqrt[4]{-1} A \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} A \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} A \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{3}{4}}} - \frac{\left(-1\right)^{\frac{3}{4}} B \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} c \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} B \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} c \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} B \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{\sqrt[4]{a} c \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) - 2*B/sqrt(x)), Eq(a, 0) & Eq(c, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/c, Eq(a, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/a, Eq(c, 0)), (-(-1)**(1/4)*A*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(3/4)) + (-1)**(1/4)*A*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(3/4)) - (-1)**(1/4)*A*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/a**(3/4) - (-1)**(3/4)*B*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(1/4)*c*(1/c)**(1/4)) + (-1)**(3/4)*B*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(1/4)*c*(1/c)**(1/4)) + (-1)**(3/4)*B*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(a**(1/4)*c*(1/c)**(1/4)), True))","A",0
416,1,355,0,14.432745," ","integrate((B*x+A)/x**(3/2)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{c} & \text{for}\: a = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{a} & \text{for}\: c = 0 \\- \frac{2 A}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} A \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} A \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} A \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\sqrt[4]{-1} B \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} B \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} B \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2))), Eq(a, 0) & Eq(c, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/c, Eq(a, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/a, Eq(c, 0)), (-2*A/(a*sqrt(x)) + (-1)**(3/4)*A*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/c)**(1/4)) - (-1)**(3/4)*A*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/c)**(1/4)) - (-1)**(3/4)*A*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(a**(5/4)*(1/c)**(1/4)) - (-1)**(1/4)*B*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(3/4)) + (-1)**(1/4)*B*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(3/4)) - (-1)**(1/4)*B*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/a**(3/4), True))","A",0
417,1,376,0,34.450880," ","integrate((B*x+A)/x**(5/2)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{a} & \text{for}\: c = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{c} & \text{for}\: a = 0 \\- \frac{2 A}{3 a x^{\frac{3}{2}}} + \frac{\sqrt[4]{-1} A c \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} A c \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} A c \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{7}{4}}} - \frac{2 B}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} B \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} B \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} B \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2))), Eq(a, 0) & Eq(c, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/a, Eq(c, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/c, Eq(a, 0)), (-2*A/(3*a*x**(3/2)) + (-1)**(1/4)*A*c*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(7/4)) - (-1)**(1/4)*A*c*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(7/4)) + (-1)**(1/4)*A*c*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/a**(7/4) - 2*B/(a*sqrt(x)) + (-1)**(3/4)*B*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/c)**(1/4)) - (-1)**(3/4)*B*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/c)**(1/4)) - (-1)**(3/4)*B*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(a**(5/4)*(1/c)**(1/4)), True))","A",0
418,1,398,0,108.650433," ","integrate((B*x+A)/x**(7/2)/(c*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{a} & \text{for}\: c = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{c} & \text{for}\: a = 0 \\- \frac{2 A}{5 a x^{\frac{5}{2}}} + \frac{2 A c}{a^{2} \sqrt{x}} - \frac{\left(-1\right)^{\frac{3}{4}} A c \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{9}{4}} \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} A c \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{9}{4}} \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} A c \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{9}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{2 B}{3 a x^{\frac{3}{2}}} + \frac{\sqrt[4]{-1} B c \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} B c \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} B c \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{a^{\frac{7}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(a, 0) & Eq(c, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/a, Eq(c, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/c, Eq(a, 0)), (-2*A/(5*a*x**(5/2)) + 2*A*c/(a**2*sqrt(x)) - (-1)**(3/4)*A*c*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(9/4)*(1/c)**(1/4)) + (-1)**(3/4)*A*c*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(9/4)*(1/c)**(1/4)) + (-1)**(3/4)*A*c*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(a**(9/4)*(1/c)**(1/4)) - 2*B/(3*a*x**(3/2)) + (-1)**(1/4)*B*c*(1/c)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(7/4)) - (-1)**(1/4)*B*c*(1/c)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*a**(7/4)) + (-1)**(1/4)*B*c*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/a**(7/4), True))","A",0
419,-1,0,0,0.000000," ","integrate((B*x+A)/x**(9/2)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,1,1374,0,170.565961," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+a)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{c^{2}} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{7}{2}}}{7} + \frac{2 B x^{\frac{9}{2}}}{9}}{a^{2}} & \text{for}\: c = 0 \\- \frac{4 \sqrt[4]{-1} A \sqrt[4]{a} c x^{\frac{3}{2}} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{3 A a \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{3 A a \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{6 A a \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{3 A c x^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{3 A c x^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{6 A c x^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{20 \sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{16 \sqrt[4]{-1} B \sqrt[4]{a} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{5 i B a^{\frac{3}{2}} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{5 i B a^{\frac{3}{2}} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{10 i B a^{\frac{3}{2}} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{5 i B \sqrt{a} c x^{2} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{5 i B \sqrt{a} c x^{2} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{10 i B \sqrt{a} c x^{2} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} \sqrt[4]{a} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*sqrt(x)), Eq(a, 0) & Eq(c, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/c**2, Eq(a, 0)), ((2*A*x**(7/2)/7 + 2*B*x**(9/2)/9)/a**2, Eq(c, 0)), (-4*(-1)**(1/4)*A*a**(1/4)*c*x**(3/2)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 3*A*a*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) - 3*A*a*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) - 6*A*a*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 3*A*c*x**2*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) - 3*A*c*x**2*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) - 6*A*c*x**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 20*(-1)**(1/4)*B*a**(5/4)*sqrt(x)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 16*(-1)**(1/4)*B*a**(1/4)*c*x**(5/2)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 5*I*B*a**(3/2)*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) - 5*I*B*a**(3/2)*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 10*I*B*a**(3/2)*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 5*I*B*sqrt(a)*c*x**2*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) - 5*I*B*sqrt(a)*c*x**2*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)) + 10*I*B*sqrt(a)*c*x**2*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(5/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*c**3*x**2*(1/c)**(1/4)), True))","A",0
421,1,1316,0,90.986481," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+a)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{c^{2}} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}}{a^{2}} & \text{for}\: c = 0 \\- \frac{4 \sqrt[4]{-1} A a^{\frac{5}{4}} c \sqrt{x} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{i A a^{\frac{3}{2}} c \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{i A a^{\frac{3}{2}} c \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 i A a^{\frac{3}{2}} c \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{i A \sqrt{a} c^{2} x^{2} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{i A \sqrt{a} c^{2} x^{2} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 i A \sqrt{a} c^{2} x^{2} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{4 \sqrt[4]{-1} B a^{\frac{5}{4}} c x^{\frac{3}{2}} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{3 B a^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{3 B a^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{6 B a^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{3 B a c x^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{3 B a c x^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{6 B a c x^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{3} x^{2} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) - 2*B/sqrt(x)), Eq(a, 0) & Eq(c, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/c**2, Eq(a, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(7/2)/7)/a**2, Eq(c, 0)), (-4*(-1)**(1/4)*A*a**(5/4)*c*sqrt(x)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - I*A*a**(3/2)*c*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) + I*A*a**(3/2)*c*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 2*I*A*a**(3/2)*c*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - I*A*sqrt(a)*c**2*x**2*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) + I*A*sqrt(a)*c**2*x**2*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 2*I*A*sqrt(a)*c**2*x**2*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 4*(-1)**(1/4)*B*a**(5/4)*c*x**(3/2)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) + 3*B*a**2*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 3*B*a**2*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 6*B*a**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) + 3*B*a*c*x**2*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 3*B*a*c*x**2*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)) - 6*B*a*c*x**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c**2*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**3*x**2*(1/c)**(1/4)), True))","A",0
422,1,1266,0,52.793913," ","integrate(x**(1/2)*(B*x+A)/(c*x**2+a)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{c^{2}} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{a^{2}} & \text{for}\: c = 0 \\\frac{4 \sqrt[4]{-1} A \sqrt[4]{a} c x^{\frac{3}{2}} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{A a \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{A a \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 A a \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{A c x^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{A c x^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 A c x^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{4 \sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{i B a^{\frac{3}{2}} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{i B a^{\frac{3}{2}} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 i B a^{\frac{3}{2}} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{i B \sqrt{a} c x^{2} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{i B \sqrt{a} c x^{2} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 i B \sqrt{a} c x^{2} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2))), Eq(a, 0) & Eq(c, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/c**2, Eq(a, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/a**2, Eq(c, 0)), (4*(-1)**(1/4)*A*a**(1/4)*c*x**(3/2)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) + A*a*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - A*a*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - 2*A*a*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) + A*c*x**2*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - A*c*x**2*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - 2*A*c*x**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - 4*(-1)**(1/4)*B*a**(5/4)*sqrt(x)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - I*B*a**(3/2)*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) + I*B*a**(3/2)*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - 2*I*B*a**(3/2)*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - I*B*sqrt(a)*c*x**2*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) + I*B*sqrt(a)*c*x**2*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)) - 2*I*B*sqrt(a)*c*x**2*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*c**2*x**2*(1/c)**(1/4)), True))","A",0
423,1,1294,0,77.783248," ","integrate((B*x+A)/x**(1/2)/(c*x**2+a)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{c^{2}} & \text{for}\: a = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{a^{2}} & \text{for}\: c = 0 \\\frac{4 \sqrt[4]{-1} A a^{\frac{5}{4}} c \sqrt{x} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{3 i A a^{\frac{3}{2}} c \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{3 i A a^{\frac{3}{2}} c \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{6 i A a^{\frac{3}{2}} c \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{3 i A \sqrt{a} c^{2} x^{2} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{3 i A \sqrt{a} c^{2} x^{2} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{6 i A \sqrt{a} c^{2} x^{2} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{4 \sqrt[4]{-1} B a^{\frac{5}{4}} c x^{\frac{3}{2}} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{B a^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{B a^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 B a^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} + \frac{B a c x^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{B a c x^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} - \frac{2 B a c x^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} c \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c^{2} x^{2} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2))), Eq(a, 0) & Eq(c, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/c**2, Eq(a, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/a**2, Eq(c, 0)), (4*(-1)**(1/4)*A*a**(5/4)*c*sqrt(x)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - 3*I*A*a**(3/2)*c*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) + 3*I*A*a**(3/2)*c*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - 6*I*A*a**(3/2)*c*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - 3*I*A*sqrt(a)*c**2*x**2*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) + 3*I*A*sqrt(a)*c**2*x**2*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - 6*I*A*sqrt(a)*c**2*x**2*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) + 4*(-1)**(1/4)*B*a**(5/4)*c*x**(3/2)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) + B*a**2*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - B*a**2*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - 2*B*a**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) + B*a*c*x**2*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - B*a*c*x**2*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)) - 2*B*a*c*x**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*c*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c**2*x**2*(1/c)**(1/4)), True))","A",0
424,1,1435,0,149.464938," ","integrate((B*x+A)/x**(3/2)/(c*x**2+a)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: a = 0 \wedge c = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{c^{2}} & \text{for}\: a = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{a^{2}} & \text{for}\: c = 0 \\- \frac{16 \sqrt[4]{-1} A a^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{20 \sqrt[4]{-1} A \sqrt[4]{a} c x^{2} \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{5 A a \sqrt{x} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{5 A a \sqrt{x} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{10 A a \sqrt{x} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{5 A c x^{\frac{5}{2}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{5 A c x^{\frac{5}{2}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{10 A c x^{\frac{5}{2}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{4 \sqrt[4]{-1} B a^{\frac{5}{4}} x \sqrt[4]{\frac{1}{c}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{3 i B a^{\frac{3}{2}} \sqrt{x} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{3 i B a^{\frac{3}{2}} \sqrt{x} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{6 i B a^{\frac{3}{2}} \sqrt{x} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{3 i B \sqrt{a} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} + \frac{3 i B \sqrt{a} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} - \frac{6 i B \sqrt{a} c x^{\frac{5}{2}} \sqrt{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{c}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{c}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} c x^{\frac{5}{2}} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(a, 0) & Eq(c, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/c**2, Eq(a, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/a**2, Eq(c, 0)), (-16*(-1)**(1/4)*A*a**(5/4)*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 20*(-1)**(1/4)*A*a**(1/4)*c*x**2*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 5*A*a*sqrt(x)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 5*A*a*sqrt(x)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 10*A*a*sqrt(x)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 5*A*c*x**(5/2)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 5*A*c*x**(5/2)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 10*A*c*x**(5/2)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 4*(-1)**(1/4)*B*a**(5/4)*x*(1/c)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 3*I*B*a**(3/2)*sqrt(x)*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 3*I*B*a**(3/2)*sqrt(x)*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 6*I*B*a**(3/2)*sqrt(x)*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 3*I*B*sqrt(a)*c*x**(5/2)*sqrt(1/c)*log(-(-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) + 3*I*B*sqrt(a)*c*x**(5/2)*sqrt(1/c)*log((-1)**(1/4)*a**(1/4)*(1/c)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)) - 6*I*B*sqrt(a)*c*x**(5/2)*sqrt(1/c)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/c)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/c)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*c*x**(5/2)*(1/c)**(1/4)), True))","A",0
425,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(x**(1/2)*(B*x+A)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate((B*x+A)/x**(1/2)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,1,49,0,0.691555," ","integrate((1-x)/(x**2+1)/x**(1/2),x)","- \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{2} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{2}"," ",0,"-sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/2 + sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/2","A",0
433,1,97,0,77.118480," ","integrate((e*x)**(7/2)*(B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} e^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)} + \frac{B \sqrt{a} e^{\frac{7}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{15}{4}\right)}"," ",0,"A*sqrt(a)*e**(7/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4)) + B*sqrt(a)*e**(7/2)*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(15/4))","C",0
434,1,97,0,27.583365," ","integrate((e*x)**(5/2)*(B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)} + \frac{B \sqrt{a} e^{\frac{5}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*sqrt(a)*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4)) + B*sqrt(a)*e**(5/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4))","C",0
435,1,97,0,8.753025," ","integrate((e*x)**(3/2)*(B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{B \sqrt{a} e^{\frac{3}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*sqrt(a)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4)) + B*sqrt(a)*e**(3/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4))","C",0
436,1,95,0,3.701456," ","integrate((e*x)**(1/2)*(B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{a} \left(e x\right)^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{2} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(a)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e*gamma(7/4)) + B*sqrt(a)*(e*x)**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**2*gamma(9/4))","C",0
437,1,97,0,3.557323," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x)**(1/2),x)","\frac{A \sqrt{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B \sqrt{a} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*sqrt(a)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(5/4)) + B*sqrt(a)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(7/4))","C",0
438,1,100,0,4.141040," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x)**(3/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + B*sqrt(a)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(5/4))","C",0
439,1,104,0,7.502733," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x)**(5/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + B*sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*sqrt(x)*gamma(3/4))","C",0
440,1,107,0,22.464732," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x)**(7/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + B*sqrt(a)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(3/2)*gamma(1/4))","C",0
441,1,110,0,66.625028," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x)**(9/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(7/2)*gamma(-3/4)) + B*sqrt(a)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(5/2)*gamma(-1/4))","C",0
442,1,199,0,68.099507," ","integrate((e*x)**(5/2)*(B*x+A)*(c*x**2+a)**(3/2),x)","\frac{A a^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)} + \frac{A \sqrt{a} c e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{15}{4}\right)} + \frac{B a^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)} + \frac{B \sqrt{a} c e^{\frac{5}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{17}{4}\right)}"," ",0,"A*a**(3/2)*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4)) + A*sqrt(a)*c*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(15/4)) + B*a**(3/2)*e**(5/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4)) + B*sqrt(a)*c*e**(5/2)*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(17/4))","C",0
443,1,199,0,22.267019," ","integrate((e*x)**(3/2)*(B*x+A)*(c*x**2+a)**(3/2),x)","\frac{A a^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{A \sqrt{a} c e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)} + \frac{B a^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)} + \frac{B \sqrt{a} c e^{\frac{3}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{15}{4}\right)}"," ",0,"A*a**(3/2)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4)) + A*sqrt(a)*c*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4)) + B*a**(3/2)*e**(3/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4)) + B*sqrt(a)*c*e**(3/2)*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(15/4))","C",0
444,1,197,0,7.505105," ","integrate((e*x)**(1/2)*(B*x+A)*(c*x**2+a)**(3/2),x)","\frac{A a^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{A \sqrt{a} c \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{B a^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{2} \Gamma\left(\frac{9}{4}\right)} + \frac{B \sqrt{a} c \left(e x\right)^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{4} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*a**(3/2)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e*gamma(7/4)) + A*sqrt(a)*c*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**3*gamma(11/4)) + B*a**(3/2)*(e*x)**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**2*gamma(9/4)) + B*sqrt(a)*c*(e*x)**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**4*gamma(13/4))","C",0
445,1,199,0,8.349536," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x)**(1/2),x)","\frac{A a^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{A \sqrt{a} c x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{B a^{\frac{3}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{a} c x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*a**(3/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(5/4)) + A*sqrt(a)*c*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(9/4)) + B*a**(3/2)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(7/4)) + B*sqrt(a)*c*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(11/4))","C",0
446,1,202,0,8.623234," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x)**(3/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{A \sqrt{a} c x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B a^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B \sqrt{a} c x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + A*sqrt(a)*c*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(7/4)) + B*a**(3/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(5/4)) + B*sqrt(a)*c*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(9/4))","C",0
447,1,206,0,13.699335," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x)**(5/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{A \sqrt{a} c \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B a^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{a} c x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + A*sqrt(a)*c*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(5/4)) + B*a**(3/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*sqrt(x)*gamma(3/4)) + B*sqrt(a)*c*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(7/4))","C",0
448,1,212,0,37.891948," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x)**(7/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{A \sqrt{a} c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B a^{\frac{3}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \sqrt{a} c \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + A*sqrt(a)*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*sqrt(x)*gamma(3/4)) + B*a**(3/2)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(3/2)*gamma(1/4)) + B*sqrt(a)*c*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*gamma(5/4))","C",0
449,1,219,0,115.628677," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x)**(9/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{A \sqrt{a} c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B a^{\frac{3}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \sqrt{a} c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(7/2)*gamma(-3/4)) + A*sqrt(a)*c*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(3/2)*gamma(1/4)) + B*a**(3/2)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(5/2)*gamma(-1/4)) + B*sqrt(a)*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*sqrt(x)*gamma(3/4))","C",0
450,1,301,0,53.612413," ","integrate((e*x)**(3/2)*(B*x+A)*(c*x**2+a)**(5/2),x)","\frac{A a^{\frac{5}{2}} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{A a^{\frac{3}{2}} c e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{13}{4}\right)} + \frac{A \sqrt{a} c^{2} e^{\frac{3}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{17}{4}\right)} + \frac{B a^{\frac{5}{2}} e^{\frac{3}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)} + \frac{B a^{\frac{3}{2}} c e^{\frac{3}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{15}{4}\right)} + \frac{B \sqrt{a} c^{2} e^{\frac{3}{2}} x^{\frac{15}{2}} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{19}{4}\right)}"," ",0,"A*a**(5/2)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4)) + A*a**(3/2)*c*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/gamma(13/4) + A*sqrt(a)*c**2*e**(3/2)*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(17/4)) + B*a**(5/2)*e**(3/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4)) + B*a**(3/2)*c*e**(3/2)*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/gamma(15/4) + B*sqrt(a)*c**2*e**(3/2)*x**(15/2)*gamma(15/4)*hyper((-1/2, 15/4), (19/4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(19/4))","C",0
451,1,299,0,15.275810," ","integrate((e*x)**(1/2)*(B*x+A)*(c*x**2+a)**(5/2),x)","\frac{A a^{\frac{5}{2}} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{A a^{\frac{3}{2}} c \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{A \sqrt{a} c^{2} \left(e x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{5} \Gamma\left(\frac{15}{4}\right)} + \frac{B a^{\frac{5}{2}} \left(e x\right)^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{2} \Gamma\left(\frac{9}{4}\right)} + \frac{B a^{\frac{3}{2}} c \left(e x\right)^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{4} \Gamma\left(\frac{13}{4}\right)} + \frac{B \sqrt{a} c^{2} \left(e x\right)^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{6} \Gamma\left(\frac{17}{4}\right)}"," ",0,"A*a**(5/2)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e*gamma(7/4)) + A*a**(3/2)*c*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(e**3*gamma(11/4)) + A*sqrt(a)*c**2*(e*x)**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**5*gamma(15/4)) + B*a**(5/2)*(e*x)**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**2*gamma(9/4)) + B*a**(3/2)*c*(e*x)**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(e**4*gamma(13/4)) + B*sqrt(a)*c**2*(e*x)**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**6*gamma(17/4))","C",0
452,1,301,0,18.199801," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/(e*x)**(1/2),x)","\frac{A a^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{A a^{\frac{3}{2}} c x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{A \sqrt{a} c^{2} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{13}{4}\right)} + \frac{B a^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{7}{4}\right)} + \frac{B a^{\frac{3}{2}} c x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\sqrt{e} \Gamma\left(\frac{11}{4}\right)} + \frac{B \sqrt{a} c^{2} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{15}{4}\right)}"," ",0,"A*a**(5/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(5/4)) + A*a**(3/2)*c*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(sqrt(e)*gamma(9/4)) + A*sqrt(a)*c**2*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(13/4)) + B*a**(5/2)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(7/4)) + B*a**(3/2)*c*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(sqrt(e)*gamma(11/4)) + B*sqrt(a)*c**2*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(15/4))","C",0
453,1,304,0,18.553227," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/(e*x)**(3/2),x)","\frac{A a^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{A a^{\frac{3}{2}} c x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{A \sqrt{a} c^{2} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)} + \frac{B a^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B a^{\frac{3}{2}} c x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{B \sqrt{a} c^{2} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*a**(5/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + A*a**(3/2)*c*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(e**(3/2)*gamma(7/4)) + A*sqrt(a)*c**2*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(11/4)) + B*a**(5/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(5/4)) + B*a**(3/2)*c*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(e**(3/2)*gamma(9/4)) + B*sqrt(a)*c**2*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(13/4))","C",0
454,1,308,0,24.275526," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/(e*x)**(5/2),x)","\frac{A a^{\frac{5}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{A a^{\frac{3}{2}} c \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{A \sqrt{a} c^{2} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{B a^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B a^{\frac{3}{2}} c x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{a} c^{2} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*a**(5/2)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + A*a**(3/2)*c*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(e**(5/2)*gamma(5/4)) + A*sqrt(a)*c**2*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(9/4)) + B*a**(5/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*sqrt(x)*gamma(3/4)) + B*a**(3/2)*c*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(e**(5/2)*gamma(7/4)) + B*sqrt(a)*c**2*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(11/4))","C",0
455,1,314,0,56.589014," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/(e*x)**(7/2),x)","\frac{A a^{\frac{5}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{A a^{\frac{3}{2}} c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{A \sqrt{a} c^{2} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B a^{\frac{5}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B a^{\frac{3}{2}} c \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{7}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B \sqrt{a} c^{2} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*a**(5/2)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + A*a**(3/2)*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(e**(7/2)*sqrt(x)*gamma(3/4)) + A*sqrt(a)*c**2*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*gamma(7/4)) + B*a**(5/2)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(3/2)*gamma(1/4)) + B*a**(3/2)*c*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(e**(7/2)*gamma(5/4)) + B*sqrt(a)*c**2*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*gamma(9/4))","C",0
456,1,321,0,163.470062," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/(e*x)**(9/2),x)","\frac{A a^{\frac{5}{2}} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{A a^{\frac{3}{2}} c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{9}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{A \sqrt{a} c^{2} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B a^{\frac{5}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B a^{\frac{3}{2}} c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{e^{\frac{9}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{a} c^{2} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{9}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*a**(5/2)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(7/2)*gamma(-3/4)) + A*a**(3/2)*c*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(e**(9/2)*x**(3/2)*gamma(1/4)) + A*sqrt(a)*c**2*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*gamma(5/4)) + B*a**(5/2)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*x**(5/2)*gamma(-1/4)) + B*a**(3/2)*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), c*x**2*exp_polar(I*pi)/a)/(e**(9/2)*sqrt(x)*gamma(3/4)) + B*sqrt(a)*c**2*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*e**(9/2)*gamma(7/4))","C",0
457,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(5/2)/(e*x)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,1,94,0,55.517732," ","integrate((e*x)**(7/2)*(B*x+A)/(c*x**2+a)**(1/2),x)","\frac{A e^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{13}{4}\right)} + \frac{B e^{\frac{7}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"A*e**(7/2)*x**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(13/4)) + B*e**(7/2)*x**(11/2)*gamma(11/4)*hyper((1/2, 11/4), (15/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(15/4))","C",0
459,1,94,0,20.008368," ","integrate((e*x)**(5/2)*(B*x+A)/(c*x**2+a)**(1/2),x)","\frac{A e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{11}{4}\right)} + \frac{B e^{\frac{5}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(11/4)) + B*e**(5/2)*x**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(13/4))","C",0
460,1,94,0,6.711908," ","integrate((e*x)**(3/2)*(B*x+A)/(c*x**2+a)**(1/2),x)","\frac{A e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{B e^{\frac{3}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(9/4)) + B*e**(3/2)*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(11/4))","C",0
461,1,92,0,3.746188," ","integrate((e*x)**(1/2)*(B*x+A)/(c*x**2+a)**(1/2),x)","\frac{A \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e \Gamma\left(\frac{7}{4}\right)} + \frac{B \left(e x\right)^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{2} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*(e*x)**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e*gamma(7/4)) + B*(e*x)**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**2*gamma(9/4))","C",0
462,1,94,0,2.994682," ","integrate((B*x+A)/(e*x)**(1/2)/(c*x**2+a)**(1/2),x)","\frac{A \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \sqrt{e} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*sqrt(e)*gamma(5/4)) + B*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*sqrt(e)*gamma(7/4))","C",0
463,1,97,0,4.211413," ","integrate((B*x+A)/(e*x)**(3/2)/(c*x**2+a)**(1/2),x)","\frac{A \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(3/2)*sqrt(x)*gamma(3/4)) + B*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(3/2)*gamma(5/4))","C",0
464,1,100,0,9.104653," ","integrate((B*x+A)/(e*x)**(5/2)/(c*x**2+a)**(1/2),x)","\frac{A \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(5/2)*x**(3/2)*gamma(1/4)) + B*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(5/2)*sqrt(x)*gamma(3/4))","C",0
465,1,104,0,29.241103," ","integrate((B*x+A)/(e*x)**(7/2)/(c*x**2+a)**(1/2),x)","\frac{A \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{7}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"A*gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(7/2)*x**(5/2)*gamma(-1/4)) + B*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(7/2)*x**(3/2)*gamma(1/4))","C",0
466,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(B*x+A)/(c*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,1,94,0,141.569041," ","integrate((e*x)**(5/2)*(B*x+A)/(c*x**2+a)**(3/2),x)","\frac{A e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)} + \frac{B e^{\frac{5}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((3/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(11/4)) + B*e**(5/2)*x**(9/2)*gamma(9/4)*hyper((3/2, 9/4), (13/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(13/4))","C",0
468,1,94,0,28.548510," ","integrate((e*x)**(3/2)*(B*x+A)/(c*x**2+a)**(3/2),x)","\frac{A e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{B e^{\frac{3}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 3/2), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(9/4)) + B*e**(3/2)*x**(7/2)*gamma(7/4)*hyper((3/2, 7/4), (11/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(11/4))","C",0
469,1,94,0,13.194360," ","integrate((e*x)**(1/2)*(B*x+A)/(c*x**2+a)**(3/2),x)","\frac{A \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{e} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(e)*x**(3/2)*gamma(3/4)*hyper((3/4, 3/2), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(7/4)) + B*sqrt(e)*x**(5/2)*gamma(5/4)*hyper((5/4, 3/2), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(9/4))","C",0
470,1,94,0,14.741647," ","integrate((B*x+A)/(e*x)**(1/2)/(c*x**2+a)**(3/2),x)","\frac{A \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \sqrt{e} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*sqrt(x)*gamma(1/4)*hyper((1/4, 3/2), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*sqrt(e)*gamma(5/4)) + B*x**(3/2)*gamma(3/4)*hyper((3/4, 3/2), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*sqrt(e)*gamma(7/4))","C",0
471,1,97,0,29.207531," ","integrate((B*x+A)/(e*x)**(3/2)/(c*x**2+a)**(3/2),x)","\frac{A \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(3/2)*sqrt(x)*gamma(3/4)) + B*sqrt(x)*gamma(1/4)*hyper((1/4, 3/2), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(3/2)*gamma(5/4))","C",0
472,1,100,0,65.584108," ","integrate((B*x+A)/(e*x)**(5/2)/(c*x**2+a)**(3/2),x)","\frac{A \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(5/2)*x**(3/2)*gamma(1/4)) + B*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(5/2)*sqrt(x)*gamma(3/4))","C",0
473,1,104,0,150.956766," ","integrate((B*x+A)/(e*x)**(7/2)/(c*x**2+a)**(3/2),x)","\frac{A \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{7}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"A*gamma(-5/4)*hyper((-5/4, 3/2), (-1/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(7/2)*x**(5/2)*gamma(-1/4)) + B*gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(7/2)*x**(3/2)*gamma(1/4))","C",0
474,-1,0,0,0.000000," ","integrate((e*x)**(13/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate((e*x)**(11/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate((e*x)**(9/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate((e*x)**(3/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,1,94,0,64.643960," ","integrate((e*x)**(1/2)*(B*x+A)/(c*x**2+a)**(5/2),x)","\frac{A \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{e} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(e)*x**(3/2)*gamma(3/4)*hyper((3/4, 5/2), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(7/4)) + B*sqrt(e)*x**(5/2)*gamma(5/4)*hyper((5/4, 5/2), (9/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(9/4))","C",0
481,1,94,0,130.849596," ","integrate((B*x+A)/(e*x)**(1/2)/(c*x**2+a)**(5/2),x)","\frac{A \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \sqrt{e} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*sqrt(x)*gamma(1/4)*hyper((1/4, 5/2), (5/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*sqrt(e)*gamma(5/4)) + B*x**(3/2)*gamma(3/4)*hyper((3/4, 5/2), (7/4,), c*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*sqrt(e)*gamma(7/4))","C",0
482,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x)**(3/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x)**(5/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x)**(7/2)/(c*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,1,8202,0,5.167176," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**4,x)","\begin{cases} \frac{- \frac{A a^{4}}{9 x^{9}} - \frac{4 A a^{3} c}{7 x^{7}} - \frac{6 A a^{2} c^{2}}{5 x^{5}} - \frac{4 A a c^{3}}{3 x^{3}} - \frac{A c^{4}}{x} - \frac{B a^{4}}{8 x^{8}} - \frac{2 B a^{3} c}{3 x^{6}} - \frac{3 B a^{2} c^{2}}{2 x^{4}} - \frac{2 B a c^{3}}{x^{2}} + B c^{4} \log{\left(x \right)}}{e^{10}} & \text{for}\: m = -10 \\\frac{- \frac{A a^{4}}{8 x^{8}} - \frac{2 A a^{3} c}{3 x^{6}} - \frac{3 A a^{2} c^{2}}{2 x^{4}} - \frac{2 A a c^{3}}{x^{2}} + A c^{4} \log{\left(x \right)} - \frac{B a^{4}}{7 x^{7}} - \frac{4 B a^{3} c}{5 x^{5}} - \frac{2 B a^{2} c^{2}}{x^{3}} - \frac{4 B a c^{3}}{x} + B c^{4} x}{e^{9}} & \text{for}\: m = -9 \\\frac{- \frac{A a^{4}}{7 x^{7}} - \frac{4 A a^{3} c}{5 x^{5}} - \frac{2 A a^{2} c^{2}}{x^{3}} - \frac{4 A a c^{3}}{x} + A c^{4} x - \frac{B a^{4}}{6 x^{6}} - \frac{B a^{3} c}{x^{4}} - \frac{3 B a^{2} c^{2}}{x^{2}} + 4 B a c^{3} \log{\left(x \right)} + \frac{B c^{4} x^{2}}{2}}{e^{8}} & \text{for}\: m = -8 \\\frac{- \frac{A a^{4}}{6 x^{6}} - \frac{A a^{3} c}{x^{4}} - \frac{3 A a^{2} c^{2}}{x^{2}} + 4 A a c^{3} \log{\left(x \right)} + \frac{A c^{4} x^{2}}{2} - \frac{B a^{4}}{5 x^{5}} - \frac{4 B a^{3} c}{3 x^{3}} - \frac{6 B a^{2} c^{2}}{x} + 4 B a c^{3} x + \frac{B c^{4} x^{3}}{3}}{e^{7}} & \text{for}\: m = -7 \\\frac{- \frac{A a^{4}}{5 x^{5}} - \frac{4 A a^{3} c}{3 x^{3}} - \frac{6 A a^{2} c^{2}}{x} + 4 A a c^{3} x + \frac{A c^{4} x^{3}}{3} - \frac{B a^{4}}{4 x^{4}} - \frac{2 B a^{3} c}{x^{2}} + 6 B a^{2} c^{2} \log{\left(x \right)} + 2 B a c^{3} x^{2} + \frac{B c^{4} x^{4}}{4}}{e^{6}} & \text{for}\: m = -6 \\\frac{- \frac{A a^{4}}{4 x^{4}} - \frac{2 A a^{3} c}{x^{2}} + 6 A a^{2} c^{2} \log{\left(x \right)} + 2 A a c^{3} x^{2} + \frac{A c^{4} x^{4}}{4} - \frac{B a^{4}}{3 x^{3}} - \frac{4 B a^{3} c}{x} + 6 B a^{2} c^{2} x + \frac{4 B a c^{3} x^{3}}{3} + \frac{B c^{4} x^{5}}{5}}{e^{5}} & \text{for}\: m = -5 \\\frac{- \frac{A a^{4}}{3 x^{3}} - \frac{4 A a^{3} c}{x} + 6 A a^{2} c^{2} x + \frac{4 A a c^{3} x^{3}}{3} + \frac{A c^{4} x^{5}}{5} - \frac{B a^{4}}{2 x^{2}} + 4 B a^{3} c \log{\left(x \right)} + 3 B a^{2} c^{2} x^{2} + B a c^{3} x^{4} + \frac{B c^{4} x^{6}}{6}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a^{4}}{2 x^{2}} + 4 A a^{3} c \log{\left(x \right)} + 3 A a^{2} c^{2} x^{2} + A a c^{3} x^{4} + \frac{A c^{4} x^{6}}{6} - \frac{B a^{4}}{x} + 4 B a^{3} c x + 2 B a^{2} c^{2} x^{3} + \frac{4 B a c^{3} x^{5}}{5} + \frac{B c^{4} x^{7}}{7}}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a^{4}}{x} + 4 A a^{3} c x + 2 A a^{2} c^{2} x^{3} + \frac{4 A a c^{3} x^{5}}{5} + \frac{A c^{4} x^{7}}{7} + B a^{4} \log{\left(x \right)} + 2 B a^{3} c x^{2} + \frac{3 B a^{2} c^{2} x^{4}}{2} + \frac{2 B a c^{3} x^{6}}{3} + \frac{B c^{4} x^{8}}{8}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a^{4} \log{\left(x \right)} + 2 A a^{3} c x^{2} + \frac{3 A a^{2} c^{2} x^{4}}{2} + \frac{2 A a c^{3} x^{6}}{3} + \frac{A c^{4} x^{8}}{8} + B a^{4} x + \frac{4 B a^{3} c x^{3}}{3} + \frac{6 B a^{2} c^{2} x^{5}}{5} + \frac{4 B a c^{3} x^{7}}{7} + \frac{B c^{4} x^{9}}{9}}{e} & \text{for}\: m = -1 \\\frac{A a^{4} e^{m} m^{9} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{54 A a^{4} e^{m} m^{8} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1266 A a^{4} e^{m} m^{7} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{16884 A a^{4} e^{m} m^{6} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{140889 A a^{4} e^{m} m^{5} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{761166 A a^{4} e^{m} m^{4} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{2655764 A a^{4} e^{m} m^{3} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{5753736 A a^{4} e^{m} m^{2} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6999840 A a^{4} e^{m} m x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3628800 A a^{4} e^{m} x x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4 A a^{3} c e^{m} m^{9} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{208 A a^{3} c e^{m} m^{8} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4656 A a^{3} c e^{m} m^{7} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{58632 A a^{3} c e^{m} m^{6} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{455196 A a^{3} c e^{m} m^{5} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{2242632 A a^{3} c e^{m} m^{4} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6939824 A a^{3} c e^{m} m^{3} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{12818528 A a^{3} c e^{m} m^{2} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{12558720 A a^{3} c e^{m} m x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4838400 A a^{3} c e^{m} x^{3} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6 A a^{2} c^{2} e^{m} m^{9} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{300 A a^{2} c^{2} e^{m} m^{8} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6420 A a^{2} c^{2} e^{m} m^{7} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{76800 A a^{2} c^{2} e^{m} m^{6} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{562638 A a^{2} c^{2} e^{m} m^{5} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{2599140 A a^{2} c^{2} e^{m} m^{4} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{7505880 A a^{2} c^{2} e^{m} m^{3} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{12927600 A a^{2} c^{2} e^{m} m^{2} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{11883456 A a^{2} c^{2} e^{m} m x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4354560 A a^{2} c^{2} e^{m} x^{5} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4 A a c^{3} e^{m} m^{9} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{192 A a c^{3} e^{m} m^{8} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3936 A a c^{3} e^{m} m^{7} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{45048 A a c^{3} e^{m} m^{6} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{315756 A a c^{3} e^{m} m^{5} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1397928 A a c^{3} e^{m} m^{4} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3882224 A a c^{3} e^{m} m^{3} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6462432 A a c^{3} e^{m} m^{2} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{5777280 A a c^{3} e^{m} m x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{2073600 A a c^{3} e^{m} x^{7} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{A c^{4} e^{m} m^{9} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{46 A c^{4} e^{m} m^{8} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{906 A c^{4} e^{m} m^{7} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{9996 A c^{4} e^{m} m^{6} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{67809 A c^{4} e^{m} m^{5} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{291774 A c^{4} e^{m} m^{4} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{790964 A c^{4} e^{m} m^{3} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1290824 A c^{4} e^{m} m^{2} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1136160 A c^{4} e^{m} m x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{403200 A c^{4} e^{m} x^{9} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{B a^{4} e^{m} m^{9} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{53 B a^{4} e^{m} m^{8} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1214 B a^{4} e^{m} m^{7} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{15722 B a^{4} e^{m} m^{6} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{126329 B a^{4} e^{m} m^{5} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{649397 B a^{4} e^{m} m^{4} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{2118136 B a^{4} e^{m} m^{3} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4173228 B a^{4} e^{m} m^{2} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4407120 B a^{4} e^{m} m x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1814400 B a^{4} e^{m} x^{2} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4 B a^{3} c e^{m} m^{9} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{204 B a^{3} c e^{m} m^{8} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4464 B a^{3} c e^{m} m^{7} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{54744 B a^{3} c e^{m} m^{6} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{412116 B a^{3} c e^{m} m^{5} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1959756 B a^{3} c e^{m} m^{4} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{5828696 B a^{3} c e^{m} m^{3} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{10323216 B a^{3} c e^{m} m^{2} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{9721440 B a^{3} c e^{m} m x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3628800 B a^{3} c e^{m} x^{4} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6 B a^{2} c^{2} e^{m} m^{9} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{294 B a^{2} c^{2} e^{m} m^{8} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6156 B a^{2} c^{2} e^{m} m^{7} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{71964 B a^{2} c^{2} e^{m} m^{6} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{514854 B a^{2} c^{2} e^{m} m^{5} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{2323206 B a^{2} c^{2} e^{m} m^{4} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{6562344 B a^{2} c^{2} e^{m} m^{3} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{11082936 B a^{2} c^{2} e^{m} m^{2} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{10023840 B a^{2} c^{2} e^{m} m x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3628800 B a^{2} c^{2} e^{m} x^{6} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{4 B a c^{3} e^{m} m^{9} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{188 B a c^{3} e^{m} m^{8} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3776 B a c^{3} e^{m} m^{7} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{42392 B a c^{3} e^{m} m^{6} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{291956 B a c^{3} e^{m} m^{5} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1272572 B a c^{3} e^{m} m^{4} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{3487144 B a c^{3} e^{m} m^{3} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{5740848 B a c^{3} e^{m} m^{2} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{5087520 B a c^{3} e^{m} m x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1814400 B a c^{3} e^{m} x^{8} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{B c^{4} e^{m} m^{9} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{45 B c^{4} e^{m} m^{8} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{870 B c^{4} e^{m} m^{7} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{9450 B c^{4} e^{m} m^{6} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{63273 B c^{4} e^{m} m^{5} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{269325 B c^{4} e^{m} m^{4} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{723680 B c^{4} e^{m} m^{3} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1172700 B c^{4} e^{m} m^{2} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{1026576 B c^{4} e^{m} m x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} + \frac{362880 B c^{4} e^{m} x^{10} x^{m}}{m^{10} + 55 m^{9} + 1320 m^{8} + 18150 m^{7} + 157773 m^{6} + 902055 m^{5} + 3416930 m^{4} + 8409500 m^{3} + 12753576 m^{2} + 10628640 m + 3628800} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a**4/(9*x**9) - 4*A*a**3*c/(7*x**7) - 6*A*a**2*c**2/(5*x**5) - 4*A*a*c**3/(3*x**3) - A*c**4/x - B*a**4/(8*x**8) - 2*B*a**3*c/(3*x**6) - 3*B*a**2*c**2/(2*x**4) - 2*B*a*c**3/x**2 + B*c**4*log(x))/e**10, Eq(m, -10)), ((-A*a**4/(8*x**8) - 2*A*a**3*c/(3*x**6) - 3*A*a**2*c**2/(2*x**4) - 2*A*a*c**3/x**2 + A*c**4*log(x) - B*a**4/(7*x**7) - 4*B*a**3*c/(5*x**5) - 2*B*a**2*c**2/x**3 - 4*B*a*c**3/x + B*c**4*x)/e**9, Eq(m, -9)), ((-A*a**4/(7*x**7) - 4*A*a**3*c/(5*x**5) - 2*A*a**2*c**2/x**3 - 4*A*a*c**3/x + A*c**4*x - B*a**4/(6*x**6) - B*a**3*c/x**4 - 3*B*a**2*c**2/x**2 + 4*B*a*c**3*log(x) + B*c**4*x**2/2)/e**8, Eq(m, -8)), ((-A*a**4/(6*x**6) - A*a**3*c/x**4 - 3*A*a**2*c**2/x**2 + 4*A*a*c**3*log(x) + A*c**4*x**2/2 - B*a**4/(5*x**5) - 4*B*a**3*c/(3*x**3) - 6*B*a**2*c**2/x + 4*B*a*c**3*x + B*c**4*x**3/3)/e**7, Eq(m, -7)), ((-A*a**4/(5*x**5) - 4*A*a**3*c/(3*x**3) - 6*A*a**2*c**2/x + 4*A*a*c**3*x + A*c**4*x**3/3 - B*a**4/(4*x**4) - 2*B*a**3*c/x**2 + 6*B*a**2*c**2*log(x) + 2*B*a*c**3*x**2 + B*c**4*x**4/4)/e**6, Eq(m, -6)), ((-A*a**4/(4*x**4) - 2*A*a**3*c/x**2 + 6*A*a**2*c**2*log(x) + 2*A*a*c**3*x**2 + A*c**4*x**4/4 - B*a**4/(3*x**3) - 4*B*a**3*c/x + 6*B*a**2*c**2*x + 4*B*a*c**3*x**3/3 + B*c**4*x**5/5)/e**5, Eq(m, -5)), ((-A*a**4/(3*x**3) - 4*A*a**3*c/x + 6*A*a**2*c**2*x + 4*A*a*c**3*x**3/3 + A*c**4*x**5/5 - B*a**4/(2*x**2) + 4*B*a**3*c*log(x) + 3*B*a**2*c**2*x**2 + B*a*c**3*x**4 + B*c**4*x**6/6)/e**4, Eq(m, -4)), ((-A*a**4/(2*x**2) + 4*A*a**3*c*log(x) + 3*A*a**2*c**2*x**2 + A*a*c**3*x**4 + A*c**4*x**6/6 - B*a**4/x + 4*B*a**3*c*x + 2*B*a**2*c**2*x**3 + 4*B*a*c**3*x**5/5 + B*c**4*x**7/7)/e**3, Eq(m, -3)), ((-A*a**4/x + 4*A*a**3*c*x + 2*A*a**2*c**2*x**3 + 4*A*a*c**3*x**5/5 + A*c**4*x**7/7 + B*a**4*log(x) + 2*B*a**3*c*x**2 + 3*B*a**2*c**2*x**4/2 + 2*B*a*c**3*x**6/3 + B*c**4*x**8/8)/e**2, Eq(m, -2)), ((A*a**4*log(x) + 2*A*a**3*c*x**2 + 3*A*a**2*c**2*x**4/2 + 2*A*a*c**3*x**6/3 + A*c**4*x**8/8 + B*a**4*x + 4*B*a**3*c*x**3/3 + 6*B*a**2*c**2*x**5/5 + 4*B*a*c**3*x**7/7 + B*c**4*x**9/9)/e, Eq(m, -1)), (A*a**4*e**m*m**9*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 54*A*a**4*e**m*m**8*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1266*A*a**4*e**m*m**7*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 16884*A*a**4*e**m*m**6*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 140889*A*a**4*e**m*m**5*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 761166*A*a**4*e**m*m**4*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2655764*A*a**4*e**m*m**3*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5753736*A*a**4*e**m*m**2*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6999840*A*a**4*e**m*m*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3628800*A*a**4*e**m*x*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*A*a**3*c*e**m*m**9*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 208*A*a**3*c*e**m*m**8*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4656*A*a**3*c*e**m*m**7*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 58632*A*a**3*c*e**m*m**6*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 455196*A*a**3*c*e**m*m**5*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2242632*A*a**3*c*e**m*m**4*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6939824*A*a**3*c*e**m*m**3*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 12818528*A*a**3*c*e**m*m**2*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 12558720*A*a**3*c*e**m*m*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4838400*A*a**3*c*e**m*x**3*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6*A*a**2*c**2*e**m*m**9*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 300*A*a**2*c**2*e**m*m**8*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6420*A*a**2*c**2*e**m*m**7*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 76800*A*a**2*c**2*e**m*m**6*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 562638*A*a**2*c**2*e**m*m**5*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2599140*A*a**2*c**2*e**m*m**4*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 7505880*A*a**2*c**2*e**m*m**3*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 12927600*A*a**2*c**2*e**m*m**2*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 11883456*A*a**2*c**2*e**m*m*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4354560*A*a**2*c**2*e**m*x**5*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*A*a*c**3*e**m*m**9*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 192*A*a*c**3*e**m*m**8*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3936*A*a*c**3*e**m*m**7*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 45048*A*a*c**3*e**m*m**6*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 315756*A*a*c**3*e**m*m**5*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1397928*A*a*c**3*e**m*m**4*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3882224*A*a*c**3*e**m*m**3*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6462432*A*a*c**3*e**m*m**2*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5777280*A*a*c**3*e**m*m*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2073600*A*a*c**3*e**m*x**7*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + A*c**4*e**m*m**9*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 46*A*c**4*e**m*m**8*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 906*A*c**4*e**m*m**7*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 9996*A*c**4*e**m*m**6*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 67809*A*c**4*e**m*m**5*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 291774*A*c**4*e**m*m**4*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 790964*A*c**4*e**m*m**3*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1290824*A*c**4*e**m*m**2*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1136160*A*c**4*e**m*m*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 403200*A*c**4*e**m*x**9*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + B*a**4*e**m*m**9*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 53*B*a**4*e**m*m**8*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1214*B*a**4*e**m*m**7*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 15722*B*a**4*e**m*m**6*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 126329*B*a**4*e**m*m**5*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 649397*B*a**4*e**m*m**4*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2118136*B*a**4*e**m*m**3*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4173228*B*a**4*e**m*m**2*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4407120*B*a**4*e**m*m*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1814400*B*a**4*e**m*x**2*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*B*a**3*c*e**m*m**9*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 204*B*a**3*c*e**m*m**8*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4464*B*a**3*c*e**m*m**7*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 54744*B*a**3*c*e**m*m**6*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 412116*B*a**3*c*e**m*m**5*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1959756*B*a**3*c*e**m*m**4*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5828696*B*a**3*c*e**m*m**3*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 10323216*B*a**3*c*e**m*m**2*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 9721440*B*a**3*c*e**m*m*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3628800*B*a**3*c*e**m*x**4*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6*B*a**2*c**2*e**m*m**9*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 294*B*a**2*c**2*e**m*m**8*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6156*B*a**2*c**2*e**m*m**7*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 71964*B*a**2*c**2*e**m*m**6*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 514854*B*a**2*c**2*e**m*m**5*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2323206*B*a**2*c**2*e**m*m**4*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6562344*B*a**2*c**2*e**m*m**3*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 11082936*B*a**2*c**2*e**m*m**2*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 10023840*B*a**2*c**2*e**m*m*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3628800*B*a**2*c**2*e**m*x**6*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*B*a*c**3*e**m*m**9*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 188*B*a*c**3*e**m*m**8*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3776*B*a*c**3*e**m*m**7*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 42392*B*a*c**3*e**m*m**6*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 291956*B*a*c**3*e**m*m**5*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1272572*B*a*c**3*e**m*m**4*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3487144*B*a*c**3*e**m*m**3*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5740848*B*a*c**3*e**m*m**2*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5087520*B*a*c**3*e**m*m*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1814400*B*a*c**3*e**m*x**8*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + B*c**4*e**m*m**9*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 45*B*c**4*e**m*m**8*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 870*B*c**4*e**m*m**7*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 9450*B*c**4*e**m*m**6*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 63273*B*c**4*e**m*m**5*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 269325*B*c**4*e**m*m**4*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 723680*B*c**4*e**m*m**3*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1172700*B*c**4*e**m*m**2*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1026576*B*c**4*e**m*m*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 362880*B*c**4*e**m*x**10*x**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800), True))","A",0
486,1,4507,0,3.177525," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**3,x)","\begin{cases} \frac{- \frac{A a^{3}}{7 x^{7}} - \frac{3 A a^{2} c}{5 x^{5}} - \frac{A a c^{2}}{x^{3}} - \frac{A c^{3}}{x} - \frac{B a^{3}}{6 x^{6}} - \frac{3 B a^{2} c}{4 x^{4}} - \frac{3 B a c^{2}}{2 x^{2}} + B c^{3} \log{\left(x \right)}}{e^{8}} & \text{for}\: m = -8 \\\frac{- \frac{A a^{3}}{6 x^{6}} - \frac{3 A a^{2} c}{4 x^{4}} - \frac{3 A a c^{2}}{2 x^{2}} + A c^{3} \log{\left(x \right)} - \frac{B a^{3}}{5 x^{5}} - \frac{B a^{2} c}{x^{3}} - \frac{3 B a c^{2}}{x} + B c^{3} x}{e^{7}} & \text{for}\: m = -7 \\\frac{- \frac{A a^{3}}{5 x^{5}} - \frac{A a^{2} c}{x^{3}} - \frac{3 A a c^{2}}{x} + A c^{3} x - \frac{B a^{3}}{4 x^{4}} - \frac{3 B a^{2} c}{2 x^{2}} + 3 B a c^{2} \log{\left(x \right)} + \frac{B c^{3} x^{2}}{2}}{e^{6}} & \text{for}\: m = -6 \\\frac{- \frac{A a^{3}}{4 x^{4}} - \frac{3 A a^{2} c}{2 x^{2}} + 3 A a c^{2} \log{\left(x \right)} + \frac{A c^{3} x^{2}}{2} - \frac{B a^{3}}{3 x^{3}} - \frac{3 B a^{2} c}{x} + 3 B a c^{2} x + \frac{B c^{3} x^{3}}{3}}{e^{5}} & \text{for}\: m = -5 \\\frac{- \frac{A a^{3}}{3 x^{3}} - \frac{3 A a^{2} c}{x} + 3 A a c^{2} x + \frac{A c^{3} x^{3}}{3} - \frac{B a^{3}}{2 x^{2}} + 3 B a^{2} c \log{\left(x \right)} + \frac{3 B a c^{2} x^{2}}{2} + \frac{B c^{3} x^{4}}{4}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a^{3}}{2 x^{2}} + 3 A a^{2} c \log{\left(x \right)} + \frac{3 A a c^{2} x^{2}}{2} + \frac{A c^{3} x^{4}}{4} - \frac{B a^{3}}{x} + 3 B a^{2} c x + B a c^{2} x^{3} + \frac{B c^{3} x^{5}}{5}}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a^{3}}{x} + 3 A a^{2} c x + A a c^{2} x^{3} + \frac{A c^{3} x^{5}}{5} + B a^{3} \log{\left(x \right)} + \frac{3 B a^{2} c x^{2}}{2} + \frac{3 B a c^{2} x^{4}}{4} + \frac{B c^{3} x^{6}}{6}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a^{3} \log{\left(x \right)} + \frac{3 A a^{2} c x^{2}}{2} + \frac{3 A a c^{2} x^{4}}{4} + \frac{A c^{3} x^{6}}{6} + B a^{3} x + B a^{2} c x^{3} + \frac{3 B a c^{2} x^{5}}{5} + \frac{B c^{3} x^{7}}{7}}{e} & \text{for}\: m = -1 \\\frac{A a^{3} e^{m} m^{7} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35 A a^{3} e^{m} m^{6} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{511 A a^{3} e^{m} m^{5} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{4025 A a^{3} e^{m} m^{4} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{18424 A a^{3} e^{m} m^{3} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{48860 A a^{3} e^{m} m^{2} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69264 A a^{3} e^{m} m x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a^{3} e^{m} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A a^{2} c e^{m} m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{99 A a^{2} c e^{m} m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1341 A a^{2} c e^{m} m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{9585 A a^{2} c e^{m} m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{38592 A a^{2} c e^{m} m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{86076 A a^{2} c e^{m} m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96144 A a^{2} c e^{m} m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a^{2} c e^{m} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A a c^{2} e^{m} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{93 A a c^{2} e^{m} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1173 A a c^{2} e^{m} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7743 A a c^{2} e^{m} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28632 A a c^{2} e^{m} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{58692 A a c^{2} e^{m} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{60912 A a c^{2} e^{m} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{24192 A a c^{2} e^{m} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{A c^{3} e^{m} m^{7} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{29 A c^{3} e^{m} m^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{343 A c^{3} e^{m} m^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2135 A c^{3} e^{m} m^{4} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7504 A c^{3} e^{m} m^{3} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14756 A c^{3} e^{m} m^{2} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14832 A c^{3} e^{m} m x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5760 A c^{3} e^{m} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B a^{3} e^{m} m^{7} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{34 B a^{3} e^{m} m^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{478 B a^{3} e^{m} m^{5} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3580 B a^{3} e^{m} m^{4} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15289 B a^{3} e^{m} m^{3} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{36706 B a^{3} e^{m} m^{2} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{44712 B a^{3} e^{m} m x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 B a^{3} e^{m} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B a^{2} c e^{m} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96 B a^{2} c e^{m} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1254 B a^{2} c e^{m} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{8592 B a^{2} c e^{m} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{32979 B a^{2} c e^{m} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69936 B a^{2} c e^{m} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{74628 B a^{2} c e^{m} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{30240 B a^{2} c e^{m} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B a c^{2} e^{m} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{90 B a c^{2} e^{m} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1098 B a c^{2} e^{m} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7020 B a c^{2} e^{m} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{25227 B a c^{2} e^{m} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{50490 B a c^{2} e^{m} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{51432 B a c^{2} e^{m} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 B a c^{2} e^{m} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B c^{3} e^{m} m^{7} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28 B c^{3} e^{m} m^{6} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{322 B c^{3} e^{m} m^{5} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1960 B c^{3} e^{m} m^{4} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6769 B c^{3} e^{m} m^{3} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13132 B c^{3} e^{m} m^{2} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13068 B c^{3} e^{m} m x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5040 B c^{3} e^{m} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a**3/(7*x**7) - 3*A*a**2*c/(5*x**5) - A*a*c**2/x**3 - A*c**3/x - B*a**3/(6*x**6) - 3*B*a**2*c/(4*x**4) - 3*B*a*c**2/(2*x**2) + B*c**3*log(x))/e**8, Eq(m, -8)), ((-A*a**3/(6*x**6) - 3*A*a**2*c/(4*x**4) - 3*A*a*c**2/(2*x**2) + A*c**3*log(x) - B*a**3/(5*x**5) - B*a**2*c/x**3 - 3*B*a*c**2/x + B*c**3*x)/e**7, Eq(m, -7)), ((-A*a**3/(5*x**5) - A*a**2*c/x**3 - 3*A*a*c**2/x + A*c**3*x - B*a**3/(4*x**4) - 3*B*a**2*c/(2*x**2) + 3*B*a*c**2*log(x) + B*c**3*x**2/2)/e**6, Eq(m, -6)), ((-A*a**3/(4*x**4) - 3*A*a**2*c/(2*x**2) + 3*A*a*c**2*log(x) + A*c**3*x**2/2 - B*a**3/(3*x**3) - 3*B*a**2*c/x + 3*B*a*c**2*x + B*c**3*x**3/3)/e**5, Eq(m, -5)), ((-A*a**3/(3*x**3) - 3*A*a**2*c/x + 3*A*a*c**2*x + A*c**3*x**3/3 - B*a**3/(2*x**2) + 3*B*a**2*c*log(x) + 3*B*a*c**2*x**2/2 + B*c**3*x**4/4)/e**4, Eq(m, -4)), ((-A*a**3/(2*x**2) + 3*A*a**2*c*log(x) + 3*A*a*c**2*x**2/2 + A*c**3*x**4/4 - B*a**3/x + 3*B*a**2*c*x + B*a*c**2*x**3 + B*c**3*x**5/5)/e**3, Eq(m, -3)), ((-A*a**3/x + 3*A*a**2*c*x + A*a*c**2*x**3 + A*c**3*x**5/5 + B*a**3*log(x) + 3*B*a**2*c*x**2/2 + 3*B*a*c**2*x**4/4 + B*c**3*x**6/6)/e**2, Eq(m, -2)), ((A*a**3*log(x) + 3*A*a**2*c*x**2/2 + 3*A*a*c**2*x**4/4 + A*c**3*x**6/6 + B*a**3*x + B*a**2*c*x**3 + 3*B*a*c**2*x**5/5 + B*c**3*x**7/7)/e, Eq(m, -1)), (A*a**3*e**m*m**7*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35*A*a**3*e**m*m**6*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 511*A*a**3*e**m*m**5*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 4025*A*a**3*e**m*m**4*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 18424*A*a**3*e**m*m**3*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 48860*A*a**3*e**m*m**2*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69264*A*a**3*e**m*m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a**3*e**m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*a**2*c*e**m*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 99*A*a**2*c*e**m*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1341*A*a**2*c*e**m*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 9585*A*a**2*c*e**m*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 38592*A*a**2*c*e**m*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 86076*A*a**2*c*e**m*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96144*A*a**2*c*e**m*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a**2*c*e**m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*a*c**2*e**m*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 93*A*a*c**2*e**m*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1173*A*a*c**2*e**m*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7743*A*a*c**2*e**m*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28632*A*a*c**2*e**m*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 58692*A*a*c**2*e**m*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 60912*A*a*c**2*e**m*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 24192*A*a*c**2*e**m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + A*c**3*e**m*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 29*A*c**3*e**m*m**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 343*A*c**3*e**m*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2135*A*c**3*e**m*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7504*A*c**3*e**m*m**3*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14756*A*c**3*e**m*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14832*A*c**3*e**m*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5760*A*c**3*e**m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*a**3*e**m*m**7*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 34*B*a**3*e**m*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 478*B*a**3*e**m*m**5*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3580*B*a**3*e**m*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15289*B*a**3*e**m*m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 36706*B*a**3*e**m*m**2*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 44712*B*a**3*e**m*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*B*a**3*e**m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*a**2*c*e**m*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96*B*a**2*c*e**m*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1254*B*a**2*c*e**m*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 8592*B*a**2*c*e**m*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 32979*B*a**2*c*e**m*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69936*B*a**2*c*e**m*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 74628*B*a**2*c*e**m*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 30240*B*a**2*c*e**m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*a*c**2*e**m*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 90*B*a*c**2*e**m*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1098*B*a*c**2*e**m*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7020*B*a*c**2*e**m*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 25227*B*a*c**2*e**m*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 50490*B*a*c**2*e**m*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 51432*B*a*c**2*e**m*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*B*a*c**2*e**m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*c**3*e**m*m**7*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28*B*c**3*e**m*m**6*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 322*B*c**3*e**m*m**5*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1960*B*c**3*e**m*m**4*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6769*B*c**3*e**m*m**3*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13132*B*c**3*e**m*m**2*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13068*B*c**3*e**m*m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5040*B*c**3*e**m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320), True))","A",0
487,1,2076,0,1.732225," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**2,x)","\begin{cases} \frac{- \frac{A a^{2}}{5 x^{5}} - \frac{2 A a c}{3 x^{3}} - \frac{A c^{2}}{x} - \frac{B a^{2}}{4 x^{4}} - \frac{B a c}{x^{2}} + B c^{2} \log{\left(x \right)}}{e^{6}} & \text{for}\: m = -6 \\\frac{- \frac{A a^{2}}{4 x^{4}} - \frac{A a c}{x^{2}} + A c^{2} \log{\left(x \right)} - \frac{B a^{2}}{3 x^{3}} - \frac{2 B a c}{x} + B c^{2} x}{e^{5}} & \text{for}\: m = -5 \\\frac{- \frac{A a^{2}}{3 x^{3}} - \frac{2 A a c}{x} + A c^{2} x - \frac{B a^{2}}{2 x^{2}} + 2 B a c \log{\left(x \right)} + \frac{B c^{2} x^{2}}{2}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a^{2}}{2 x^{2}} + 2 A a c \log{\left(x \right)} + \frac{A c^{2} x^{2}}{2} - \frac{B a^{2}}{x} + 2 B a c x + \frac{B c^{2} x^{3}}{3}}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a^{2}}{x} + 2 A a c x + \frac{A c^{2} x^{3}}{3} + B a^{2} \log{\left(x \right)} + B a c x^{2} + \frac{B c^{2} x^{4}}{4}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a^{2} \log{\left(x \right)} + A a c x^{2} + \frac{A c^{2} x^{4}}{4} + B a^{2} x + \frac{2 B a c x^{3}}{3} + \frac{B c^{2} x^{5}}{5}}{e} & \text{for}\: m = -1 \\\frac{A a^{2} e^{m} m^{5} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{20 A a^{2} e^{m} m^{4} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{155 A a^{2} e^{m} m^{3} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{580 A a^{2} e^{m} m^{2} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1044 A a^{2} e^{m} m x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{720 A a^{2} e^{m} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 A a c e^{m} m^{5} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{36 A a c e^{m} m^{4} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{242 A a c e^{m} m^{3} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{744 A a c e^{m} m^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1016 A a c e^{m} m x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{480 A a c e^{m} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{A c^{2} e^{m} m^{5} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{16 A c^{2} e^{m} m^{4} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{95 A c^{2} e^{m} m^{3} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{260 A c^{2} e^{m} m^{2} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{324 A c^{2} e^{m} m x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{144 A c^{2} e^{m} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B a^{2} e^{m} m^{5} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{19 B a^{2} e^{m} m^{4} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{137 B a^{2} e^{m} m^{3} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{461 B a^{2} e^{m} m^{2} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{702 B a^{2} e^{m} m x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{360 B a^{2} e^{m} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 B a c e^{m} m^{5} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{34 B a c e^{m} m^{4} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{214 B a c e^{m} m^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{614 B a c e^{m} m^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{792 B a c e^{m} m x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{360 B a c e^{m} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B c^{2} e^{m} m^{5} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{15 B c^{2} e^{m} m^{4} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{85 B c^{2} e^{m} m^{3} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{225 B c^{2} e^{m} m^{2} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{274 B c^{2} e^{m} m x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{120 B c^{2} e^{m} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a**2/(5*x**5) - 2*A*a*c/(3*x**3) - A*c**2/x - B*a**2/(4*x**4) - B*a*c/x**2 + B*c**2*log(x))/e**6, Eq(m, -6)), ((-A*a**2/(4*x**4) - A*a*c/x**2 + A*c**2*log(x) - B*a**2/(3*x**3) - 2*B*a*c/x + B*c**2*x)/e**5, Eq(m, -5)), ((-A*a**2/(3*x**3) - 2*A*a*c/x + A*c**2*x - B*a**2/(2*x**2) + 2*B*a*c*log(x) + B*c**2*x**2/2)/e**4, Eq(m, -4)), ((-A*a**2/(2*x**2) + 2*A*a*c*log(x) + A*c**2*x**2/2 - B*a**2/x + 2*B*a*c*x + B*c**2*x**3/3)/e**3, Eq(m, -3)), ((-A*a**2/x + 2*A*a*c*x + A*c**2*x**3/3 + B*a**2*log(x) + B*a*c*x**2 + B*c**2*x**4/4)/e**2, Eq(m, -2)), ((A*a**2*log(x) + A*a*c*x**2 + A*c**2*x**4/4 + B*a**2*x + 2*B*a*c*x**3/3 + B*c**2*x**5/5)/e, Eq(m, -1)), (A*a**2*e**m*m**5*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 20*A*a**2*e**m*m**4*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 155*A*a**2*e**m*m**3*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 580*A*a**2*e**m*m**2*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1044*A*a**2*e**m*m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 720*A*a**2*e**m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*A*a*c*e**m*m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 36*A*a*c*e**m*m**4*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 242*A*a*c*e**m*m**3*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 744*A*a*c*e**m*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1016*A*a*c*e**m*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 480*A*a*c*e**m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + A*c**2*e**m*m**5*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 16*A*c**2*e**m*m**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 95*A*c**2*e**m*m**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 260*A*c**2*e**m*m**2*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 324*A*c**2*e**m*m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 144*A*c**2*e**m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*a**2*e**m*m**5*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 19*B*a**2*e**m*m**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 137*B*a**2*e**m*m**3*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 461*B*a**2*e**m*m**2*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 702*B*a**2*e**m*m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 360*B*a**2*e**m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*B*a*c*e**m*m**5*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 34*B*a*c*e**m*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 214*B*a*c*e**m*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 614*B*a*c*e**m*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 792*B*a*c*e**m*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 360*B*a*c*e**m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*c**2*e**m*m**5*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 15*B*c**2*e**m*m**4*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 85*B*c**2*e**m*m**3*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 225*B*c**2*e**m*m**2*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 274*B*c**2*e**m*m*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 120*B*c**2*e**m*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720), True))","A",0
488,1,685,0,0.860740," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a),x)","\begin{cases} \frac{- \frac{A a}{3 x^{3}} - \frac{A c}{x} - \frac{B a}{2 x^{2}} + B c \log{\left(x \right)}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a}{2 x^{2}} + A c \log{\left(x \right)} - \frac{B a}{x} + B c x}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a}{x} + A c x + B a \log{\left(x \right)} + \frac{B c x^{2}}{2}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a \log{\left(x \right)} + \frac{A c x^{2}}{2} + B a x + \frac{B c x^{3}}{3}}{e} & \text{for}\: m = -1 \\\frac{A a e^{m} m^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{9 A a e^{m} m^{2} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{26 A a e^{m} m x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 A a e^{m} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{A c e^{m} m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{7 A c e^{m} m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{14 A c e^{m} m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 A c e^{m} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B a e^{m} m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 B a e^{m} m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{19 B a e^{m} m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{12 B a e^{m} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B c e^{m} m^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 B c e^{m} m^{2} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{11 B c e^{m} m x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 B c e^{m} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a/(3*x**3) - A*c/x - B*a/(2*x**2) + B*c*log(x))/e**4, Eq(m, -4)), ((-A*a/(2*x**2) + A*c*log(x) - B*a/x + B*c*x)/e**3, Eq(m, -3)), ((-A*a/x + A*c*x + B*a*log(x) + B*c*x**2/2)/e**2, Eq(m, -2)), ((A*a*log(x) + A*c*x**2/2 + B*a*x + B*c*x**3/3)/e, Eq(m, -1)), (A*a*e**m*m**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 9*A*a*e**m*m**2*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 26*A*a*e**m*m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*A*a*e**m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + A*c*e**m*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 7*A*c*e**m*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 14*A*c*e**m*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*A*c*e**m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*a*e**m*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*B*a*e**m*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 19*B*a*e**m*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 12*B*a*e**m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*c*e**m*m**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*B*c*e**m*m**2*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 11*B*c*e**m*m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*B*c*e**m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24), True))","A",0
489,1,192,0,4.207247," ","integrate((e*x)**m*(B*x+A)/(c*x**2+a),x)","\frac{A e^{m} m x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{A e^{m} x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B e^{m} m x^{2} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{4 a \Gamma\left(\frac{m}{2} + 2\right)} + \frac{B e^{m} x^{2} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{2 a \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*e**m*m*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + A*e**m*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + B*e**m*m*x**2*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(4*a*gamma(m/2 + 2)) + B*e**m*x**2*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(2*a*gamma(m/2 + 2))","C",0
490,1,770,0,34.158755," ","integrate((e*x)**m*(B*x+A)/(c*x**2+a)**2,x)","A \left(- \frac{a e^{m} m^{2} x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a e^{m} m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a e^{m} x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{c e^{m} m^{2} x^{3} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c e^{m} x^{3} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}\right) + B \left(- \frac{a e^{m} m^{2} x^{2} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + 2\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 a e^{m} m x^{2} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + 2\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{2 a e^{m} m x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + 2\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{4 a e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + 2\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{c e^{m} m^{2} x^{4} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + 2\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 c e^{m} m x^{4} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + 2\right) + 8 a^{2} c x^{2} \Gamma\left(\frac{m}{2} + 2\right)}\right)"," ",0,"A*(-a*e**m*m**2*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*c*x**2*gamma(m/2 + 3/2)) + 2*a*e**m*m*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*c*x**2*gamma(m/2 + 3/2)) + a*e**m*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*c*x**2*gamma(m/2 + 3/2)) + 2*a*e**m*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*c*x**2*gamma(m/2 + 3/2)) - c*e**m*m**2*x**3*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*c*x**2*gamma(m/2 + 3/2)) + c*e**m*x**3*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*c*x**2*gamma(m/2 + 3/2))) + B*(-a*e**m*m**2*x**2*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**3*gamma(m/2 + 2) + 8*a**2*c*x**2*gamma(m/2 + 2)) - 2*a*e**m*m*x**2*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**3*gamma(m/2 + 2) + 8*a**2*c*x**2*gamma(m/2 + 2)) + 2*a*e**m*m*x**2*x**m*gamma(m/2 + 1)/(8*a**3*gamma(m/2 + 2) + 8*a**2*c*x**2*gamma(m/2 + 2)) + 4*a*e**m*x**2*x**m*gamma(m/2 + 1)/(8*a**3*gamma(m/2 + 2) + 8*a**2*c*x**2*gamma(m/2 + 2)) - c*e**m*m**2*x**4*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**3*gamma(m/2 + 2) + 8*a**2*c*x**2*gamma(m/2 + 2)) - 2*c*e**m*m*x**4*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**3*gamma(m/2 + 2) + 8*a**2*c*x**2*gamma(m/2 + 2)))","C",0
491,1,2509,0,117.117790," ","integrate((e*x)**m*(B*x+A)/(c*x**2+a)**3,x)","A \left(\frac{a^{2} e^{m} m^{3} x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{3 a^{2} e^{m} m^{2} x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a^{2} e^{m} m^{2} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{a^{2} e^{m} m x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{8 a^{2} e^{m} m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 a^{2} e^{m} x x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{10 a^{2} e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a c e^{m} m^{3} x^{3} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{6 a c e^{m} m^{2} x^{3} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a c e^{m} m^{2} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a c e^{m} m x^{3} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{4 a c e^{m} m x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{6 a c e^{m} x^{3} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{6 a c e^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c^{2} e^{m} m^{3} x^{5} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{3 c^{2} e^{m} m^{2} x^{5} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{c^{2} e^{m} m x^{5} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 c^{2} e^{m} x^{5} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}\right) + B \left(\frac{a^{2} e^{m} m^{3} x^{2} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 a^{2} e^{m} m^{2} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{4 a^{2} e^{m} m x^{2} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{4 a^{2} e^{m} m x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{16 a^{2} e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{2 a c e^{m} m^{3} x^{4} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 a c e^{m} m^{2} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{8 a c e^{m} m x^{4} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{8 a c e^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} + \frac{c^{2} e^{m} m^{3} x^{6} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)} - \frac{4 c^{2} e^{m} m x^{6} x^{m} \Phi\left(\frac{c x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + 2\right) + 64 a^{4} c x^{2} \Gamma\left(\frac{m}{2} + 2\right) + 32 a^{3} c^{2} x^{4} \Gamma\left(\frac{m}{2} + 2\right)}\right)"," ",0,"A*(a**2*e**m*m**3*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - 3*a**2*e**m*m**2*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - 2*a**2*e**m*m**2*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - a**2*e**m*m*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 8*a**2*e**m*m*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 3*a**2*e**m*x*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 10*a**2*e**m*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 2*a*c*e**m*m**3*x**3*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - 6*a*c*e**m*m**2*x**3*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - 2*a*c*e**m*m**2*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - 2*a*c*e**m*m*x**3*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 4*a*c*e**m*m*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 6*a*c*e**m*x**3*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 6*a*c*e**m*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + c**2*e**m*m**3*x**5*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - 3*c**2*e**m*m**2*x**5*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) - c**2*e**m*m*x**5*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2)) + 3*c**2*e**m*x**5*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*c*x**2*gamma(m/2 + 3/2) + 32*a**3*c**2*x**4*gamma(m/2 + 3/2))) + B*(a**2*e**m*m**3*x**2*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) - 2*a**2*e**m*m**2*x**2*x**m*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) - 4*a**2*e**m*m*x**2*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) + 4*a**2*e**m*m*x**2*x**m*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) + 16*a**2*e**m*x**2*x**m*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) + 2*a*c*e**m*m**3*x**4*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) - 2*a*c*e**m*m**2*x**4*x**m*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) - 8*a*c*e**m*m*x**4*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) + 8*a*c*e**m*x**4*x**m*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) + c**2*e**m*m**3*x**6*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)) - 4*c**2*e**m*m*x**6*x**m*lerchphi(c*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(32*a**5*gamma(m/2 + 2) + 64*a**4*c*x**2*gamma(m/2 + 2) + 32*a**3*c**2*x**4*gamma(m/2 + 2)))","C",0
492,1,360,0,21.116496," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**(5/2),x)","\frac{A a^{\frac{5}{2}} e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{A a^{\frac{3}{2}} c e^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{A \sqrt{a} c^{2} e^{m} x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{5}{2} \\ \frac{m}{2} + \frac{7}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{B a^{\frac{5}{2}} e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{B a^{\frac{3}{2}} c e^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{m}{2} + 3\right)} + \frac{B \sqrt{a} c^{2} e^{m} x^{6} x^{m} \Gamma\left(\frac{m}{2} + 3\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 3 \\ \frac{m}{2} + 4 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 4\right)}"," ",0,"A*a**(5/2)*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2)) + A*a**(3/2)*c*e**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), c*x**2*exp_polar(I*pi)/a)/gamma(m/2 + 5/2) + A*sqrt(a)*c**2*e**m*x**5*x**m*gamma(m/2 + 5/2)*hyper((-1/2, m/2 + 5/2), (m/2 + 7/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 7/2)) + B*a**(5/2)*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2)) + B*a**(3/2)*c*e**m*x**4*x**m*gamma(m/2 + 2)*hyper((-1/2, m/2 + 2), (m/2 + 3,), c*x**2*exp_polar(I*pi)/a)/gamma(m/2 + 3) + B*sqrt(a)*c**2*e**m*x**6*x**m*gamma(m/2 + 3)*hyper((-1/2, m/2 + 3), (m/2 + 4,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 4))","C",0
493,1,238,0,9.548038," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**(3/2),x)","\frac{A a^{\frac{3}{2}} e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{A \sqrt{a} c e^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{B a^{\frac{3}{2}} e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{B \sqrt{a} c e^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 3\right)}"," ",0,"A*a**(3/2)*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2)) + A*sqrt(a)*c*e**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 5/2)) + B*a**(3/2)*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2)) + B*sqrt(a)*c*e**m*x**4*x**m*gamma(m/2 + 2)*hyper((-1/2, m/2 + 2), (m/2 + 3,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3))","C",0
494,1,116,0,3.863480," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**(1/2),x)","\frac{A \sqrt{a} e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B \sqrt{a} e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*sqrt(a)*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2)) + B*sqrt(a)*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2))","C",0
495,1,112,0,3.648612," ","integrate((e*x)**m*(B*x+A)/(c*x**2+a)**(1/2),x)","\frac{A e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((1/2, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 3/2)) + B*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((1/2, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 2))","C",0
496,1,112,0,12.660325," ","integrate((e*x)**m*(B*x+A)/(c*x**2+a)**(3/2),x)","\frac{A e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((3/2, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/2 + 3/2)) + B*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((3/2, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/2 + 2))","C",0
497,1,112,0,159.103236," ","integrate((e*x)**m*(B*x+A)/(c*x**2+a)**(5/2),x)","\frac{A e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((5/2, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(m/2 + 3/2)) + B*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((5/2, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(m/2 + 2))","C",0
498,1,673,0,6.368254," ","integrate(x**m*(a*x+1)/(-a**2*x**2+1)**2,x)","- \frac{a^{2} m^{2} x^{3} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a^{2} x^{3} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + a \left(- \frac{a^{2} m^{2} x^{4} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 a^{2} m x^{4} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{m^{2} x^{2} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{2 m x^{2} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 m x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{4 x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)}\right) + \frac{m^{2} x x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{x x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"-a**2*m**2*x**3*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) + a**2*x**3*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) + a*(-a**2*m**2*x**4*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) - 2*a**2*m*x**4*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) + m**2*x**2*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) + 2*m*x**2*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) - 2*m*x**2*x**m*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) - 4*x**2*x**m*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2))) + m**2*x*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) - 2*m*x*x**m*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) - x*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) - 2*x*x**m*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2))","C",0
499,1,313,0,2.320056," ","integrate(x**m/(-a*x+1)**2/(a*x+1),x)","\frac{2 a m^{2} x x^{m} \Phi\left(\frac{1}{a x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)} - \frac{a m x x^{m} \Phi\left(\frac{1}{a x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)} + \frac{a m x x^{m} \Phi\left(\frac{e^{i \pi}}{a x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)} + \frac{2 a m x x^{m} \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)} - \frac{2 m^{2} x^{m} \Phi\left(\frac{1}{a x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)} + \frac{m x^{m} \Phi\left(\frac{1}{a x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)} - \frac{m x^{m} \Phi\left(\frac{e^{i \pi}}{a x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{4 a^{2} x \Gamma\left(1 - m\right) - 4 a \Gamma\left(1 - m\right)}"," ",0,"2*a*m**2*x*x**m*lerchphi(1/(a*x), 1, m*exp_polar(I*pi))*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m)) - a*m*x*x**m*lerchphi(1/(a*x), 1, m*exp_polar(I*pi))*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m)) + a*m*x*x**m*lerchphi(exp_polar(I*pi)/(a*x), 1, m*exp_polar(I*pi))*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m)) + 2*a*m*x*x**m*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m)) - 2*m**2*x**m*lerchphi(1/(a*x), 1, m*exp_polar(I*pi))*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m)) + m*x**m*lerchphi(1/(a*x), 1, m*exp_polar(I*pi))*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m)) - m*x**m*lerchphi(exp_polar(I*pi)/(a*x), 1, m*exp_polar(I*pi))*gamma(-m)/(4*a**2*x*gamma(1 - m) - 4*a*gamma(1 - m))","C",0
500,1,673,0,2.790081," ","integrate(x**m/(-a**2*x**2+1)**2+a*x**(1+m)/(-a**2*x**2+1)**2,x)","- \frac{a^{2} m^{2} x^{3} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a^{2} x^{3} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + a \left(- \frac{a^{2} m^{2} x^{4} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 a^{2} m x^{4} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{m^{2} x^{2} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{2 m x^{2} x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{2 m x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{4 x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + 2\right) - 8 \Gamma\left(\frac{m}{2} + 2\right)}\right) + \frac{m^{2} x x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{x x^{m} \Phi\left(a^{2} x^{2} e^{2 i \pi}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{2} x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) - 8 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"-a**2*m**2*x**3*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) + a**2*x**3*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) + a*(-a**2*m**2*x**4*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) - 2*a**2*m*x**4*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) + m**2*x**2*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) + 2*m*x**2*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1)*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) - 2*m*x**2*x**m*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2)) - 4*x**2*x**m*gamma(m/2 + 1)/(8*a**2*x**2*gamma(m/2 + 2) - 8*gamma(m/2 + 2))) + m**2*x*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) - 2*m*x*x**m*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) - x*x**m*lerchphi(a**2*x**2*exp_polar(2*I*pi), 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2)) - 2*x*x**m*gamma(m/2 + 1/2)/(8*a**2*x**2*gamma(m/2 + 3/2) - 8*gamma(m/2 + 3/2))","C",0
501,0,0,0,0.000000," ","integrate(x**m/(-a*x+1)/(-a**2*x**2+1),x)","\int \frac{x^{m}}{\left(a x - 1\right)^{2} \left(a x + 1\right)}\, dx"," ",0,"Integral(x**m/((a*x - 1)**2*(a*x + 1)), x)","F",0
502,1,109,0,83.444781," ","integrate((e*x)**m*(B*x+A)*(c*x**2+a)**p,x)","\frac{A a^{p} e^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B a^{p} e^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*a**p*e**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2)) + B*a**p*e**m*x**2*x**m*gamma(m/2 + 1)*hyper((-p, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2))","C",0
503,1,394,0,15.848090," ","integrate(x**3*(e*x+d)*(c*x**2+a)**p,x)","\frac{a^{p} e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{5} + d \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: c = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{a}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{c x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{c x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 c^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 c^{2}} + \frac{x^{2}}{2 c} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{a c p x^{2} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{c^{2} p x^{4} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{c^{2} x^{4} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*e*x**5*hyper((5/2, -p), (7/2,), c*x**2*exp_polar(I*pi)/a)/5 + d*Piecewise((a**p*x**4/4, Eq(c, 0)), (a*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + a*log(I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + a/(2*a*c**2 + 2*c**3*x**2) + c*x**2*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + c*x**2*log(I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*c**2) - a*log(I*sqrt(a)*sqrt(1/c) + x)/(2*c**2) + x**2/(2*c), Eq(p, -1)), (-a**2*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + a*c*p*x**2*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + c**2*p*x**4*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + c**2*x**4*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2), True))","C",0
504,1,394,0,11.456590," ","integrate(x**2*(e*x+d)*(c*x**2+a)**p,x)","\frac{a^{p} d x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{3} + e \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: c = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{a}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{c x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} + \frac{c x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 a c^{2} + 2 c^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 c^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{c}} + x \right)}}{2 c^{2}} + \frac{x^{2}}{2 c} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{a c p x^{2} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{c^{2} p x^{4} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} + \frac{c^{2} x^{4} \left(a + c x^{2}\right)^{p}}{2 c^{2} p^{2} + 6 c^{2} p + 4 c^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x**3*hyper((3/2, -p), (5/2,), c*x**2*exp_polar(I*pi)/a)/3 + e*Piecewise((a**p*x**4/4, Eq(c, 0)), (a*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + a*log(I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + a/(2*a*c**2 + 2*c**3*x**2) + c*x**2*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2) + c*x**2*log(I*sqrt(a)*sqrt(1/c) + x)/(2*a*c**2 + 2*c**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/c) + x)/(2*c**2) - a*log(I*sqrt(a)*sqrt(1/c) + x)/(2*c**2) + x**2/(2*c), Eq(p, -1)), (-a**2*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + a*c*p*x**2*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + c**2*p*x**4*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2) + c**2*x**4*(a + c*x**2)**p/(2*c**2*p**2 + 6*c**2*p + 4*c**2), True))","C",0
505,1,65,0,8.818496," ","integrate(x*(e*x+d)*(c*x**2+a)**p,x)","\frac{a^{p} e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{3} + d \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\begin{cases} \frac{\left(a + c x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + c x^{2} \right)} & \text{otherwise} \end{cases}}{2 c} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*e*x**3*hyper((3/2, -p), (5/2,), c*x**2*exp_polar(I*pi)/a)/3 + d*Piecewise((a**p*x**2/2, Eq(c, 0)), (Piecewise(((a + c*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + c*x**2), True))/(2*c), True))","A",0
506,1,61,0,6.192670," ","integrate((e*x+d)*(c*x**2+a)**p,x)","a^{p} d x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)} + e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\begin{cases} \frac{\left(a + c x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + c x^{2} \right)} & \text{otherwise} \end{cases}}{2 c} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x*hyper((1/2, -p), (3/2,), c*x**2*exp_polar(I*pi)/a) + e*Piecewise((a**p*x**2/2, Eq(c, 0)), (Piecewise(((a + c*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + c*x**2), True))/(2*c), True))","A",0
507,1,65,0,9.448009," ","integrate((e*x+d)*(c*x**2+a)**p/x,x)","a^{p} e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)} - \frac{c^{p} d x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{c x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"a**p*e*x*hyper((1/2, -p), (3/2,), c*x**2*exp_polar(I*pi)/a) - c**p*d*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(c*x**2))/(2*gamma(1 - p))","C",0
508,1,68,0,9.892274," ","integrate((e*x+d)*(c*x**2+a)**p/x**2,x)","- \frac{a^{p} d {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{x} - \frac{c^{p} e x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{c x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-a**p*d*hyper((-1/2, -p), (1/2,), c*x**2*exp_polar(I*pi)/a)/x - c**p*e*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(c*x**2))/(2*gamma(1 - p))","C",0
509,1,71,0,13.601032," ","integrate((e*x+d)*(c*x**2+a)**p/x**3,x)","- \frac{a^{p} e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{x} - \frac{c^{p} d x^{2 p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{c x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)}"," ",0,"-a**p*e*hyper((-1/2, -p), (1/2,), c*x**2*exp_polar(I*pi)/a)/x - c**p*d*x**(2*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), a*exp_polar(I*pi)/(c*x**2))/(2*x**2*gamma(2 - p))","C",0
510,1,54,0,0.073421," ","integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{A a^{2} x^{5}}{5} + \frac{B b^{2} x^{8}}{8} + x^{7} \left(\frac{A b^{2}}{7} + \frac{2 B a b}{7}\right) + x^{6} \left(\frac{A a b}{3} + \frac{B a^{2}}{6}\right)"," ",0,"A*a**2*x**5/5 + B*b**2*x**8/8 + x**7*(A*b**2/7 + 2*B*a*b/7) + x**6*(A*a*b/3 + B*a**2/6)","A",0
511,1,54,0,0.074168," ","integrate(x**3*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{A a^{2} x^{4}}{4} + \frac{B b^{2} x^{7}}{7} + x^{6} \left(\frac{A b^{2}}{6} + \frac{B a b}{3}\right) + x^{5} \left(\frac{2 A a b}{5} + \frac{B a^{2}}{5}\right)"," ",0,"A*a**2*x**4/4 + B*b**2*x**7/7 + x**6*(A*b**2/6 + B*a*b/3) + x**5*(2*A*a*b/5 + B*a**2/5)","A",0
512,1,54,0,0.075186," ","integrate(x**2*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{A a^{2} x^{3}}{3} + \frac{B b^{2} x^{6}}{6} + x^{5} \left(\frac{A b^{2}}{5} + \frac{2 B a b}{5}\right) + x^{4} \left(\frac{A a b}{2} + \frac{B a^{2}}{4}\right)"," ",0,"A*a**2*x**3/3 + B*b**2*x**6/6 + x**5*(A*b**2/5 + 2*B*a*b/5) + x**4*(A*a*b/2 + B*a**2/4)","A",0
513,1,54,0,0.073235," ","integrate(x*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{A a^{2} x^{2}}{2} + \frac{B b^{2} x^{5}}{5} + x^{4} \left(\frac{A b^{2}}{4} + \frac{B a b}{2}\right) + x^{3} \left(\frac{2 A a b}{3} + \frac{B a^{2}}{3}\right)"," ",0,"A*a**2*x**2/2 + B*b**2*x**5/5 + x**4*(A*b**2/4 + B*a*b/2) + x**3*(2*A*a*b/3 + B*a**2/3)","A",0
514,1,49,0,0.071359," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} x + \frac{B b^{2} x^{4}}{4} + x^{3} \left(\frac{A b^{2}}{3} + \frac{2 B a b}{3}\right) + x^{2} \left(A a b + \frac{B a^{2}}{2}\right)"," ",0,"A*a**2*x + B*b**2*x**4/4 + x**3*(A*b**2/3 + 2*B*a*b/3) + x**2*(A*a*b + B*a**2/2)","A",0
515,1,46,0,0.136743," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x,x)","A a^{2} \log{\left(x \right)} + \frac{B b^{2} x^{3}}{3} + x^{2} \left(\frac{A b^{2}}{2} + B a b\right) + x \left(2 A a b + B a^{2}\right)"," ",0,"A*a**2*log(x) + B*b**2*x**3/3 + x**2*(A*b**2/2 + B*a*b) + x*(2*A*a*b + B*a**2)","A",0
516,1,42,0,0.183343," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**2,x)","- \frac{A a^{2}}{x} + \frac{B b^{2} x^{2}}{2} + a \left(2 A b + B a\right) \log{\left(x \right)} + x \left(A b^{2} + 2 B a b\right)"," ",0,"-A*a**2/x + B*b**2*x**2/2 + a*(2*A*b + B*a)*log(x) + x*(A*b**2 + 2*B*a*b)","A",0
517,1,46,0,0.325347," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**3,x)","B b^{2} x + b \left(A b + 2 B a\right) \log{\left(x \right)} + \frac{- A a^{2} + x \left(- 4 A a b - 2 B a^{2}\right)}{2 x^{2}}"," ",0,"B*b**2*x + b*(A*b + 2*B*a)*log(x) + (-A*a**2 + x*(-4*A*a*b - 2*B*a**2))/(2*x**2)","A",0
518,1,54,0,0.519160," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**4,x)","B b^{2} \log{\left(x \right)} + \frac{- 2 A a^{2} + x^{2} \left(- 6 A b^{2} - 12 B a b\right) + x \left(- 6 A a b - 3 B a^{2}\right)}{6 x^{3}}"," ",0,"B*b**2*log(x) + (-2*A*a**2 + x**2*(-6*A*b**2 - 12*B*a*b) + x*(-6*A*a*b - 3*B*a**2))/(6*x**3)","A",0
519,1,56,0,0.660658," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**5,x)","\frac{- 3 A a^{2} - 12 B b^{2} x^{3} + x^{2} \left(- 6 A b^{2} - 12 B a b\right) + x \left(- 8 A a b - 4 B a^{2}\right)}{12 x^{4}}"," ",0,"(-3*A*a**2 - 12*B*b**2*x**3 + x**2*(-6*A*b**2 - 12*B*a*b) + x*(-8*A*a*b - 4*B*a**2))/(12*x**4)","A",0
520,1,56,0,0.858633," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**6,x)","\frac{- 12 A a^{2} - 30 B b^{2} x^{3} + x^{2} \left(- 20 A b^{2} - 40 B a b\right) + x \left(- 30 A a b - 15 B a^{2}\right)}{60 x^{5}}"," ",0,"(-12*A*a**2 - 30*B*b**2*x**3 + x**2*(-20*A*b**2 - 40*B*a*b) + x*(-30*A*a*b - 15*B*a**2))/(60*x**5)","A",0
521,1,56,0,1.007581," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**7,x)","\frac{- 10 A a^{2} - 20 B b^{2} x^{3} + x^{2} \left(- 15 A b^{2} - 30 B a b\right) + x \left(- 24 A a b - 12 B a^{2}\right)}{60 x^{6}}"," ",0,"(-10*A*a**2 - 20*B*b**2*x**3 + x**2*(-15*A*b**2 - 30*B*a*b) + x*(-24*A*a*b - 12*B*a**2))/(60*x**6)","A",0
522,1,56,0,1.239890," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**8,x)","\frac{- 60 A a^{2} - 105 B b^{2} x^{3} + x^{2} \left(- 84 A b^{2} - 168 B a b\right) + x \left(- 140 A a b - 70 B a^{2}\right)}{420 x^{7}}"," ",0,"(-60*A*a**2 - 105*B*b**2*x**3 + x**2*(-84*A*b**2 - 168*B*a*b) + x*(-140*A*a*b - 70*B*a**2))/(420*x**7)","A",0
523,1,109,0,0.087296," ","integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{A a^{4} x^{5}}{5} + \frac{B b^{4} x^{10}}{10} + x^{9} \left(\frac{A b^{4}}{9} + \frac{4 B a b^{3}}{9}\right) + x^{8} \left(\frac{A a b^{3}}{2} + \frac{3 B a^{2} b^{2}}{4}\right) + x^{7} \left(\frac{6 A a^{2} b^{2}}{7} + \frac{4 B a^{3} b}{7}\right) + x^{6} \left(\frac{2 A a^{3} b}{3} + \frac{B a^{4}}{6}\right)"," ",0,"A*a**4*x**5/5 + B*b**4*x**10/10 + x**9*(A*b**4/9 + 4*B*a*b**3/9) + x**8*(A*a*b**3/2 + 3*B*a**2*b**2/4) + x**7*(6*A*a**2*b**2/7 + 4*B*a**3*b/7) + x**6*(2*A*a**3*b/3 + B*a**4/6)","A",0
524,1,105,0,0.087544," ","integrate(x**3*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{A a^{4} x^{4}}{4} + \frac{B b^{4} x^{9}}{9} + x^{8} \left(\frac{A b^{4}}{8} + \frac{B a b^{3}}{2}\right) + x^{7} \left(\frac{4 A a b^{3}}{7} + \frac{6 B a^{2} b^{2}}{7}\right) + x^{6} \left(A a^{2} b^{2} + \frac{2 B a^{3} b}{3}\right) + x^{5} \left(\frac{4 A a^{3} b}{5} + \frac{B a^{4}}{5}\right)"," ",0,"A*a**4*x**4/4 + B*b**4*x**9/9 + x**8*(A*b**4/8 + B*a*b**3/2) + x**7*(4*A*a*b**3/7 + 6*B*a**2*b**2/7) + x**6*(A*a**2*b**2 + 2*B*a**3*b/3) + x**5*(4*A*a**3*b/5 + B*a**4/5)","A",0
525,1,104,0,0.086710," ","integrate(x**2*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{A a^{4} x^{3}}{3} + \frac{B b^{4} x^{8}}{8} + x^{7} \left(\frac{A b^{4}}{7} + \frac{4 B a b^{3}}{7}\right) + x^{6} \left(\frac{2 A a b^{3}}{3} + B a^{2} b^{2}\right) + x^{5} \left(\frac{6 A a^{2} b^{2}}{5} + \frac{4 B a^{3} b}{5}\right) + x^{4} \left(A a^{3} b + \frac{B a^{4}}{4}\right)"," ",0,"A*a**4*x**3/3 + B*b**4*x**8/8 + x**7*(A*b**4/7 + 4*B*a*b**3/7) + x**6*(2*A*a*b**3/3 + B*a**2*b**2) + x**5*(6*A*a**2*b**2/5 + 4*B*a**3*b/5) + x**4*(A*a**3*b + B*a**4/4)","A",0
526,1,107,0,0.085761," ","integrate(x*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{A a^{4} x^{2}}{2} + \frac{B b^{4} x^{7}}{7} + x^{6} \left(\frac{A b^{4}}{6} + \frac{2 B a b^{3}}{3}\right) + x^{5} \left(\frac{4 A a b^{3}}{5} + \frac{6 B a^{2} b^{2}}{5}\right) + x^{4} \left(\frac{3 A a^{2} b^{2}}{2} + B a^{3} b\right) + x^{3} \left(\frac{4 A a^{3} b}{3} + \frac{B a^{4}}{3}\right)"," ",0,"A*a**4*x**2/2 + B*b**4*x**7/7 + x**6*(A*b**4/6 + 2*B*a*b**3/3) + x**5*(4*A*a*b**3/5 + 6*B*a**2*b**2/5) + x**4*(3*A*a**2*b**2/2 + B*a**3*b) + x**3*(4*A*a**3*b/3 + B*a**4/3)","B",0
527,1,100,0,0.088045," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} x + \frac{B b^{4} x^{6}}{6} + x^{5} \left(\frac{A b^{4}}{5} + \frac{4 B a b^{3}}{5}\right) + x^{4} \left(A a b^{3} + \frac{3 B a^{2} b^{2}}{2}\right) + x^{3} \left(2 A a^{2} b^{2} + \frac{4 B a^{3} b}{3}\right) + x^{2} \left(2 A a^{3} b + \frac{B a^{4}}{2}\right)"," ",0,"A*a**4*x + B*b**4*x**6/6 + x**5*(A*b**4/5 + 4*B*a*b**3/5) + x**4*(A*a*b**3 + 3*B*a**2*b**2/2) + x**3*(2*A*a**2*b**2 + 4*B*a**3*b/3) + x**2*(2*A*a**3*b + B*a**4/2)","B",0
528,1,95,0,0.206275," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x,x)","A a^{4} \log{\left(x \right)} + \frac{B b^{4} x^{5}}{5} + x^{4} \left(\frac{A b^{4}}{4} + B a b^{3}\right) + x^{3} \left(\frac{4 A a b^{3}}{3} + 2 B a^{2} b^{2}\right) + x^{2} \left(3 A a^{2} b^{2} + 2 B a^{3} b\right) + x \left(4 A a^{3} b + B a^{4}\right)"," ",0,"A*a**4*log(x) + B*b**4*x**5/5 + x**4*(A*b**4/4 + B*a*b**3) + x**3*(4*A*a*b**3/3 + 2*B*a**2*b**2) + x**2*(3*A*a**2*b**2 + 2*B*a**3*b) + x*(4*A*a**3*b + B*a**4)","A",0
529,1,94,0,0.256852," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**2,x)","- \frac{A a^{4}}{x} + \frac{B b^{4} x^{4}}{4} + a^{3} \left(4 A b + B a\right) \log{\left(x \right)} + x^{3} \left(\frac{A b^{4}}{3} + \frac{4 B a b^{3}}{3}\right) + x^{2} \left(2 A a b^{3} + 3 B a^{2} b^{2}\right) + x \left(6 A a^{2} b^{2} + 4 B a^{3} b\right)"," ",0,"-A*a**4/x + B*b**4*x**4/4 + a**3*(4*A*b + B*a)*log(x) + x**3*(A*b**4/3 + 4*B*a*b**3/3) + x**2*(2*A*a*b**3 + 3*B*a**2*b**2) + x*(6*A*a**2*b**2 + 4*B*a**3*b)","A",0
530,1,97,0,0.416885," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**3,x)","\frac{B b^{4} x^{3}}{3} + 2 a^{2} b \left(3 A b + 2 B a\right) \log{\left(x \right)} + x^{2} \left(\frac{A b^{4}}{2} + 2 B a b^{3}\right) + x \left(4 A a b^{3} + 6 B a^{2} b^{2}\right) + \frac{- A a^{4} + x \left(- 8 A a^{3} b - 2 B a^{4}\right)}{2 x^{2}}"," ",0,"B*b**4*x**3/3 + 2*a**2*b*(3*A*b + 2*B*a)*log(x) + x**2*(A*b**4/2 + 2*B*a*b**3) + x*(4*A*a*b**3 + 6*B*a**2*b**2) + (-A*a**4 + x*(-8*A*a**3*b - 2*B*a**4))/(2*x**2)","A",0
531,1,99,0,0.730813," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**4,x)","\frac{B b^{4} x^{2}}{2} + 2 a b^{2} \left(2 A b + 3 B a\right) \log{\left(x \right)} + x \left(A b^{4} + 4 B a b^{3}\right) + \frac{- 2 A a^{4} + x^{2} \left(- 36 A a^{2} b^{2} - 24 B a^{3} b\right) + x \left(- 12 A a^{3} b - 3 B a^{4}\right)}{6 x^{3}}"," ",0,"B*b**4*x**2/2 + 2*a*b**2*(2*A*b + 3*B*a)*log(x) + x*(A*b**4 + 4*B*a*b**3) + (-2*A*a**4 + x**2*(-36*A*a**2*b**2 - 24*B*a**3*b) + x*(-12*A*a**3*b - 3*B*a**4))/(6*x**3)","A",0
532,1,99,0,1.223414," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**5,x)","B b^{4} x + b^{3} \left(A b + 4 B a\right) \log{\left(x \right)} + \frac{- 3 A a^{4} + x^{3} \left(- 48 A a b^{3} - 72 B a^{2} b^{2}\right) + x^{2} \left(- 36 A a^{2} b^{2} - 24 B a^{3} b\right) + x \left(- 16 A a^{3} b - 4 B a^{4}\right)}{12 x^{4}}"," ",0,"B*b**4*x + b**3*(A*b + 4*B*a)*log(x) + (-3*A*a**4 + x**3*(-48*A*a*b**3 - 72*B*a**2*b**2) + x**2*(-36*A*a**2*b**2 - 24*B*a**3*b) + x*(-16*A*a**3*b - 4*B*a**4))/(12*x**4)","A",0
533,1,105,0,1.750044," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**6,x)","B b^{4} \log{\left(x \right)} + \frac{- 12 A a^{4} + x^{4} \left(- 60 A b^{4} - 240 B a b^{3}\right) + x^{3} \left(- 120 A a b^{3} - 180 B a^{2} b^{2}\right) + x^{2} \left(- 120 A a^{2} b^{2} - 80 B a^{3} b\right) + x \left(- 60 A a^{3} b - 15 B a^{4}\right)}{60 x^{5}}"," ",0,"B*b**4*log(x) + (-12*A*a**4 + x**4*(-60*A*b**4 - 240*B*a*b**3) + x**3*(-120*A*a*b**3 - 180*B*a**2*b**2) + x**2*(-120*A*a**2*b**2 - 80*B*a**3*b) + x*(-60*A*a**3*b - 15*B*a**4))/(60*x**5)","A",0
534,1,107,0,2.350132," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**7,x)","\frac{- 5 A a^{4} - 30 B b^{4} x^{5} + x^{4} \left(- 15 A b^{4} - 60 B a b^{3}\right) + x^{3} \left(- 40 A a b^{3} - 60 B a^{2} b^{2}\right) + x^{2} \left(- 45 A a^{2} b^{2} - 30 B a^{3} b\right) + x \left(- 24 A a^{3} b - 6 B a^{4}\right)}{30 x^{6}}"," ",0,"(-5*A*a**4 - 30*B*b**4*x**5 + x**4*(-15*A*b**4 - 60*B*a*b**3) + x**3*(-40*A*a*b**3 - 60*B*a**2*b**2) + x**2*(-45*A*a**2*b**2 - 30*B*a**3*b) + x*(-24*A*a**3*b - 6*B*a**4))/(30*x**6)","B",0
535,1,107,0,2.851671," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**8,x)","\frac{- 30 A a^{4} - 105 B b^{4} x^{5} + x^{4} \left(- 70 A b^{4} - 280 B a b^{3}\right) + x^{3} \left(- 210 A a b^{3} - 315 B a^{2} b^{2}\right) + x^{2} \left(- 252 A a^{2} b^{2} - 168 B a^{3} b\right) + x \left(- 140 A a^{3} b - 35 B a^{4}\right)}{210 x^{7}}"," ",0,"(-30*A*a**4 - 105*B*b**4*x**5 + x**4*(-70*A*b**4 - 280*B*a*b**3) + x**3*(-210*A*a*b**3 - 315*B*a**2*b**2) + x**2*(-252*A*a**2*b**2 - 168*B*a**3*b) + x*(-140*A*a**3*b - 35*B*a**4))/(210*x**7)","A",0
536,1,107,0,3.706899," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**9,x)","\frac{- 105 A a^{4} - 280 B b^{4} x^{5} + x^{4} \left(- 210 A b^{4} - 840 B a b^{3}\right) + x^{3} \left(- 672 A a b^{3} - 1008 B a^{2} b^{2}\right) + x^{2} \left(- 840 A a^{2} b^{2} - 560 B a^{3} b\right) + x \left(- 480 A a^{3} b - 120 B a^{4}\right)}{840 x^{8}}"," ",0,"(-105*A*a**4 - 280*B*b**4*x**5 + x**4*(-210*A*b**4 - 840*B*a*b**3) + x**3*(-672*A*a*b**3 - 1008*B*a**2*b**2) + x**2*(-840*A*a**2*b**2 - 560*B*a**3*b) + x*(-480*A*a**3*b - 120*B*a**4))/(840*x**8)","A",0
537,1,107,0,4.554909," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**10,x)","\frac{- 280 A a^{4} - 630 B b^{4} x^{5} + x^{4} \left(- 504 A b^{4} - 2016 B a b^{3}\right) + x^{3} \left(- 1680 A a b^{3} - 2520 B a^{2} b^{2}\right) + x^{2} \left(- 2160 A a^{2} b^{2} - 1440 B a^{3} b\right) + x \left(- 1260 A a^{3} b - 315 B a^{4}\right)}{2520 x^{9}}"," ",0,"(-280*A*a**4 - 630*B*b**4*x**5 + x**4*(-504*A*b**4 - 2016*B*a*b**3) + x**3*(-1680*A*a*b**3 - 2520*B*a**2*b**2) + x**2*(-2160*A*a**2*b**2 - 1440*B*a**3*b) + x*(-1260*A*a**3*b - 315*B*a**4))/(2520*x**9)","A",0
538,1,107,0,5.449816," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**11,x)","\frac{- 126 A a^{4} - 252 B b^{4} x^{5} + x^{4} \left(- 210 A b^{4} - 840 B a b^{3}\right) + x^{3} \left(- 720 A a b^{3} - 1080 B a^{2} b^{2}\right) + x^{2} \left(- 945 A a^{2} b^{2} - 630 B a^{3} b\right) + x \left(- 560 A a^{3} b - 140 B a^{4}\right)}{1260 x^{10}}"," ",0,"(-126*A*a**4 - 252*B*b**4*x**5 + x**4*(-210*A*b**4 - 840*B*a*b**3) + x**3*(-720*A*a*b**3 - 1080*B*a**2*b**2) + x**2*(-945*A*a**2*b**2 - 630*B*a**3*b) + x*(-560*A*a**3*b - 140*B*a**4))/(1260*x**10)","A",0
539,1,162,0,0.101629," ","integrate(x**5*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{A a^{6} x^{6}}{6} + \frac{B b^{6} x^{13}}{13} + x^{12} \left(\frac{A b^{6}}{12} + \frac{B a b^{5}}{2}\right) + x^{11} \left(\frac{6 A a b^{5}}{11} + \frac{15 B a^{2} b^{4}}{11}\right) + x^{10} \left(\frac{3 A a^{2} b^{4}}{2} + 2 B a^{3} b^{3}\right) + x^{9} \left(\frac{20 A a^{3} b^{3}}{9} + \frac{5 B a^{4} b^{2}}{3}\right) + x^{8} \left(\frac{15 A a^{4} b^{2}}{8} + \frac{3 B a^{5} b}{4}\right) + x^{7} \left(\frac{6 A a^{5} b}{7} + \frac{B a^{6}}{7}\right)"," ",0,"A*a**6*x**6/6 + B*b**6*x**13/13 + x**12*(A*b**6/12 + B*a*b**5/2) + x**11*(6*A*a*b**5/11 + 15*B*a**2*b**4/11) + x**10*(3*A*a**2*b**4/2 + 2*B*a**3*b**3) + x**9*(20*A*a**3*b**3/9 + 5*B*a**4*b**2/3) + x**8*(15*A*a**4*b**2/8 + 3*B*a**5*b/4) + x**7*(6*A*a**5*b/7 + B*a**6/7)","A",0
540,1,162,0,0.099689," ","integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{A a^{6} x^{5}}{5} + \frac{B b^{6} x^{12}}{12} + x^{11} \left(\frac{A b^{6}}{11} + \frac{6 B a b^{5}}{11}\right) + x^{10} \left(\frac{3 A a b^{5}}{5} + \frac{3 B a^{2} b^{4}}{2}\right) + x^{9} \left(\frac{5 A a^{2} b^{4}}{3} + \frac{20 B a^{3} b^{3}}{9}\right) + x^{8} \left(\frac{5 A a^{3} b^{3}}{2} + \frac{15 B a^{4} b^{2}}{8}\right) + x^{7} \left(\frac{15 A a^{4} b^{2}}{7} + \frac{6 B a^{5} b}{7}\right) + x^{6} \left(A a^{5} b + \frac{B a^{6}}{6}\right)"," ",0,"A*a**6*x**5/5 + B*b**6*x**12/12 + x**11*(A*b**6/11 + 6*B*a*b**5/11) + x**10*(3*A*a*b**5/5 + 3*B*a**2*b**4/2) + x**9*(5*A*a**2*b**4/3 + 20*B*a**3*b**3/9) + x**8*(5*A*a**3*b**3/2 + 15*B*a**4*b**2/8) + x**7*(15*A*a**4*b**2/7 + 6*B*a**5*b/7) + x**6*(A*a**5*b + B*a**6/6)","A",0
541,1,162,0,0.099992," ","integrate(x**3*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{A a^{6} x^{4}}{4} + \frac{B b^{6} x^{11}}{11} + x^{10} \left(\frac{A b^{6}}{10} + \frac{3 B a b^{5}}{5}\right) + x^{9} \left(\frac{2 A a b^{5}}{3} + \frac{5 B a^{2} b^{4}}{3}\right) + x^{8} \left(\frac{15 A a^{2} b^{4}}{8} + \frac{5 B a^{3} b^{3}}{2}\right) + x^{7} \left(\frac{20 A a^{3} b^{3}}{7} + \frac{15 B a^{4} b^{2}}{7}\right) + x^{6} \left(\frac{5 A a^{4} b^{2}}{2} + B a^{5} b\right) + x^{5} \left(\frac{6 A a^{5} b}{5} + \frac{B a^{6}}{5}\right)"," ",0,"A*a**6*x**4/4 + B*b**6*x**11/11 + x**10*(A*b**6/10 + 3*B*a*b**5/5) + x**9*(2*A*a*b**5/3 + 5*B*a**2*b**4/3) + x**8*(15*A*a**2*b**4/8 + 5*B*a**3*b**3/2) + x**7*(20*A*a**3*b**3/7 + 15*B*a**4*b**2/7) + x**6*(5*A*a**4*b**2/2 + B*a**5*b) + x**5*(6*A*a**5*b/5 + B*a**6/5)","A",0
542,1,163,0,0.101527," ","integrate(x**2*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{A a^{6} x^{3}}{3} + \frac{B b^{6} x^{10}}{10} + x^{9} \left(\frac{A b^{6}}{9} + \frac{2 B a b^{5}}{3}\right) + x^{8} \left(\frac{3 A a b^{5}}{4} + \frac{15 B a^{2} b^{4}}{8}\right) + x^{7} \left(\frac{15 A a^{2} b^{4}}{7} + \frac{20 B a^{3} b^{3}}{7}\right) + x^{6} \left(\frac{10 A a^{3} b^{3}}{3} + \frac{5 B a^{4} b^{2}}{2}\right) + x^{5} \left(3 A a^{4} b^{2} + \frac{6 B a^{5} b}{5}\right) + x^{4} \left(\frac{3 A a^{5} b}{2} + \frac{B a^{6}}{4}\right)"," ",0,"A*a**6*x**3/3 + B*b**6*x**10/10 + x**9*(A*b**6/9 + 2*B*a*b**5/3) + x**8*(3*A*a*b**5/4 + 15*B*a**2*b**4/8) + x**7*(15*A*a**2*b**4/7 + 20*B*a**3*b**3/7) + x**6*(10*A*a**3*b**3/3 + 5*B*a**4*b**2/2) + x**5*(3*A*a**4*b**2 + 6*B*a**5*b/5) + x**4*(3*A*a**5*b/2 + B*a**6/4)","B",0
543,1,160,0,0.098693," ","integrate(x*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{A a^{6} x^{2}}{2} + \frac{B b^{6} x^{9}}{9} + x^{8} \left(\frac{A b^{6}}{8} + \frac{3 B a b^{5}}{4}\right) + x^{7} \left(\frac{6 A a b^{5}}{7} + \frac{15 B a^{2} b^{4}}{7}\right) + x^{6} \left(\frac{5 A a^{2} b^{4}}{2} + \frac{10 B a^{3} b^{3}}{3}\right) + x^{5} \left(4 A a^{3} b^{3} + 3 B a^{4} b^{2}\right) + x^{4} \left(\frac{15 A a^{4} b^{2}}{4} + \frac{3 B a^{5} b}{2}\right) + x^{3} \left(2 A a^{5} b + \frac{B a^{6}}{3}\right)"," ",0,"A*a**6*x**2/2 + B*b**6*x**9/9 + x**8*(A*b**6/8 + 3*B*a*b**5/4) + x**7*(6*A*a*b**5/7 + 15*B*a**2*b**4/7) + x**6*(5*A*a**2*b**4/2 + 10*B*a**3*b**3/3) + x**5*(4*A*a**3*b**3 + 3*B*a**4*b**2) + x**4*(15*A*a**4*b**2/4 + 3*B*a**5*b/2) + x**3*(2*A*a**5*b + B*a**6/3)","B",0
544,1,148,0,0.097714," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","A a^{6} x + \frac{B b^{6} x^{8}}{8} + x^{7} \left(\frac{A b^{6}}{7} + \frac{6 B a b^{5}}{7}\right) + x^{6} \left(A a b^{5} + \frac{5 B a^{2} b^{4}}{2}\right) + x^{5} \left(3 A a^{2} b^{4} + 4 B a^{3} b^{3}\right) + x^{4} \left(5 A a^{3} b^{3} + \frac{15 B a^{4} b^{2}}{4}\right) + x^{3} \left(5 A a^{4} b^{2} + 2 B a^{5} b\right) + x^{2} \left(3 A a^{5} b + \frac{B a^{6}}{2}\right)"," ",0,"A*a**6*x + B*b**6*x**8/8 + x**7*(A*b**6/7 + 6*B*a*b**5/7) + x**6*(A*a*b**5 + 5*B*a**2*b**4/2) + x**5*(3*A*a**2*b**4 + 4*B*a**3*b**3) + x**4*(5*A*a**3*b**3 + 15*B*a**4*b**2/4) + x**3*(5*A*a**4*b**2 + 2*B*a**5*b) + x**2*(3*A*a**5*b + B*a**6/2)","B",0
545,1,148,0,0.280591," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x,x)","A a^{6} \log{\left(x \right)} + \frac{B b^{6} x^{7}}{7} + x^{6} \left(\frac{A b^{6}}{6} + B a b^{5}\right) + x^{5} \left(\frac{6 A a b^{5}}{5} + 3 B a^{2} b^{4}\right) + x^{4} \left(\frac{15 A a^{2} b^{4}}{4} + 5 B a^{3} b^{3}\right) + x^{3} \left(\frac{20 A a^{3} b^{3}}{3} + 5 B a^{4} b^{2}\right) + x^{2} \left(\frac{15 A a^{4} b^{2}}{2} + 3 B a^{5} b\right) + x \left(6 A a^{5} b + B a^{6}\right)"," ",0,"A*a**6*log(x) + B*b**6*x**7/7 + x**6*(A*b**6/6 + B*a*b**5) + x**5*(6*A*a*b**5/5 + 3*B*a**2*b**4) + x**4*(15*A*a**2*b**4/4 + 5*B*a**3*b**3) + x**3*(20*A*a**3*b**3/3 + 5*B*a**4*b**2) + x**2*(15*A*a**4*b**2/2 + 3*B*a**5*b) + x*(6*A*a**5*b + B*a**6)","A",0
546,1,148,0,0.329605," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**2,x)","- \frac{A a^{6}}{x} + \frac{B b^{6} x^{6}}{6} + a^{5} \left(6 A b + B a\right) \log{\left(x \right)} + x^{5} \left(\frac{A b^{6}}{5} + \frac{6 B a b^{5}}{5}\right) + x^{4} \left(\frac{3 A a b^{5}}{2} + \frac{15 B a^{2} b^{4}}{4}\right) + x^{3} \left(5 A a^{2} b^{4} + \frac{20 B a^{3} b^{3}}{3}\right) + x^{2} \left(10 A a^{3} b^{3} + \frac{15 B a^{4} b^{2}}{2}\right) + x \left(15 A a^{4} b^{2} + 6 B a^{5} b\right)"," ",0,"-A*a**6/x + B*b**6*x**6/6 + a**5*(6*A*b + B*a)*log(x) + x**5*(A*b**6/5 + 6*B*a*b**5/5) + x**4*(3*A*a*b**5/2 + 15*B*a**2*b**4/4) + x**3*(5*A*a**2*b**4 + 20*B*a**3*b**3/3) + x**2*(10*A*a**3*b**3 + 15*B*a**4*b**2/2) + x*(15*A*a**4*b**2 + 6*B*a**5*b)","A",0
547,1,148,0,0.512874," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**3,x)","\frac{B b^{6} x^{5}}{5} + 3 a^{4} b \left(5 A b + 2 B a\right) \log{\left(x \right)} + x^{4} \left(\frac{A b^{6}}{4} + \frac{3 B a b^{5}}{2}\right) + x^{3} \left(2 A a b^{5} + 5 B a^{2} b^{4}\right) + x^{2} \left(\frac{15 A a^{2} b^{4}}{2} + 10 B a^{3} b^{3}\right) + x \left(20 A a^{3} b^{3} + 15 B a^{4} b^{2}\right) + \frac{- A a^{6} + x \left(- 12 A a^{5} b - 2 B a^{6}\right)}{2 x^{2}}"," ",0,"B*b**6*x**5/5 + 3*a**4*b*(5*A*b + 2*B*a)*log(x) + x**4*(A*b**6/4 + 3*B*a*b**5/2) + x**3*(2*A*a*b**5 + 5*B*a**2*b**4) + x**2*(15*A*a**2*b**4/2 + 10*B*a**3*b**3) + x*(20*A*a**3*b**3 + 15*B*a**4*b**2) + (-A*a**6 + x*(-12*A*a**5*b - 2*B*a**6))/(2*x**2)","A",0
548,1,150,0,0.828642," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**4,x)","\frac{B b^{6} x^{4}}{4} + 5 a^{3} b^{2} \left(4 A b + 3 B a\right) \log{\left(x \right)} + x^{3} \left(\frac{A b^{6}}{3} + 2 B a b^{5}\right) + x^{2} \left(3 A a b^{5} + \frac{15 B a^{2} b^{4}}{2}\right) + x \left(15 A a^{2} b^{4} + 20 B a^{3} b^{3}\right) + \frac{- 2 A a^{6} + x^{2} \left(- 90 A a^{4} b^{2} - 36 B a^{5} b\right) + x \left(- 18 A a^{5} b - 3 B a^{6}\right)}{6 x^{3}}"," ",0,"B*b**6*x**4/4 + 5*a**3*b**2*(4*A*b + 3*B*a)*log(x) + x**3*(A*b**6/3 + 2*B*a*b**5) + x**2*(3*A*a*b**5 + 15*B*a**2*b**4/2) + x*(15*A*a**2*b**4 + 20*B*a**3*b**3) + (-2*A*a**6 + x**2*(-90*A*a**4*b**2 - 36*B*a**5*b) + x*(-18*A*a**5*b - 3*B*a**6))/(6*x**3)","A",0
549,1,150,0,1.346934," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**5,x)","\frac{B b^{6} x^{3}}{3} + 5 a^{2} b^{3} \left(3 A b + 4 B a\right) \log{\left(x \right)} + x^{2} \left(\frac{A b^{6}}{2} + 3 B a b^{5}\right) + x \left(6 A a b^{5} + 15 B a^{2} b^{4}\right) + \frac{- 3 A a^{6} + x^{3} \left(- 240 A a^{3} b^{3} - 180 B a^{4} b^{2}\right) + x^{2} \left(- 90 A a^{4} b^{2} - 36 B a^{5} b\right) + x \left(- 24 A a^{5} b - 4 B a^{6}\right)}{12 x^{4}}"," ",0,"B*b**6*x**3/3 + 5*a**2*b**3*(3*A*b + 4*B*a)*log(x) + x**2*(A*b**6/2 + 3*B*a*b**5) + x*(6*A*a*b**5 + 15*B*a**2*b**4) + (-3*A*a**6 + x**3*(-240*A*a**3*b**3 - 180*B*a**4*b**2) + x**2*(-90*A*a**4*b**2 - 36*B*a**5*b) + x*(-24*A*a**5*b - 4*B*a**6))/(12*x**4)","A",0
550,1,150,0,2.091780," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**6,x)","\frac{B b^{6} x^{2}}{2} + 3 a b^{4} \left(2 A b + 5 B a\right) \log{\left(x \right)} + x \left(A b^{6} + 6 B a b^{5}\right) + \frac{- 4 A a^{6} + x^{4} \left(- 300 A a^{2} b^{4} - 400 B a^{3} b^{3}\right) + x^{3} \left(- 200 A a^{3} b^{3} - 150 B a^{4} b^{2}\right) + x^{2} \left(- 100 A a^{4} b^{2} - 40 B a^{5} b\right) + x \left(- 30 A a^{5} b - 5 B a^{6}\right)}{20 x^{5}}"," ",0,"B*b**6*x**2/2 + 3*a*b**4*(2*A*b + 5*B*a)*log(x) + x*(A*b**6 + 6*B*a*b**5) + (-4*A*a**6 + x**4*(-300*A*a**2*b**4 - 400*B*a**3*b**3) + x**3*(-200*A*a**3*b**3 - 150*B*a**4*b**2) + x**2*(-100*A*a**4*b**2 - 40*B*a**5*b) + x*(-30*A*a**5*b - 5*B*a**6))/(20*x**5)","A",0
551,1,150,0,3.159984," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**7,x)","B b^{6} x + b^{5} \left(A b + 6 B a\right) \log{\left(x \right)} + \frac{- 10 A a^{6} + x^{5} \left(- 360 A a b^{5} - 900 B a^{2} b^{4}\right) + x^{4} \left(- 450 A a^{2} b^{4} - 600 B a^{3} b^{3}\right) + x^{3} \left(- 400 A a^{3} b^{3} - 300 B a^{4} b^{2}\right) + x^{2} \left(- 225 A a^{4} b^{2} - 90 B a^{5} b\right) + x \left(- 72 A a^{5} b - 12 B a^{6}\right)}{60 x^{6}}"," ",0,"B*b**6*x + b**5*(A*b + 6*B*a)*log(x) + (-10*A*a**6 + x**5*(-360*A*a*b**5 - 900*B*a**2*b**4) + x**4*(-450*A*a**2*b**4 - 600*B*a**3*b**3) + x**3*(-400*A*a**3*b**3 - 300*B*a**4*b**2) + x**2*(-225*A*a**4*b**2 - 90*B*a**5*b) + x*(-72*A*a**5*b - 12*B*a**6))/(60*x**6)","A",0
552,1,156,0,4.372184," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**8,x)","B b^{6} \log{\left(x \right)} + \frac{- 60 A a^{6} + x^{6} \left(- 420 A b^{6} - 2520 B a b^{5}\right) + x^{5} \left(- 1260 A a b^{5} - 3150 B a^{2} b^{4}\right) + x^{4} \left(- 2100 A a^{2} b^{4} - 2800 B a^{3} b^{3}\right) + x^{3} \left(- 2100 A a^{3} b^{3} - 1575 B a^{4} b^{2}\right) + x^{2} \left(- 1260 A a^{4} b^{2} - 504 B a^{5} b\right) + x \left(- 420 A a^{5} b - 70 B a^{6}\right)}{420 x^{7}}"," ",0,"B*b**6*log(x) + (-60*A*a**6 + x**6*(-420*A*b**6 - 2520*B*a*b**5) + x**5*(-1260*A*a*b**5 - 3150*B*a**2*b**4) + x**4*(-2100*A*a**2*b**4 - 2800*B*a**3*b**3) + x**3*(-2100*A*a**3*b**3 - 1575*B*a**4*b**2) + x**2*(-1260*A*a**4*b**2 - 504*B*a**5*b) + x*(-420*A*a**5*b - 70*B*a**6))/(420*x**7)","A",0
553,1,158,0,5.522521," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**9,x)","\frac{- 7 A a^{6} - 56 B b^{6} x^{7} + x^{6} \left(- 28 A b^{6} - 168 B a b^{5}\right) + x^{5} \left(- 112 A a b^{5} - 280 B a^{2} b^{4}\right) + x^{4} \left(- 210 A a^{2} b^{4} - 280 B a^{3} b^{3}\right) + x^{3} \left(- 224 A a^{3} b^{3} - 168 B a^{4} b^{2}\right) + x^{2} \left(- 140 A a^{4} b^{2} - 56 B a^{5} b\right) + x \left(- 48 A a^{5} b - 8 B a^{6}\right)}{56 x^{8}}"," ",0,"(-7*A*a**6 - 56*B*b**6*x**7 + x**6*(-28*A*b**6 - 168*B*a*b**5) + x**5*(-112*A*a*b**5 - 280*B*a**2*b**4) + x**4*(-210*A*a**2*b**4 - 280*B*a**3*b**3) + x**3*(-224*A*a**3*b**3 - 168*B*a**4*b**2) + x**2*(-140*A*a**4*b**2 - 56*B*a**5*b) + x*(-48*A*a**5*b - 8*B*a**6))/(56*x**8)","B",0
554,1,158,0,6.878868," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**10,x)","\frac{- 56 A a^{6} - 252 B b^{6} x^{7} + x^{6} \left(- 168 A b^{6} - 1008 B a b^{5}\right) + x^{5} \left(- 756 A a b^{5} - 1890 B a^{2} b^{4}\right) + x^{4} \left(- 1512 A a^{2} b^{4} - 2016 B a^{3} b^{3}\right) + x^{3} \left(- 1680 A a^{3} b^{3} - 1260 B a^{4} b^{2}\right) + x^{2} \left(- 1080 A a^{4} b^{2} - 432 B a^{5} b\right) + x \left(- 378 A a^{5} b - 63 B a^{6}\right)}{504 x^{9}}"," ",0,"(-56*A*a**6 - 252*B*b**6*x**7 + x**6*(-168*A*b**6 - 1008*B*a*b**5) + x**5*(-756*A*a*b**5 - 1890*B*a**2*b**4) + x**4*(-1512*A*a**2*b**4 - 2016*B*a**3*b**3) + x**3*(-1680*A*a**3*b**3 - 1260*B*a**4*b**2) + x**2*(-1080*A*a**4*b**2 - 432*B*a**5*b) + x*(-378*A*a**5*b - 63*B*a**6))/(504*x**9)","B",0
555,1,158,0,9.000960," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**11,x)","\frac{- 252 A a^{6} - 840 B b^{6} x^{7} + x^{6} \left(- 630 A b^{6} - 3780 B a b^{5}\right) + x^{5} \left(- 3024 A a b^{5} - 7560 B a^{2} b^{4}\right) + x^{4} \left(- 6300 A a^{2} b^{4} - 8400 B a^{3} b^{3}\right) + x^{3} \left(- 7200 A a^{3} b^{3} - 5400 B a^{4} b^{2}\right) + x^{2} \left(- 4725 A a^{4} b^{2} - 1890 B a^{5} b\right) + x \left(- 1680 A a^{5} b - 280 B a^{6}\right)}{2520 x^{10}}"," ",0,"(-252*A*a**6 - 840*B*b**6*x**7 + x**6*(-630*A*b**6 - 3780*B*a*b**5) + x**5*(-3024*A*a*b**5 - 7560*B*a**2*b**4) + x**4*(-6300*A*a**2*b**4 - 8400*B*a**3*b**3) + x**3*(-7200*A*a**3*b**3 - 5400*B*a**4*b**2) + x**2*(-4725*A*a**4*b**2 - 1890*B*a**5*b) + x*(-1680*A*a**5*b - 280*B*a**6))/(2520*x**10)","A",0
556,1,158,0,11.113651," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**12,x)","\frac{- 840 A a^{6} - 2310 B b^{6} x^{7} + x^{6} \left(- 1848 A b^{6} - 11088 B a b^{5}\right) + x^{5} \left(- 9240 A a b^{5} - 23100 B a^{2} b^{4}\right) + x^{4} \left(- 19800 A a^{2} b^{4} - 26400 B a^{3} b^{3}\right) + x^{3} \left(- 23100 A a^{3} b^{3} - 17325 B a^{4} b^{2}\right) + x^{2} \left(- 15400 A a^{4} b^{2} - 6160 B a^{5} b\right) + x \left(- 5544 A a^{5} b - 924 B a^{6}\right)}{9240 x^{11}}"," ",0,"(-840*A*a**6 - 2310*B*b**6*x**7 + x**6*(-1848*A*b**6 - 11088*B*a*b**5) + x**5*(-9240*A*a*b**5 - 23100*B*a**2*b**4) + x**4*(-19800*A*a**2*b**4 - 26400*B*a**3*b**3) + x**3*(-23100*A*a**3*b**3 - 17325*B*a**4*b**2) + x**2*(-15400*A*a**4*b**2 - 6160*B*a**5*b) + x*(-5544*A*a**5*b - 924*B*a**6))/(9240*x**11)","A",0
557,1,158,0,13.840608," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**13,x)","\frac{- 2310 A a^{6} - 5544 B b^{6} x^{7} + x^{6} \left(- 4620 A b^{6} - 27720 B a b^{5}\right) + x^{5} \left(- 23760 A a b^{5} - 59400 B a^{2} b^{4}\right) + x^{4} \left(- 51975 A a^{2} b^{4} - 69300 B a^{3} b^{3}\right) + x^{3} \left(- 61600 A a^{3} b^{3} - 46200 B a^{4} b^{2}\right) + x^{2} \left(- 41580 A a^{4} b^{2} - 16632 B a^{5} b\right) + x \left(- 15120 A a^{5} b - 2520 B a^{6}\right)}{27720 x^{12}}"," ",0,"(-2310*A*a**6 - 5544*B*b**6*x**7 + x**6*(-4620*A*b**6 - 27720*B*a*b**5) + x**5*(-23760*A*a*b**5 - 59400*B*a**2*b**4) + x**4*(-51975*A*a**2*b**4 - 69300*B*a**3*b**3) + x**3*(-61600*A*a**3*b**3 - 46200*B*a**4*b**2) + x**2*(-41580*A*a**4*b**2 - 16632*B*a**5*b) + x*(-15120*A*a**5*b - 2520*B*a**6))/(27720*x**12)","A",0
558,1,158,0,17.514286," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**14,x)","\frac{- 5544 A a^{6} - 12012 B b^{6} x^{7} + x^{6} \left(- 10296 A b^{6} - 61776 B a b^{5}\right) + x^{5} \left(- 54054 A a b^{5} - 135135 B a^{2} b^{4}\right) + x^{4} \left(- 120120 A a^{2} b^{4} - 160160 B a^{3} b^{3}\right) + x^{3} \left(- 144144 A a^{3} b^{3} - 108108 B a^{4} b^{2}\right) + x^{2} \left(- 98280 A a^{4} b^{2} - 39312 B a^{5} b\right) + x \left(- 36036 A a^{5} b - 6006 B a^{6}\right)}{72072 x^{13}}"," ",0,"(-5544*A*a**6 - 12012*B*b**6*x**7 + x**6*(-10296*A*b**6 - 61776*B*a*b**5) + x**5*(-54054*A*a*b**5 - 135135*B*a**2*b**4) + x**4*(-120120*A*a**2*b**4 - 160160*B*a**3*b**3) + x**3*(-144144*A*a**3*b**3 - 108108*B*a**4*b**2) + x**2*(-98280*A*a**4*b**2 - 39312*B*a**5*b) + x*(-36036*A*a**5*b - 6006*B*a**6))/(72072*x**13)","A",0
559,1,133,0,0.098333," ","integrate(x**7*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{8}}{8} + \frac{e x^{19}}{19} + x^{18} \left(\frac{d}{18} + \frac{5 e}{9}\right) + x^{17} \left(\frac{10 d}{17} + \frac{45 e}{17}\right) + x^{16} \left(\frac{45 d}{16} + \frac{15 e}{2}\right) + x^{15} \left(8 d + 14 e\right) + x^{14} \left(15 d + 18 e\right) + x^{13} \left(\frac{252 d}{13} + \frac{210 e}{13}\right) + x^{12} \left(\frac{35 d}{2} + 10 e\right) + x^{11} \left(\frac{120 d}{11} + \frac{45 e}{11}\right) + x^{10} \left(\frac{9 d}{2} + e\right) + x^{9} \left(\frac{10 d}{9} + \frac{e}{9}\right)"," ",0,"d*x**8/8 + e*x**19/19 + x**18*(d/18 + 5*e/9) + x**17*(10*d/17 + 45*e/17) + x**16*(45*d/16 + 15*e/2) + x**15*(8*d + 14*e) + x**14*(15*d + 18*e) + x**13*(252*d/13 + 210*e/13) + x**12*(35*d/2 + 10*e) + x**11*(120*d/11 + 45*e/11) + x**10*(9*d/2 + e) + x**9*(10*d/9 + e/9)","A",0
560,1,134,0,0.096811," ","integrate(x**6*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{7}}{7} + \frac{e x^{18}}{18} + x^{17} \left(\frac{d}{17} + \frac{10 e}{17}\right) + x^{16} \left(\frac{5 d}{8} + \frac{45 e}{16}\right) + x^{15} \left(3 d + 8 e\right) + x^{14} \left(\frac{60 d}{7} + 15 e\right) + x^{13} \left(\frac{210 d}{13} + \frac{252 e}{13}\right) + x^{12} \left(21 d + \frac{35 e}{2}\right) + x^{11} \left(\frac{210 d}{11} + \frac{120 e}{11}\right) + x^{10} \left(12 d + \frac{9 e}{2}\right) + x^{9} \left(5 d + \frac{10 e}{9}\right) + x^{8} \left(\frac{5 d}{4} + \frac{e}{8}\right)"," ",0,"d*x**7/7 + e*x**18/18 + x**17*(d/17 + 10*e/17) + x**16*(5*d/8 + 45*e/16) + x**15*(3*d + 8*e) + x**14*(60*d/7 + 15*e) + x**13*(210*d/13 + 252*e/13) + x**12*(21*d + 35*e/2) + x**11*(210*d/11 + 120*e/11) + x**10*(12*d + 9*e/2) + x**9*(5*d + 10*e/9) + x**8*(5*d/4 + e/8)","A",0
561,1,136,0,0.097585," ","integrate(x**5*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{6}}{6} + \frac{e x^{17}}{17} + x^{16} \left(\frac{d}{16} + \frac{5 e}{8}\right) + x^{15} \left(\frac{2 d}{3} + 3 e\right) + x^{14} \left(\frac{45 d}{14} + \frac{60 e}{7}\right) + x^{13} \left(\frac{120 d}{13} + \frac{210 e}{13}\right) + x^{12} \left(\frac{35 d}{2} + 21 e\right) + x^{11} \left(\frac{252 d}{11} + \frac{210 e}{11}\right) + x^{10} \left(21 d + 12 e\right) + x^{9} \left(\frac{40 d}{3} + 5 e\right) + x^{8} \left(\frac{45 d}{8} + \frac{5 e}{4}\right) + x^{7} \left(\frac{10 d}{7} + \frac{e}{7}\right)"," ",0,"d*x**6/6 + e*x**17/17 + x**16*(d/16 + 5*e/8) + x**15*(2*d/3 + 3*e) + x**14*(45*d/14 + 60*e/7) + x**13*(120*d/13 + 210*e/13) + x**12*(35*d/2 + 21*e) + x**11*(252*d/11 + 210*e/11) + x**10*(21*d + 12*e) + x**9*(40*d/3 + 5*e) + x**8*(45*d/8 + 5*e/4) + x**7*(10*d/7 + e/7)","A",0
562,1,139,0,0.095803," ","integrate(x**4*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{5}}{5} + \frac{e x^{16}}{16} + x^{15} \left(\frac{d}{15} + \frac{2 e}{3}\right) + x^{14} \left(\frac{5 d}{7} + \frac{45 e}{14}\right) + x^{13} \left(\frac{45 d}{13} + \frac{120 e}{13}\right) + x^{12} \left(10 d + \frac{35 e}{2}\right) + x^{11} \left(\frac{210 d}{11} + \frac{252 e}{11}\right) + x^{10} \left(\frac{126 d}{5} + 21 e\right) + x^{9} \left(\frac{70 d}{3} + \frac{40 e}{3}\right) + x^{8} \left(15 d + \frac{45 e}{8}\right) + x^{7} \left(\frac{45 d}{7} + \frac{10 e}{7}\right) + x^{6} \left(\frac{5 d}{3} + \frac{e}{6}\right)"," ",0,"d*x**5/5 + e*x**16/16 + x**15*(d/15 + 2*e/3) + x**14*(5*d/7 + 45*e/14) + x**13*(45*d/13 + 120*e/13) + x**12*(10*d + 35*e/2) + x**11*(210*d/11 + 252*e/11) + x**10*(126*d/5 + 21*e) + x**9*(70*d/3 + 40*e/3) + x**8*(15*d + 45*e/8) + x**7*(45*d/7 + 10*e/7) + x**6*(5*d/3 + e/6)","A",0
563,1,136,0,0.096356," ","integrate(x**3*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{4}}{4} + \frac{e x^{15}}{15} + x^{14} \left(\frac{d}{14} + \frac{5 e}{7}\right) + x^{13} \left(\frac{10 d}{13} + \frac{45 e}{13}\right) + x^{12} \left(\frac{15 d}{4} + 10 e\right) + x^{11} \left(\frac{120 d}{11} + \frac{210 e}{11}\right) + x^{10} \left(21 d + \frac{126 e}{5}\right) + x^{9} \left(28 d + \frac{70 e}{3}\right) + x^{8} \left(\frac{105 d}{4} + 15 e\right) + x^{7} \left(\frac{120 d}{7} + \frac{45 e}{7}\right) + x^{6} \left(\frac{15 d}{2} + \frac{5 e}{3}\right) + x^{5} \left(2 d + \frac{e}{5}\right)"," ",0,"d*x**4/4 + e*x**15/15 + x**14*(d/14 + 5*e/7) + x**13*(10*d/13 + 45*e/13) + x**12*(15*d/4 + 10*e) + x**11*(120*d/11 + 210*e/11) + x**10*(21*d + 126*e/5) + x**9*(28*d + 70*e/3) + x**8*(105*d/4 + 15*e) + x**7*(120*d/7 + 45*e/7) + x**6*(15*d/2 + 5*e/3) + x**5*(2*d + e/5)","B",0
564,1,133,0,0.097298," ","integrate(x**2*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{3}}{3} + \frac{e x^{14}}{14} + x^{13} \left(\frac{d}{13} + \frac{10 e}{13}\right) + x^{12} \left(\frac{5 d}{6} + \frac{15 e}{4}\right) + x^{11} \left(\frac{45 d}{11} + \frac{120 e}{11}\right) + x^{10} \left(12 d + 21 e\right) + x^{9} \left(\frac{70 d}{3} + 28 e\right) + x^{8} \left(\frac{63 d}{2} + \frac{105 e}{4}\right) + x^{7} \left(30 d + \frac{120 e}{7}\right) + x^{6} \left(20 d + \frac{15 e}{2}\right) + x^{5} \left(9 d + 2 e\right) + x^{4} \left(\frac{5 d}{2} + \frac{e}{4}\right)"," ",0,"d*x**3/3 + e*x**14/14 + x**13*(d/13 + 10*e/13) + x**12*(5*d/6 + 15*e/4) + x**11*(45*d/11 + 120*e/11) + x**10*(12*d + 21*e) + x**9*(70*d/3 + 28*e) + x**8*(63*d/2 + 105*e/4) + x**7*(30*d + 120*e/7) + x**6*(20*d + 15*e/2) + x**5*(9*d + 2*e) + x**4*(5*d/2 + e/4)","B",0
565,1,133,0,0.097188," ","integrate(x*(e*x+d)*(x**2+2*x+1)**5,x)","\frac{d x^{2}}{2} + \frac{e x^{13}}{13} + x^{12} \left(\frac{d}{12} + \frac{5 e}{6}\right) + x^{11} \left(\frac{10 d}{11} + \frac{45 e}{11}\right) + x^{10} \left(\frac{9 d}{2} + 12 e\right) + x^{9} \left(\frac{40 d}{3} + \frac{70 e}{3}\right) + x^{8} \left(\frac{105 d}{4} + \frac{63 e}{2}\right) + x^{7} \left(36 d + 30 e\right) + x^{6} \left(35 d + 20 e\right) + x^{5} \left(24 d + 9 e\right) + x^{4} \left(\frac{45 d}{4} + \frac{5 e}{2}\right) + x^{3} \left(\frac{10 d}{3} + \frac{e}{3}\right)"," ",0,"d*x**2/2 + e*x**13/13 + x**12*(d/12 + 5*e/6) + x**11*(10*d/11 + 45*e/11) + x**10*(9*d/2 + 12*e) + x**9*(40*d/3 + 70*e/3) + x**8*(105*d/4 + 63*e/2) + x**7*(36*d + 30*e) + x**6*(35*d + 20*e) + x**5*(24*d + 9*e) + x**4*(45*d/4 + 5*e/2) + x**3*(10*d/3 + e/3)","B",0
566,1,119,0,0.097412," ","integrate((e*x+d)*(x**2+2*x+1)**5,x)","d x + \frac{e x^{12}}{12} + x^{11} \left(\frac{d}{11} + \frac{10 e}{11}\right) + x^{10} \left(d + \frac{9 e}{2}\right) + x^{9} \left(5 d + \frac{40 e}{3}\right) + x^{8} \left(15 d + \frac{105 e}{4}\right) + x^{7} \left(30 d + 36 e\right) + x^{6} \left(42 d + 35 e\right) + x^{5} \left(42 d + 24 e\right) + x^{4} \left(30 d + \frac{45 e}{4}\right) + x^{3} \left(15 d + \frac{10 e}{3}\right) + x^{2} \left(5 d + \frac{e}{2}\right)"," ",0,"d*x + e*x**12/12 + x**11*(d/11 + 10*e/11) + x**10*(d + 9*e/2) + x**9*(5*d + 40*e/3) + x**8*(15*d + 105*e/4) + x**7*(30*d + 36*e) + x**6*(42*d + 35*e) + x**5*(42*d + 24*e) + x**4*(30*d + 45*e/4) + x**3*(15*d + 10*e/3) + x**2*(5*d + e/2)","B",0
567,1,117,0,0.313103," ","integrate((e*x+d)*(x**2+2*x+1)**5/x,x)","d \log{\left(x \right)} + \frac{e x^{11}}{11} + x^{10} \left(\frac{d}{10} + e\right) + x^{9} \left(\frac{10 d}{9} + 5 e\right) + x^{8} \left(\frac{45 d}{8} + 15 e\right) + x^{7} \left(\frac{120 d}{7} + 30 e\right) + x^{6} \left(35 d + 42 e\right) + x^{5} \left(\frac{252 d}{5} + 42 e\right) + x^{4} \left(\frac{105 d}{2} + 30 e\right) + x^{3} \left(40 d + 15 e\right) + x^{2} \left(\frac{45 d}{2} + 5 e\right) + x \left(10 d + e\right)"," ",0,"d*log(x) + e*x**11/11 + x**10*(d/10 + e) + x**9*(10*d/9 + 5*e) + x**8*(45*d/8 + 15*e) + x**7*(120*d/7 + 30*e) + x**6*(35*d + 42*e) + x**5*(252*d/5 + 42*e) + x**4*(105*d/2 + 30*e) + x**3*(40*d + 15*e) + x**2*(45*d/2 + 5*e) + x*(10*d + e)","A",0
568,1,121,0,0.355379," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**2,x)","- \frac{d}{x} + \frac{e x^{10}}{10} + x^{9} \left(\frac{d}{9} + \frac{10 e}{9}\right) + x^{8} \left(\frac{5 d}{4} + \frac{45 e}{8}\right) + x^{7} \left(\frac{45 d}{7} + \frac{120 e}{7}\right) + x^{6} \left(20 d + 35 e\right) + x^{5} \left(42 d + \frac{252 e}{5}\right) + x^{4} \left(63 d + \frac{105 e}{2}\right) + x^{3} \left(70 d + 40 e\right) + x^{2} \left(60 d + \frac{45 e}{2}\right) + x \left(45 d + 10 e\right) + \left(10 d + e\right) \log{\left(x \right)}"," ",0,"-d/x + e*x**10/10 + x**9*(d/9 + 10*e/9) + x**8*(5*d/4 + 45*e/8) + x**7*(45*d/7 + 120*e/7) + x**6*(20*d + 35*e) + x**5*(42*d + 252*e/5) + x**4*(63*d + 105*e/2) + x**3*(70*d + 40*e) + x**2*(60*d + 45*e/2) + x*(45*d + 10*e) + (10*d + e)*log(x)","A",0
569,1,122,0,0.452657," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**3,x)","\frac{e x^{9}}{9} + x^{8} \left(\frac{d}{8} + \frac{5 e}{4}\right) + x^{7} \left(\frac{10 d}{7} + \frac{45 e}{7}\right) + x^{6} \left(\frac{15 d}{2} + 20 e\right) + x^{5} \left(24 d + 42 e\right) + x^{4} \left(\frac{105 d}{2} + 63 e\right) + x^{3} \left(84 d + 70 e\right) + x^{2} \left(105 d + 60 e\right) + x \left(120 d + 45 e\right) + 5 \left(9 d + 2 e\right) \log{\left(x \right)} + \frac{- d + x \left(- 20 d - 2 e\right)}{2 x^{2}}"," ",0,"e*x**9/9 + x**8*(d/8 + 5*e/4) + x**7*(10*d/7 + 45*e/7) + x**6*(15*d/2 + 20*e) + x**5*(24*d + 42*e) + x**4*(105*d/2 + 63*e) + x**3*(84*d + 70*e) + x**2*(105*d + 60*e) + x*(120*d + 45*e) + 5*(9*d + 2*e)*log(x) + (-d + x*(-20*d - 2*e))/(2*x**2)","A",0
570,1,124,0,0.650256," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**4,x)","\frac{e x^{8}}{8} + x^{7} \left(\frac{d}{7} + \frac{10 e}{7}\right) + x^{6} \left(\frac{5 d}{3} + \frac{15 e}{2}\right) + x^{5} \left(9 d + 24 e\right) + x^{4} \left(30 d + \frac{105 e}{2}\right) + x^{3} \left(70 d + 84 e\right) + x^{2} \left(126 d + 105 e\right) + x \left(210 d + 120 e\right) + 15 \left(8 d + 3 e\right) \log{\left(x \right)} + \frac{- 2 d + x^{2} \left(- 270 d - 60 e\right) + x \left(- 30 d - 3 e\right)}{6 x^{3}}"," ",0,"e*x**8/8 + x**7*(d/7 + 10*e/7) + x**6*(5*d/3 + 15*e/2) + x**5*(9*d + 24*e) + x**4*(30*d + 105*e/2) + x**3*(70*d + 84*e) + x**2*(126*d + 105*e) + x*(210*d + 120*e) + 15*(8*d + 3*e)*log(x) + (-2*d + x**2*(-270*d - 60*e) + x*(-30*d - 3*e))/(6*x**3)","A",0
571,1,122,0,1.000058," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**5,x)","\frac{e x^{7}}{7} + x^{6} \left(\frac{d}{6} + \frac{5 e}{3}\right) + x^{5} \left(2 d + 9 e\right) + x^{4} \left(\frac{45 d}{4} + 30 e\right) + x^{3} \left(40 d + 70 e\right) + x^{2} \left(105 d + 126 e\right) + x \left(252 d + 210 e\right) + 30 \left(7 d + 4 e\right) \log{\left(x \right)} + \frac{- 3 d + x^{3} \left(- 1440 d - 540 e\right) + x^{2} \left(- 270 d - 60 e\right) + x \left(- 40 d - 4 e\right)}{12 x^{4}}"," ",0,"e*x**7/7 + x**6*(d/6 + 5*e/3) + x**5*(2*d + 9*e) + x**4*(45*d/4 + 30*e) + x**3*(40*d + 70*e) + x**2*(105*d + 126*e) + x*(252*d + 210*e) + 30*(7*d + 4*e)*log(x) + (-3*d + x**3*(-1440*d - 540*e) + x**2*(-270*d - 60*e) + x*(-40*d - 4*e))/(12*x**4)","A",0
572,1,124,0,1.418752," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**6,x)","\frac{e x^{6}}{6} + x^{5} \left(\frac{d}{5} + 2 e\right) + x^{4} \left(\frac{5 d}{2} + \frac{45 e}{4}\right) + x^{3} \left(15 d + 40 e\right) + x^{2} \left(60 d + 105 e\right) + x \left(210 d + 252 e\right) + 42 \left(6 d + 5 e\right) \log{\left(x \right)} + \frac{- 12 d + x^{4} \left(- 12600 d - 7200 e\right) + x^{3} \left(- 3600 d - 1350 e\right) + x^{2} \left(- 900 d - 200 e\right) + x \left(- 150 d - 15 e\right)}{60 x^{5}}"," ",0,"e*x**6/6 + x**5*(d/5 + 2*e) + x**4*(5*d/2 + 45*e/4) + x**3*(15*d + 40*e) + x**2*(60*d + 105*e) + x*(210*d + 252*e) + 42*(6*d + 5*e)*log(x) + (-12*d + x**4*(-12600*d - 7200*e) + x**3*(-3600*d - 1350*e) + x**2*(-900*d - 200*e) + x*(-150*d - 15*e))/(60*x**5)","A",0
573,1,128,0,2.166867," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**7,x)","\frac{e x^{5}}{5} + x^{4} \left(\frac{d}{4} + \frac{5 e}{2}\right) + x^{3} \left(\frac{10 d}{3} + 15 e\right) + x^{2} \left(\frac{45 d}{2} + 60 e\right) + x \left(120 d + 210 e\right) + 42 \left(5 d + 6 e\right) \log{\left(x \right)} + \frac{- 10 d + x^{5} \left(- 15120 d - 12600 e\right) + x^{4} \left(- 6300 d - 3600 e\right) + x^{3} \left(- 2400 d - 900 e\right) + x^{2} \left(- 675 d - 150 e\right) + x \left(- 120 d - 12 e\right)}{60 x^{6}}"," ",0,"e*x**5/5 + x**4*(d/4 + 5*e/2) + x**3*(10*d/3 + 15*e) + x**2*(45*d/2 + 60*e) + x*(120*d + 210*e) + 42*(5*d + 6*e)*log(x) + (-10*d + x**5*(-15120*d - 12600*e) + x**4*(-6300*d - 3600*e) + x**3*(-2400*d - 900*e) + x**2*(-675*d - 150*e) + x*(-120*d - 12*e))/(60*x**6)","A",0
574,1,128,0,2.986118," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**8,x)","\frac{e x^{4}}{4} + x^{3} \left(\frac{d}{3} + \frac{10 e}{3}\right) + x^{2} \left(5 d + \frac{45 e}{2}\right) + x \left(45 d + 120 e\right) + 30 \left(4 d + 7 e\right) \log{\left(x \right)} + \frac{- 12 d + x^{6} \left(- 17640 d - 21168 e\right) + x^{5} \left(- 10584 d - 8820 e\right) + x^{4} \left(- 5880 d - 3360 e\right) + x^{3} \left(- 2520 d - 945 e\right) + x^{2} \left(- 756 d - 168 e\right) + x \left(- 140 d - 14 e\right)}{84 x^{7}}"," ",0,"e*x**4/4 + x**3*(d/3 + 10*e/3) + x**2*(5*d + 45*e/2) + x*(45*d + 120*e) + 30*(4*d + 7*e)*log(x) + (-12*d + x**6*(-17640*d - 21168*e) + x**5*(-10584*d - 8820*e) + x**4*(-5880*d - 3360*e) + x**3*(-2520*d - 945*e) + x**2*(-756*d - 168*e) + x*(-140*d - 14*e))/(84*x**7)","A",0
575,1,126,0,4.273008," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**9,x)","\frac{e x^{3}}{3} + x^{2} \left(\frac{d}{2} + 5 e\right) + x \left(10 d + 45 e\right) + 15 \left(3 d + 8 e\right) \log{\left(x \right)} + \frac{- 21 d + x^{7} \left(- 20160 d - 35280 e\right) + x^{6} \left(- 17640 d - 21168 e\right) + x^{5} \left(- 14112 d - 11760 e\right) + x^{4} \left(- 8820 d - 5040 e\right) + x^{3} \left(- 4032 d - 1512 e\right) + x^{2} \left(- 1260 d - 280 e\right) + x \left(- 240 d - 24 e\right)}{168 x^{8}}"," ",0,"e*x**3/3 + x**2*(d/2 + 5*e) + x*(10*d + 45*e) + 15*(3*d + 8*e)*log(x) + (-21*d + x**7*(-20160*d - 35280*e) + x**6*(-17640*d - 21168*e) + x**5*(-14112*d - 11760*e) + x**4*(-8820*d - 5040*e) + x**3*(-4032*d - 1512*e) + x**2*(-1260*d - 280*e) + x*(-240*d - 24*e))/(168*x**8)","A",0
576,1,126,0,5.587714," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**10,x)","\frac{e x^{2}}{2} + x \left(d + 10 e\right) + 5 \left(2 d + 9 e\right) \log{\left(x \right)} + \frac{- 56 d + x^{8} \left(- 22680 d - 60480 e\right) + x^{7} \left(- 30240 d - 52920 e\right) + x^{6} \left(- 35280 d - 42336 e\right) + x^{5} \left(- 31752 d - 26460 e\right) + x^{4} \left(- 21168 d - 12096 e\right) + x^{3} \left(- 10080 d - 3780 e\right) + x^{2} \left(- 3240 d - 720 e\right) + x \left(- 630 d - 63 e\right)}{504 x^{9}}"," ",0,"e*x**2/2 + x*(d + 10*e) + 5*(2*d + 9*e)*log(x) + (-56*d + x**8*(-22680*d - 60480*e) + x**7*(-30240*d - 52920*e) + x**6*(-35280*d - 42336*e) + x**5*(-31752*d - 26460*e) + x**4*(-21168*d - 12096*e) + x**3*(-10080*d - 3780*e) + x**2*(-3240*d - 720*e) + x*(-630*d - 63*e))/(504*x**9)","A",0
577,1,124,0,7.763098," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**11,x)","e x + \left(d + 10 e\right) \log{\left(x \right)} + \frac{- 252 d + x^{9} \left(- 25200 d - 113400 e\right) + x^{8} \left(- 56700 d - 151200 e\right) + x^{7} \left(- 100800 d - 176400 e\right) + x^{6} \left(- 132300 d - 158760 e\right) + x^{5} \left(- 127008 d - 105840 e\right) + x^{4} \left(- 88200 d - 50400 e\right) + x^{3} \left(- 43200 d - 16200 e\right) + x^{2} \left(- 14175 d - 3150 e\right) + x \left(- 2800 d - 280 e\right)}{2520 x^{10}}"," ",0,"e*x + (d + 10*e)*log(x) + (-252*d + x**9*(-25200*d - 113400*e) + x**8*(-56700*d - 151200*e) + x**7*(-100800*d - 176400*e) + x**6*(-132300*d - 158760*e) + x**5*(-127008*d - 105840*e) + x**4*(-88200*d - 50400*e) + x**3*(-43200*d - 16200*e) + x**2*(-14175*d - 3150*e) + x*(-2800*d - 280*e))/(2520*x**10)","A",0
578,1,129,0,9.300371," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**12,x)","e \log{\left(x \right)} + \frac{- 2520 d + x^{10} \left(- 27720 d - 277200 e\right) + x^{9} \left(- 138600 d - 623700 e\right) + x^{8} \left(- 415800 d - 1108800 e\right) + x^{7} \left(- 831600 d - 1455300 e\right) + x^{6} \left(- 1164240 d - 1397088 e\right) + x^{5} \left(- 1164240 d - 970200 e\right) + x^{4} \left(- 831600 d - 475200 e\right) + x^{3} \left(- 415800 d - 155925 e\right) + x^{2} \left(- 138600 d - 30800 e\right) + x \left(- 27720 d - 2772 e\right)}{27720 x^{11}}"," ",0,"e*log(x) + (-2520*d + x**10*(-27720*d - 277200*e) + x**9*(-138600*d - 623700*e) + x**8*(-415800*d - 1108800*e) + x**7*(-831600*d - 1455300*e) + x**6*(-1164240*d - 1397088*e) + x**5*(-1164240*d - 970200*e) + x**4*(-831600*d - 475200*e) + x**3*(-415800*d - 155925*e) + x**2*(-138600*d - 30800*e) + x*(-27720*d - 2772*e))/(27720*x**11)","A",0
579,1,131,0,11.460906," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**13,x)","\frac{- 11 d - 132 e x^{11} + x^{10} \left(- 66 d - 660 e\right) + x^{9} \left(- 440 d - 1980 e\right) + x^{8} \left(- 1485 d - 3960 e\right) + x^{7} \left(- 3168 d - 5544 e\right) + x^{6} \left(- 4620 d - 5544 e\right) + x^{5} \left(- 4752 d - 3960 e\right) + x^{4} \left(- 3465 d - 1980 e\right) + x^{3} \left(- 1760 d - 660 e\right) + x^{2} \left(- 594 d - 132 e\right) + x \left(- 120 d - 12 e\right)}{132 x^{12}}"," ",0,"(-11*d - 132*e*x**11 + x**10*(-66*d - 660*e) + x**9*(-440*d - 1980*e) + x**8*(-1485*d - 3960*e) + x**7*(-3168*d - 5544*e) + x**6*(-4620*d - 5544*e) + x**5*(-4752*d - 3960*e) + x**4*(-3465*d - 1980*e) + x**3*(-1760*d - 660*e) + x**2*(-594*d - 132*e) + x*(-120*d - 12*e))/(132*x**12)","B",0
580,1,131,0,13.824393," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**14,x)","\frac{- 132 d - 858 e x^{11} + x^{10} \left(- 572 d - 5720 e\right) + x^{9} \left(- 4290 d - 19305 e\right) + x^{8} \left(- 15444 d - 41184 e\right) + x^{7} \left(- 34320 d - 60060 e\right) + x^{6} \left(- 51480 d - 61776 e\right) + x^{5} \left(- 54054 d - 45045 e\right) + x^{4} \left(- 40040 d - 22880 e\right) + x^{3} \left(- 20592 d - 7722 e\right) + x^{2} \left(- 7020 d - 1560 e\right) + x \left(- 1430 d - 143 e\right)}{1716 x^{13}}"," ",0,"(-132*d - 858*e*x**11 + x**10*(-572*d - 5720*e) + x**9*(-4290*d - 19305*e) + x**8*(-15444*d - 41184*e) + x**7*(-34320*d - 60060*e) + x**6*(-51480*d - 61776*e) + x**5*(-54054*d - 45045*e) + x**4*(-40040*d - 22880*e) + x**3*(-20592*d - 7722*e) + x**2*(-7020*d - 1560*e) + x*(-1430*d - 143*e))/(1716*x**13)","B",0
581,1,131,0,16.090161," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**15,x)","\frac{- 858 d - 4004 e x^{11} + x^{10} \left(- 3003 d - 30030 e\right) + x^{9} \left(- 24024 d - 108108 e\right) + x^{8} \left(- 90090 d - 240240 e\right) + x^{7} \left(- 205920 d - 360360 e\right) + x^{6} \left(- 315315 d - 378378 e\right) + x^{5} \left(- 336336 d - 280280 e\right) + x^{4} \left(- 252252 d - 144144 e\right) + x^{3} \left(- 131040 d - 49140 e\right) + x^{2} \left(- 45045 d - 10010 e\right) + x \left(- 9240 d - 924 e\right)}{12012 x^{14}}"," ",0,"(-858*d - 4004*e*x**11 + x**10*(-3003*d - 30030*e) + x**9*(-24024*d - 108108*e) + x**8*(-90090*d - 240240*e) + x**7*(-205920*d - 360360*e) + x**6*(-315315*d - 378378*e) + x**5*(-336336*d - 280280*e) + x**4*(-252252*d - 144144*e) + x**3*(-131040*d - 49140*e) + x**2*(-45045*d - 10010*e) + x*(-9240*d - 924*e))/(12012*x**14)","B",0
582,1,131,0,19.111057," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**16,x)","\frac{- 4004 d - 15015 e x^{11} + x^{10} \left(- 12012 d - 120120 e\right) + x^{9} \left(- 100100 d - 450450 e\right) + x^{8} \left(- 386100 d - 1029600 e\right) + x^{7} \left(- 900900 d - 1576575 e\right) + x^{6} \left(- 1401400 d - 1681680 e\right) + x^{5} \left(- 1513512 d - 1261260 e\right) + x^{4} \left(- 1146600 d - 655200 e\right) + x^{3} \left(- 600600 d - 225225 e\right) + x^{2} \left(- 207900 d - 46200 e\right) + x \left(- 42900 d - 4290 e\right)}{60060 x^{15}}"," ",0,"(-4004*d - 15015*e*x**11 + x**10*(-12012*d - 120120*e) + x**9*(-100100*d - 450450*e) + x**8*(-386100*d - 1029600*e) + x**7*(-900900*d - 1576575*e) + x**6*(-1401400*d - 1681680*e) + x**5*(-1513512*d - 1261260*e) + x**4*(-1146600*d - 655200*e) + x**3*(-600600*d - 225225*e) + x**2*(-207900*d - 46200*e) + x*(-42900*d - 4290*e))/(60060*x**15)","A",0
583,1,131,0,21.698684," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**17,x)","\frac{- 15015 d - 48048 e x^{11} + x^{10} \left(- 40040 d - 400400 e\right) + x^{9} \left(- 343200 d - 1544400 e\right) + x^{8} \left(- 1351350 d - 3603600 e\right) + x^{7} \left(- 3203200 d - 5605600 e\right) + x^{6} \left(- 5045040 d - 6054048 e\right) + x^{5} \left(- 5503680 d - 4586400 e\right) + x^{4} \left(- 4204200 d - 2402400 e\right) + x^{3} \left(- 2217600 d - 831600 e\right) + x^{2} \left(- 772200 d - 171600 e\right) + x \left(- 160160 d - 16016 e\right)}{240240 x^{16}}"," ",0,"(-15015*d - 48048*e*x**11 + x**10*(-40040*d - 400400*e) + x**9*(-343200*d - 1544400*e) + x**8*(-1351350*d - 3603600*e) + x**7*(-3203200*d - 5605600*e) + x**6*(-5045040*d - 6054048*e) + x**5*(-5503680*d - 4586400*e) + x**4*(-4204200*d - 2402400*e) + x**3*(-2217600*d - 831600*e) + x**2*(-772200*d - 171600*e) + x*(-160160*d - 16016*e))/(240240*x**16)","A",0
584,1,131,0,24.868992," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**18,x)","\frac{- 48048 d - 136136 e x^{11} + x^{10} \left(- 116688 d - 1166880 e\right) + x^{9} \left(- 1021020 d - 4594590 e\right) + x^{8} \left(- 4084080 d - 10890880 e\right) + x^{7} \left(- 9801792 d - 17153136 e\right) + x^{6} \left(- 15593760 d - 18712512 e\right) + x^{5} \left(- 17153136 d - 14294280 e\right) + x^{4} \left(- 13194720 d - 7539840 e\right) + x^{3} \left(- 7001280 d - 2625480 e\right) + x^{2} \left(- 2450448 d - 544544 e\right) + x \left(- 510510 d - 51051 e\right)}{816816 x^{17}}"," ",0,"(-48048*d - 136136*e*x**11 + x**10*(-116688*d - 1166880*e) + x**9*(-1021020*d - 4594590*e) + x**8*(-4084080*d - 10890880*e) + x**7*(-9801792*d - 17153136*e) + x**6*(-15593760*d - 18712512*e) + x**5*(-17153136*d - 14294280*e) + x**4*(-13194720*d - 7539840*e) + x**3*(-7001280*d - 2625480*e) + x**2*(-2450448*d - 544544*e) + x*(-510510*d - 51051*e))/(816816*x**17)","A",0
585,1,131,0,27.789365," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**19,x)","\frac{- 136136 d - 350064 e x^{11} + x^{10} \left(- 306306 d - 3063060 e\right) + x^{9} \left(- 2722720 d - 12252240 e\right) + x^{8} \left(- 11027016 d - 29405376 e\right) + x^{7} \left(- 26732160 d - 46781280 e\right) + x^{6} \left(- 42882840 d - 51459408 e\right) + x^{5} \left(- 47500992 d - 39584160 e\right) + x^{4} \left(- 36756720 d - 21003840 e\right) + x^{3} \left(- 19603584 d - 7351344 e\right) + x^{2} \left(- 6891885 d - 1531530 e\right) + x \left(- 1441440 d - 144144 e\right)}{2450448 x^{18}}"," ",0,"(-136136*d - 350064*e*x**11 + x**10*(-306306*d - 3063060*e) + x**9*(-2722720*d - 12252240*e) + x**8*(-11027016*d - 29405376*e) + x**7*(-26732160*d - 46781280*e) + x**6*(-42882840*d - 51459408*e) + x**5*(-47500992*d - 39584160*e) + x**4*(-36756720*d - 21003840*e) + x**3*(-19603584*d - 7351344*e) + x**2*(-6891885*d - 1531530*e) + x*(-1441440*d - 144144*e))/(2450448*x**18)","A",0
586,1,131,0,31.790400," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**20,x)","\frac{- 350064 d - 831402 e x^{11} + x^{10} \left(- 739024 d - 7390240 e\right) + x^{9} \left(- 6651216 d - 29930472 e\right) + x^{8} \left(- 27209520 d - 72558720 e\right) + x^{7} \left(- 66512160 d - 116396280 e\right) + x^{6} \left(- 107442720 d - 128931264 e\right) + x^{5} \left(- 119721888 d - 99768240 e\right) + x^{4} \left(- 93117024 d - 53209728 e\right) + x^{3} \left(- 49884120 d - 18706545 e\right) + x^{2} \left(- 17606160 d - 3912480 e\right) + x \left(- 3695120 d - 369512 e\right)}{6651216 x^{19}}"," ",0,"(-350064*d - 831402*e*x**11 + x**10*(-739024*d - 7390240*e) + x**9*(-6651216*d - 29930472*e) + x**8*(-27209520*d - 72558720*e) + x**7*(-66512160*d - 116396280*e) + x**6*(-107442720*d - 128931264*e) + x**5*(-119721888*d - 99768240*e) + x**4*(-93117024*d - 53209728*e) + x**3*(-49884120*d - 18706545*e) + x**2*(-17606160*d - 3912480*e) + x*(-3695120*d - 369512*e))/(6651216*x**19)","A",0
587,1,131,0,35.329537," ","integrate((e*x+d)*(x**2+2*x+1)**5/x**21,x)","\frac{- 831402 d - 1847560 e x^{11} + x^{10} \left(- 1662804 d - 16628040 e\right) + x^{9} \left(- 15116400 d - 68023800 e\right) + x^{8} \left(- 62355150 d - 166280400 e\right) + x^{7} \left(- 153489600 d - 268606800 e\right) + x^{6} \left(- 249420600 d - 299304720 e\right) + x^{5} \left(- 279351072 d - 232792560 e\right) + x^{4} \left(- 218243025 d - 124710300 e\right) + x^{3} \left(- 117374400 d - 44015400 e\right) + x^{2} \left(- 41570100 d - 9237800 e\right) + x \left(- 8751600 d - 875160 e\right)}{16628040 x^{20}}"," ",0,"(-831402*d - 1847560*e*x**11 + x**10*(-1662804*d - 16628040*e) + x**9*(-15116400*d - 68023800*e) + x**8*(-62355150*d - 166280400*e) + x**7*(-153489600*d - 268606800*e) + x**6*(-249420600*d - 299304720*e) + x**5*(-279351072*d - 232792560*e) + x**4*(-218243025*d - 124710300*e) + x**3*(-117374400*d - 44015400*e) + x**2*(-41570100*d - 9237800*e) + x*(-8751600*d - 875160*e))/(16628040*x**20)","A",0
588,1,73,0,0.076558," ","integrate(x**11*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{23}}{23} + \frac{x^{22}}{2} + \frac{55 x^{21}}{21} + \frac{33 x^{20}}{4} + \frac{330 x^{19}}{19} + \frac{77 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{165 x^{16}}{8} + 11 x^{15} + \frac{55 x^{14}}{14} + \frac{11 x^{13}}{13} + \frac{x^{12}}{12}"," ",0,"x**23/23 + x**22/2 + 55*x**21/21 + 33*x**20/4 + 330*x**19/19 + 77*x**18/3 + 462*x**17/17 + 165*x**16/8 + 11*x**15 + 55*x**14/14 + 11*x**13/13 + x**12/12","A",0
589,1,75,0,0.072615," ","integrate(x**10*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{22}}{22} + \frac{11 x^{21}}{21} + \frac{11 x^{20}}{4} + \frac{165 x^{19}}{19} + \frac{55 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{231 x^{16}}{8} + 22 x^{15} + \frac{165 x^{14}}{14} + \frac{55 x^{13}}{13} + \frac{11 x^{12}}{12} + \frac{x^{11}}{11}"," ",0,"x**22/22 + 11*x**21/21 + 11*x**20/4 + 165*x**19/19 + 55*x**18/3 + 462*x**17/17 + 231*x**16/8 + 22*x**15 + 165*x**14/14 + 55*x**13/13 + 11*x**12/12 + x**11/11","A",0
590,1,73,0,0.072938," ","integrate(x**9*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{21}}{21} + \frac{11 x^{20}}{20} + \frac{55 x^{19}}{19} + \frac{55 x^{18}}{6} + \frac{330 x^{17}}{17} + \frac{231 x^{16}}{8} + \frac{154 x^{15}}{5} + \frac{165 x^{14}}{7} + \frac{165 x^{13}}{13} + \frac{55 x^{12}}{12} + x^{11} + \frac{x^{10}}{10}"," ",0,"x**21/21 + 11*x**20/20 + 55*x**19/19 + 55*x**18/6 + 330*x**17/17 + 231*x**16/8 + 154*x**15/5 + 165*x**14/7 + 165*x**13/13 + 55*x**12/12 + x**11 + x**10/10","A",0
591,1,73,0,0.071443," ","integrate(x**8*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{20}}{20} + \frac{11 x^{19}}{19} + \frac{55 x^{18}}{18} + \frac{165 x^{17}}{17} + \frac{165 x^{16}}{8} + \frac{154 x^{15}}{5} + 33 x^{14} + \frac{330 x^{13}}{13} + \frac{55 x^{12}}{4} + 5 x^{11} + \frac{11 x^{10}}{10} + \frac{x^{9}}{9}"," ",0,"x**20/20 + 11*x**19/19 + 55*x**18/18 + 165*x**17/17 + 165*x**16/8 + 154*x**15/5 + 33*x**14 + 330*x**13/13 + 55*x**12/4 + 5*x**11 + 11*x**10/10 + x**9/9","A",0
592,1,71,0,0.073251," ","integrate(x**7*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{19}}{19} + \frac{11 x^{18}}{18} + \frac{55 x^{17}}{17} + \frac{165 x^{16}}{16} + 22 x^{15} + 33 x^{14} + \frac{462 x^{13}}{13} + \frac{55 x^{12}}{2} + 15 x^{11} + \frac{11 x^{10}}{2} + \frac{11 x^{9}}{9} + \frac{x^{8}}{8}"," ",0,"x**19/19 + 11*x**18/18 + 55*x**17/17 + 165*x**16/16 + 22*x**15 + 33*x**14 + 462*x**13/13 + 55*x**12/2 + 15*x**11 + 11*x**10/2 + 11*x**9/9 + x**8/8","A",0
593,1,73,0,0.071403," ","integrate(x**6*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{18}}{18} + \frac{11 x^{17}}{17} + \frac{55 x^{16}}{16} + 11 x^{15} + \frac{165 x^{14}}{7} + \frac{462 x^{13}}{13} + \frac{77 x^{12}}{2} + 30 x^{11} + \frac{33 x^{10}}{2} + \frac{55 x^{9}}{9} + \frac{11 x^{8}}{8} + \frac{x^{7}}{7}"," ",0,"x**18/18 + 11*x**17/17 + 55*x**16/16 + 11*x**15 + 165*x**14/7 + 462*x**13/13 + 77*x**12/2 + 30*x**11 + 33*x**10/2 + 55*x**9/9 + 11*x**8/8 + x**7/7","A",0
594,1,73,0,0.071728," ","integrate(x**5*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{17}}{17} + \frac{11 x^{16}}{16} + \frac{11 x^{15}}{3} + \frac{165 x^{14}}{14} + \frac{330 x^{13}}{13} + \frac{77 x^{12}}{2} + 42 x^{11} + 33 x^{10} + \frac{55 x^{9}}{3} + \frac{55 x^{8}}{8} + \frac{11 x^{7}}{7} + \frac{x^{6}}{6}"," ",0,"x**17/17 + 11*x**16/16 + 11*x**15/3 + 165*x**14/14 + 330*x**13/13 + 77*x**12/2 + 42*x**11 + 33*x**10 + 55*x**9/3 + 55*x**8/8 + 11*x**7/7 + x**6/6","A",0
595,1,75,0,0.070766," ","integrate(x**4*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{16}}{16} + \frac{11 x^{15}}{15} + \frac{55 x^{14}}{14} + \frac{165 x^{13}}{13} + \frac{55 x^{12}}{2} + 42 x^{11} + \frac{231 x^{10}}{5} + \frac{110 x^{9}}{3} + \frac{165 x^{8}}{8} + \frac{55 x^{7}}{7} + \frac{11 x^{6}}{6} + \frac{x^{5}}{5}"," ",0,"x**16/16 + 11*x**15/15 + 55*x**14/14 + 165*x**13/13 + 55*x**12/2 + 42*x**11 + 231*x**10/5 + 110*x**9/3 + 165*x**8/8 + 55*x**7/7 + 11*x**6/6 + x**5/5","B",0
596,1,75,0,0.071020," ","integrate(x**3*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{15}}{15} + \frac{11 x^{14}}{14} + \frac{55 x^{13}}{13} + \frac{55 x^{12}}{4} + 30 x^{11} + \frac{231 x^{10}}{5} + \frac{154 x^{9}}{3} + \frac{165 x^{8}}{4} + \frac{165 x^{7}}{7} + \frac{55 x^{6}}{6} + \frac{11 x^{5}}{5} + \frac{x^{4}}{4}"," ",0,"x**15/15 + 11*x**14/14 + 55*x**13/13 + 55*x**12/4 + 30*x**11 + 231*x**10/5 + 154*x**9/3 + 165*x**8/4 + 165*x**7/7 + 55*x**6/6 + 11*x**5/5 + x**4/4","B",0
597,1,71,0,0.070516," ","integrate(x**2*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{14}}{14} + \frac{11 x^{13}}{13} + \frac{55 x^{12}}{12} + 15 x^{11} + 33 x^{10} + \frac{154 x^{9}}{3} + \frac{231 x^{8}}{4} + \frac{330 x^{7}}{7} + \frac{55 x^{6}}{2} + 11 x^{5} + \frac{11 x^{4}}{4} + \frac{x^{3}}{3}"," ",0,"x**14/14 + 11*x**13/13 + 55*x**12/12 + 15*x**11 + 33*x**10 + 154*x**9/3 + 231*x**8/4 + 330*x**7/7 + 55*x**6/2 + 11*x**5 + 11*x**4/4 + x**3/3","B",0
598,1,70,0,0.069932," ","integrate(x*(1+x)*(x**2+2*x+1)**5,x)","\frac{x^{13}}{13} + \frac{11 x^{12}}{12} + 5 x^{11} + \frac{33 x^{10}}{2} + \frac{110 x^{9}}{3} + \frac{231 x^{8}}{4} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac{55 x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{x^{2}}{2}"," ",0,"x**13/13 + 11*x**12/12 + 5*x**11 + 33*x**10/2 + 110*x**9/3 + 231*x**8/4 + 66*x**7 + 55*x**6 + 33*x**5 + 55*x**4/4 + 11*x**3/3 + x**2/2","B",0
599,1,65,0,0.076820," ","integrate((1+x)*(x**2+2*x+1)**5,x)","\frac{x^{12}}{12} + x^{11} + \frac{11 x^{10}}{2} + \frac{55 x^{9}}{3} + \frac{165 x^{8}}{4} + 66 x^{7} + 77 x^{6} + 66 x^{5} + \frac{165 x^{4}}{4} + \frac{55 x^{3}}{3} + \frac{11 x^{2}}{2} + x"," ",0,"x**12/12 + x**11 + 11*x**10/2 + 55*x**9/3 + 165*x**8/4 + 66*x**7 + 77*x**6 + 66*x**5 + 165*x**4/4 + 55*x**3/3 + 11*x**2/2 + x","B",0
600,1,68,0,0.105575," ","integrate((1+x)*(x**2+2*x+1)**5/x,x)","\frac{x^{11}}{11} + \frac{11 x^{10}}{10} + \frac{55 x^{9}}{9} + \frac{165 x^{8}}{8} + \frac{330 x^{7}}{7} + 77 x^{6} + \frac{462 x^{5}}{5} + \frac{165 x^{4}}{2} + 55 x^{3} + \frac{55 x^{2}}{2} + 11 x + \log{\left(x \right)}"," ",0,"x**11/11 + 11*x**10/10 + 55*x**9/9 + 165*x**8/8 + 330*x**7/7 + 77*x**6 + 462*x**5/5 + 165*x**4/2 + 55*x**3 + 55*x**2/2 + 11*x + log(x)","A",0
601,1,66,0,0.110109," ","integrate((1+x)*(x**2+2*x+1)**5/x**2,x)","\frac{x^{10}}{10} + \frac{11 x^{9}}{9} + \frac{55 x^{8}}{8} + \frac{165 x^{7}}{7} + 55 x^{6} + \frac{462 x^{5}}{5} + \frac{231 x^{4}}{2} + 110 x^{3} + \frac{165 x^{2}}{2} + 55 x + 11 \log{\left(x \right)} - \frac{1}{x}"," ",0,"x**10/10 + 11*x**9/9 + 55*x**8/8 + 165*x**7/7 + 55*x**6 + 462*x**5/5 + 231*x**4/2 + 110*x**3 + 165*x**2/2 + 55*x + 11*log(x) - 1/x","A",0
602,1,66,0,0.118223," ","integrate((1+x)*(x**2+2*x+1)**5/x**3,x)","\frac{x^{9}}{9} + \frac{11 x^{8}}{8} + \frac{55 x^{7}}{7} + \frac{55 x^{6}}{2} + 66 x^{5} + \frac{231 x^{4}}{2} + 154 x^{3} + 165 x^{2} + 165 x + 55 \log{\left(x \right)} + \frac{- 22 x - 1}{2 x^{2}}"," ",0,"x**9/9 + 11*x**8/8 + 55*x**7/7 + 55*x**6/2 + 66*x**5 + 231*x**4/2 + 154*x**3 + 165*x**2 + 165*x + 55*log(x) + (-22*x - 1)/(2*x**2)","A",0
603,1,65,0,0.125042," ","integrate((1+x)*(x**2+2*x+1)**5/x**4,x)","\frac{x^{8}}{8} + \frac{11 x^{7}}{7} + \frac{55 x^{6}}{6} + 33 x^{5} + \frac{165 x^{4}}{2} + 154 x^{3} + 231 x^{2} + 330 x + 165 \log{\left(x \right)} + \frac{- 330 x^{2} - 33 x - 2}{6 x^{3}}"," ",0,"x**8/8 + 11*x**7/7 + 55*x**6/6 + 33*x**5 + 165*x**4/2 + 154*x**3 + 231*x**2 + 330*x + 165*log(x) + (-330*x**2 - 33*x - 2)/(6*x**3)","A",0
604,1,63,0,0.130791," ","integrate((1+x)*(x**2+2*x+1)**5/x**5,x)","\frac{x^{7}}{7} + \frac{11 x^{6}}{6} + 11 x^{5} + \frac{165 x^{4}}{4} + 110 x^{3} + 231 x^{2} + 462 x + 330 \log{\left(x \right)} + \frac{- 1980 x^{3} - 330 x^{2} - 44 x - 3}{12 x^{4}}"," ",0,"x**7/7 + 11*x**6/6 + 11*x**5 + 165*x**4/4 + 110*x**3 + 231*x**2 + 462*x + 330*log(x) + (-1980*x**3 - 330*x**2 - 44*x - 3)/(12*x**4)","A",0
605,1,63,0,0.137015," ","integrate((1+x)*(x**2+2*x+1)**5/x**6,x)","\frac{x^{6}}{6} + \frac{11 x^{5}}{5} + \frac{55 x^{4}}{4} + 55 x^{3} + 165 x^{2} + 462 x + 462 \log{\left(x \right)} + \frac{- 19800 x^{4} - 4950 x^{3} - 1100 x^{2} - 165 x - 12}{60 x^{5}}"," ",0,"x**6/6 + 11*x**5/5 + 55*x**4/4 + 55*x**3 + 165*x**2 + 462*x + 462*log(x) + (-19800*x**4 - 4950*x**3 - 1100*x**2 - 165*x - 12)/(60*x**5)","A",0
606,1,65,0,0.142236," ","integrate((1+x)*(x**2+2*x+1)**5/x**7,x)","\frac{x^{5}}{5} + \frac{11 x^{4}}{4} + \frac{55 x^{3}}{3} + \frac{165 x^{2}}{2} + 330 x + 462 \log{\left(x \right)} + \frac{- 27720 x^{5} - 9900 x^{4} - 3300 x^{3} - 825 x^{2} - 132 x - 10}{60 x^{6}}"," ",0,"x**5/5 + 11*x**4/4 + 55*x**3/3 + 165*x**2/2 + 330*x + 462*log(x) + (-27720*x**5 - 9900*x**4 - 3300*x**3 - 825*x**2 - 132*x - 10)/(60*x**6)","A",0
607,1,63,0,0.146973," ","integrate((1+x)*(x**2+2*x+1)**5/x**8,x)","\frac{x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{55 x^{2}}{2} + 165 x + 330 \log{\left(x \right)} + \frac{- 38808 x^{6} - 19404 x^{5} - 9240 x^{4} - 3465 x^{3} - 924 x^{2} - 154 x - 12}{84 x^{7}}"," ",0,"x**4/4 + 11*x**3/3 + 55*x**2/2 + 165*x + 330*log(x) + (-38808*x**6 - 19404*x**5 - 9240*x**4 - 3465*x**3 - 924*x**2 - 154*x - 12)/(84*x**7)","A",0
608,1,61,0,0.153472," ","integrate((1+x)*(x**2+2*x+1)**5/x**9,x)","\frac{x^{3}}{3} + \frac{11 x^{2}}{2} + 55 x + 165 \log{\left(x \right)} + \frac{- 55440 x^{7} - 38808 x^{6} - 25872 x^{5} - 13860 x^{4} - 5544 x^{3} - 1540 x^{2} - 264 x - 21}{168 x^{8}}"," ",0,"x**3/3 + 11*x**2/2 + 55*x + 165*log(x) + (-55440*x**7 - 38808*x**6 - 25872*x**5 - 13860*x**4 - 5544*x**3 - 1540*x**2 - 264*x - 21)/(168*x**8)","A",0
609,1,60,0,0.161871," ","integrate((1+x)*(x**2+2*x+1)**5/x**10,x)","\frac{x^{2}}{2} + 11 x + 55 \log{\left(x \right)} + \frac{- 83160 x^{8} - 83160 x^{7} - 77616 x^{6} - 58212 x^{5} - 33264 x^{4} - 13860 x^{3} - 3960 x^{2} - 693 x - 56}{504 x^{9}}"," ",0,"x**2/2 + 11*x + 55*log(x) + (-83160*x**8 - 83160*x**7 - 77616*x**6 - 58212*x**5 - 33264*x**4 - 13860*x**3 - 3960*x**2 - 693*x - 56)/(504*x**9)","A",0
610,1,58,0,0.168966," ","integrate((1+x)*(x**2+2*x+1)**5/x**11,x)","x + 11 \log{\left(x \right)} + \frac{- 138600 x^{9} - 207900 x^{8} - 277200 x^{7} - 291060 x^{6} - 232848 x^{5} - 138600 x^{4} - 59400 x^{3} - 17325 x^{2} - 3080 x - 252}{2520 x^{10}}"," ",0,"x + 11*log(x) + (-138600*x**9 - 207900*x**8 - 277200*x**7 - 291060*x**6 - 232848*x**5 - 138600*x**4 - 59400*x**3 - 17325*x**2 - 3080*x - 252)/(2520*x**10)","A",0
611,1,60,0,0.176486," ","integrate((1+x)*(x**2+2*x+1)**5/x**12,x)","\log{\left(x \right)} + \frac{- 304920 x^{10} - 762300 x^{9} - 1524600 x^{8} - 2286900 x^{7} - 2561328 x^{6} - 2134440 x^{5} - 1306800 x^{4} - 571725 x^{3} - 169400 x^{2} - 30492 x - 2520}{27720 x^{11}}"," ",0,"log(x) + (-304920*x**10 - 762300*x**9 - 1524600*x**8 - 2286900*x**7 - 2561328*x**6 - 2134440*x**5 - 1306800*x**4 - 571725*x**3 - 169400*x**2 - 30492*x - 2520)/(27720*x**11)","A",0
612,1,61,0,0.174933," ","integrate((1+x)*(x**2+2*x+1)**5/x**13,x)","\frac{- 12 x^{11} - 66 x^{10} - 220 x^{9} - 495 x^{8} - 792 x^{7} - 924 x^{6} - 792 x^{5} - 495 x^{4} - 220 x^{3} - 66 x^{2} - 12 x - 1}{12 x^{12}}"," ",0,"(-12*x**11 - 66*x**10 - 220*x**9 - 495*x**8 - 792*x**7 - 924*x**6 - 792*x**5 - 495*x**4 - 220*x**3 - 66*x**2 - 12*x - 1)/(12*x**12)","B",0
613,1,61,0,0.181476," ","integrate((1+x)*(x**2+2*x+1)**5/x**14,x)","\frac{- 78 x^{11} - 572 x^{10} - 2145 x^{9} - 5148 x^{8} - 8580 x^{7} - 10296 x^{6} - 9009 x^{5} - 5720 x^{4} - 2574 x^{3} - 780 x^{2} - 143 x - 12}{156 x^{13}}"," ",0,"(-78*x**11 - 572*x**10 - 2145*x**9 - 5148*x**8 - 8580*x**7 - 10296*x**6 - 9009*x**5 - 5720*x**4 - 2574*x**3 - 780*x**2 - 143*x - 12)/(156*x**13)","B",0
614,1,61,0,0.184074," ","integrate((1+x)*(x**2+2*x+1)**5/x**15,x)","\frac{- 364 x^{11} - 3003 x^{10} - 12012 x^{9} - 30030 x^{8} - 51480 x^{7} - 63063 x^{6} - 56056 x^{5} - 36036 x^{4} - 16380 x^{3} - 5005 x^{2} - 924 x - 78}{1092 x^{14}}"," ",0,"(-364*x**11 - 3003*x**10 - 12012*x**9 - 30030*x**8 - 51480*x**7 - 63063*x**6 - 56056*x**5 - 36036*x**4 - 16380*x**3 - 5005*x**2 - 924*x - 78)/(1092*x**14)","B",0
615,1,61,0,0.190286," ","integrate((1+x)*(x**2+2*x+1)**5/x**16,x)","\frac{- 1365 x^{11} - 12012 x^{10} - 50050 x^{9} - 128700 x^{8} - 225225 x^{7} - 280280 x^{6} - 252252 x^{5} - 163800 x^{4} - 75075 x^{3} - 23100 x^{2} - 4290 x - 364}{5460 x^{15}}"," ",0,"(-1365*x**11 - 12012*x**10 - 50050*x**9 - 128700*x**8 - 225225*x**7 - 280280*x**6 - 252252*x**5 - 163800*x**4 - 75075*x**3 - 23100*x**2 - 4290*x - 364)/(5460*x**15)","A",0
616,1,61,0,0.193691," ","integrate((1+x)*(x**2+2*x+1)**5/x**17,x)","\frac{- 4368 x^{11} - 40040 x^{10} - 171600 x^{9} - 450450 x^{8} - 800800 x^{7} - 1009008 x^{6} - 917280 x^{5} - 600600 x^{4} - 277200 x^{3} - 85800 x^{2} - 16016 x - 1365}{21840 x^{16}}"," ",0,"(-4368*x**11 - 40040*x**10 - 171600*x**9 - 450450*x**8 - 800800*x**7 - 1009008*x**6 - 917280*x**5 - 600600*x**4 - 277200*x**3 - 85800*x**2 - 16016*x - 1365)/(21840*x**16)","A",0
617,1,61,0,0.199386," ","integrate((1+x)*(x**2+2*x+1)**5/x**18,x)","\frac{- 12376 x^{11} - 116688 x^{10} - 510510 x^{9} - 1361360 x^{8} - 2450448 x^{7} - 3118752 x^{6} - 2858856 x^{5} - 1884960 x^{4} - 875160 x^{3} - 272272 x^{2} - 51051 x - 4368}{74256 x^{17}}"," ",0,"(-12376*x**11 - 116688*x**10 - 510510*x**9 - 1361360*x**8 - 2450448*x**7 - 3118752*x**6 - 2858856*x**5 - 1884960*x**4 - 875160*x**3 - 272272*x**2 - 51051*x - 4368)/(74256*x**17)","A",0
618,1,61,0,0.207021," ","integrate((1+x)*(x**2+2*x+1)**5/x**19,x)","\frac{- 31824 x^{11} - 306306 x^{10} - 1361360 x^{9} - 3675672 x^{8} - 6683040 x^{7} - 8576568 x^{6} - 7916832 x^{5} - 5250960 x^{4} - 2450448 x^{3} - 765765 x^{2} - 144144 x - 12376}{222768 x^{18}}"," ",0,"(-31824*x**11 - 306306*x**10 - 1361360*x**9 - 3675672*x**8 - 6683040*x**7 - 8576568*x**6 - 7916832*x**5 - 5250960*x**4 - 2450448*x**3 - 765765*x**2 - 144144*x - 12376)/(222768*x**18)","A",0
619,1,61,0,0.206695," ","integrate((1+x)*(x**2+2*x+1)**5/x**20,x)","\frac{- 75582 x^{11} - 739024 x^{10} - 3325608 x^{9} - 9069840 x^{8} - 16628040 x^{7} - 21488544 x^{6} - 19953648 x^{5} - 13302432 x^{4} - 6235515 x^{3} - 1956240 x^{2} - 369512 x - 31824}{604656 x^{19}}"," ",0,"(-75582*x**11 - 739024*x**10 - 3325608*x**9 - 9069840*x**8 - 16628040*x**7 - 21488544*x**6 - 19953648*x**5 - 13302432*x**4 - 6235515*x**3 - 1956240*x**2 - 369512*x - 31824)/(604656*x**19)","A",0
620,1,61,0,0.218779," ","integrate((1+x)*(x**2+2*x+1)**5/x**21,x)","\frac{- 167960 x^{11} - 1662804 x^{10} - 7558200 x^{9} - 20785050 x^{8} - 38372400 x^{7} - 49884120 x^{6} - 46558512 x^{5} - 31177575 x^{4} - 14671800 x^{3} - 4618900 x^{2} - 875160 x - 75582}{1511640 x^{20}}"," ",0,"(-167960*x**11 - 1662804*x**10 - 7558200*x**9 - 20785050*x**8 - 38372400*x**7 - 49884120*x**6 - 46558512*x**5 - 31177575*x**4 - 14671800*x**3 - 4618900*x**2 - 875160*x - 75582)/(1511640*x**20)","A",0
621,1,61,0,0.223265," ","integrate((1+x)*(x**2+2*x+1)**5/x**22,x)","\frac{- 352716 x^{11} - 3527160 x^{10} - 16166150 x^{9} - 44767800 x^{8} - 83140200 x^{7} - 108636528 x^{6} - 101846745 x^{5} - 68468400 x^{4} - 32332300 x^{3} - 10210200 x^{2} - 1939938 x - 167960}{3527160 x^{21}}"," ",0,"(-352716*x**11 - 3527160*x**10 - 16166150*x**9 - 44767800*x**8 - 83140200*x**7 - 108636528*x**6 - 101846745*x**5 - 68468400*x**4 - 32332300*x**3 - 10210200*x**2 - 1939938*x - 167960)/(3527160*x**21)","A",0
622,1,143,0,0.506144," ","integrate(x**5*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B x^{5}}{5 b^{2}} - \frac{a^{4} \left(- 5 A b + 6 B a\right) \log{\left(a + b x \right)}}{b^{7}} + x^{4} \left(\frac{A}{4 b^{2}} - \frac{B a}{2 b^{3}}\right) + x^{3} \left(- \frac{2 A a}{3 b^{3}} + \frac{B a^{2}}{b^{4}}\right) + x^{2} \left(\frac{3 A a^{2}}{2 b^{4}} - \frac{2 B a^{3}}{b^{5}}\right) + x \left(- \frac{4 A a^{3}}{b^{5}} + \frac{5 B a^{4}}{b^{6}}\right) + \frac{A a^{5} b - B a^{6}}{a b^{7} + b^{8} x}"," ",0,"B*x**5/(5*b**2) - a**4*(-5*A*b + 6*B*a)*log(a + b*x)/b**7 + x**4*(A/(4*b**2) - B*a/(2*b**3)) + x**3*(-2*A*a/(3*b**3) + B*a**2/b**4) + x**2*(3*A*a**2/(2*b**4) - 2*B*a**3/b**5) + x*(-4*A*a**3/b**5 + 5*B*a**4/b**6) + (A*a**5*b - B*a**6)/(a*b**7 + b**8*x)","A",0
623,1,119,0,0.460023," ","integrate(x**4*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B x^{4}}{4 b^{2}} + \frac{a^{3} \left(- 4 A b + 5 B a\right) \log{\left(a + b x \right)}}{b^{6}} + x^{3} \left(\frac{A}{3 b^{2}} - \frac{2 B a}{3 b^{3}}\right) + x^{2} \left(- \frac{A a}{b^{3}} + \frac{3 B a^{2}}{2 b^{4}}\right) + x \left(\frac{3 A a^{2}}{b^{4}} - \frac{4 B a^{3}}{b^{5}}\right) + \frac{- A a^{4} b + B a^{5}}{a b^{6} + b^{7} x}"," ",0,"B*x**4/(4*b**2) + a**3*(-4*A*b + 5*B*a)*log(a + b*x)/b**6 + x**3*(A/(3*b**2) - 2*B*a/(3*b**3)) + x**2*(-A*a/b**3 + 3*B*a**2/(2*b**4)) + x*(3*A*a**2/b**4 - 4*B*a**3/b**5) + (-A*a**4*b + B*a**5)/(a*b**6 + b**7*x)","A",0
624,1,92,0,0.416157," ","integrate(x**3*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B x^{3}}{3 b^{2}} - \frac{a^{2} \left(- 3 A b + 4 B a\right) \log{\left(a + b x \right)}}{b^{5}} + x^{2} \left(\frac{A}{2 b^{2}} - \frac{B a}{b^{3}}\right) + x \left(- \frac{2 A a}{b^{3}} + \frac{3 B a^{2}}{b^{4}}\right) + \frac{A a^{3} b - B a^{4}}{a b^{5} + b^{6} x}"," ",0,"B*x**3/(3*b**2) - a**2*(-3*A*b + 4*B*a)*log(a + b*x)/b**5 + x**2*(A/(2*b**2) - B*a/b**3) + x*(-2*A*a/b**3 + 3*B*a**2/b**4) + (A*a**3*b - B*a**4)/(a*b**5 + b**6*x)","A",0
625,1,68,0,0.363327," ","integrate(x**2*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B x^{2}}{2 b^{2}} + \frac{a \left(- 2 A b + 3 B a\right) \log{\left(a + b x \right)}}{b^{4}} + x \left(\frac{A}{b^{2}} - \frac{2 B a}{b^{3}}\right) + \frac{- A a^{2} b + B a^{3}}{a b^{4} + b^{5} x}"," ",0,"B*x**2/(2*b**2) + a*(-2*A*b + 3*B*a)*log(a + b*x)/b**4 + x*(A/b**2 - 2*B*a/b**3) + (-A*a**2*b + B*a**3)/(a*b**4 + b**5*x)","A",0
626,1,44,0,0.278238," ","integrate(x*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B x}{b^{2}} + \frac{A a b - B a^{2}}{a b^{3} + b^{4} x} - \frac{\left(- A b + 2 B a\right) \log{\left(a + b x \right)}}{b^{3}}"," ",0,"B*x/b**2 + (A*a*b - B*a**2)/(a*b**3 + b**4*x) - (-A*b + 2*B*a)*log(a + b*x)/b**3","A",0
627,1,27,0,0.189350," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B \log{\left(a + b x \right)}}{b^{2}} + \frac{- A b + B a}{a b^{2} + b^{3} x}"," ",0,"B*log(a + b*x)/b**2 + (-A*b + B*a)/(a*b**2 + b**3*x)","A",0
628,1,32,0,0.290544," ","integrate((B*x+A)/x/(b**2*x**2+2*a*b*x+a**2),x)","\frac{A \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{2}} + \frac{A b - B a}{a^{2} b + a b^{2} x}"," ",0,"A*(log(x) - log(a/b + x))/a**2 + (A*b - B*a)/(a**2*b + a*b**2*x)","A",0
629,1,128,0,0.491362," ","integrate((B*x+A)/x**2/(b**2*x**2+2*a*b*x+a**2),x)","\frac{- A a + x \left(- 2 A b + B a\right)}{a^{3} x + a^{2} b x^{2}} + \frac{\left(- 2 A b + B a\right) \log{\left(x + \frac{- 2 A a b + B a^{2} - a \left(- 2 A b + B a\right)}{- 4 A b^{2} + 2 B a b} \right)}}{a^{3}} - \frac{\left(- 2 A b + B a\right) \log{\left(x + \frac{- 2 A a b + B a^{2} + a \left(- 2 A b + B a\right)}{- 4 A b^{2} + 2 B a b} \right)}}{a^{3}}"," ",0,"(-A*a + x*(-2*A*b + B*a))/(a**3*x + a**2*b*x**2) + (-2*A*b + B*a)*log(x + (-2*A*a*b + B*a**2 - a*(-2*A*b + B*a))/(-4*A*b**2 + 2*B*a*b))/a**3 - (-2*A*b + B*a)*log(x + (-2*A*a*b + B*a**2 + a*(-2*A*b + B*a))/(-4*A*b**2 + 2*B*a*b))/a**3","B",0
630,1,184,0,0.592676," ","integrate((B*x+A)/x**3/(b**2*x**2+2*a*b*x+a**2),x)","\frac{- A a^{2} + x^{2} \left(6 A b^{2} - 4 B a b\right) + x \left(3 A a b - 2 B a^{2}\right)}{2 a^{4} x^{2} + 2 a^{3} b x^{3}} - \frac{b \left(- 3 A b + 2 B a\right) \log{\left(x + \frac{- 3 A a b^{2} + 2 B a^{2} b - a b \left(- 3 A b + 2 B a\right)}{- 6 A b^{3} + 4 B a b^{2}} \right)}}{a^{4}} + \frac{b \left(- 3 A b + 2 B a\right) \log{\left(x + \frac{- 3 A a b^{2} + 2 B a^{2} b + a b \left(- 3 A b + 2 B a\right)}{- 6 A b^{3} + 4 B a b^{2}} \right)}}{a^{4}}"," ",0,"(-A*a**2 + x**2*(6*A*b**2 - 4*B*a*b) + x*(3*A*a*b - 2*B*a**2))/(2*a**4*x**2 + 2*a**3*b*x**3) - b*(-3*A*b + 2*B*a)*log(x + (-3*A*a*b**2 + 2*B*a**2*b - a*b*(-3*A*b + 2*B*a))/(-6*A*b**3 + 4*B*a*b**2))/a**4 + b*(-3*A*b + 2*B*a)*log(x + (-3*A*a*b**2 + 2*B*a**2*b + a*b*(-3*A*b + 2*B*a))/(-6*A*b**3 + 4*B*a*b**2))/a**4","B",0
631,1,219,0,0.646312," ","integrate((B*x+A)/x**4/(b**2*x**2+2*a*b*x+a**2),x)","\frac{- 2 A a^{3} + x^{3} \left(- 24 A b^{3} + 18 B a b^{2}\right) + x^{2} \left(- 12 A a b^{2} + 9 B a^{2} b\right) + x \left(4 A a^{2} b - 3 B a^{3}\right)}{6 a^{5} x^{3} + 6 a^{4} b x^{4}} + \frac{b^{2} \left(- 4 A b + 3 B a\right) \log{\left(x + \frac{- 4 A a b^{3} + 3 B a^{2} b^{2} - a b^{2} \left(- 4 A b + 3 B a\right)}{- 8 A b^{4} + 6 B a b^{3}} \right)}}{a^{5}} - \frac{b^{2} \left(- 4 A b + 3 B a\right) \log{\left(x + \frac{- 4 A a b^{3} + 3 B a^{2} b^{2} + a b^{2} \left(- 4 A b + 3 B a\right)}{- 8 A b^{4} + 6 B a b^{3}} \right)}}{a^{5}}"," ",0,"(-2*A*a**3 + x**3*(-24*A*b**3 + 18*B*a*b**2) + x**2*(-12*A*a*b**2 + 9*B*a**2*b) + x*(4*A*a**2*b - 3*B*a**3))/(6*a**5*x**3 + 6*a**4*b*x**4) + b**2*(-4*A*b + 3*B*a)*log(x + (-4*A*a*b**3 + 3*B*a**2*b**2 - a*b**2*(-4*A*b + 3*B*a))/(-8*A*b**4 + 6*B*a*b**3))/a**5 - b**2*(-4*A*b + 3*B*a)*log(x + (-4*A*a*b**3 + 3*B*a**2*b**2 + a*b**2*(-4*A*b + 3*B*a))/(-8*A*b**4 + 6*B*a*b**3))/a**5","B",0
632,1,243,0,0.728081," ","integrate((B*x+A)/x**5/(b**2*x**2+2*a*b*x+a**2),x)","\frac{- 3 A a^{4} + x^{4} \left(60 A b^{4} - 48 B a b^{3}\right) + x^{3} \left(30 A a b^{3} - 24 B a^{2} b^{2}\right) + x^{2} \left(- 10 A a^{2} b^{2} + 8 B a^{3} b\right) + x \left(5 A a^{3} b - 4 B a^{4}\right)}{12 a^{6} x^{4} + 12 a^{5} b x^{5}} - \frac{b^{3} \left(- 5 A b + 4 B a\right) \log{\left(x + \frac{- 5 A a b^{4} + 4 B a^{2} b^{3} - a b^{3} \left(- 5 A b + 4 B a\right)}{- 10 A b^{5} + 8 B a b^{4}} \right)}}{a^{6}} + \frac{b^{3} \left(- 5 A b + 4 B a\right) \log{\left(x + \frac{- 5 A a b^{4} + 4 B a^{2} b^{3} + a b^{3} \left(- 5 A b + 4 B a\right)}{- 10 A b^{5} + 8 B a b^{4}} \right)}}{a^{6}}"," ",0,"(-3*A*a**4 + x**4*(60*A*b**4 - 48*B*a*b**3) + x**3*(30*A*a*b**3 - 24*B*a**2*b**2) + x**2*(-10*A*a**2*b**2 + 8*B*a**3*b) + x*(5*A*a**3*b - 4*B*a**4))/(12*a**6*x**4 + 12*a**5*b*x**5) - b**3*(-5*A*b + 4*B*a)*log(x + (-5*A*a*b**4 + 4*B*a**2*b**3 - a*b**3*(-5*A*b + 4*B*a))/(-10*A*b**5 + 8*B*a*b**4))/a**6 + b**3*(-5*A*b + 4*B*a)*log(x + (-5*A*a*b**4 + 4*B*a**2*b**3 + a*b**3*(-5*A*b + 4*B*a))/(-10*A*b**5 + 8*B*a*b**4))/a**6","A",0
633,1,168,0,1.252718," ","integrate(x**5*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B x^{3}}{3 b^{4}} - \frac{10 a^{2} \left(- A b + 2 B a\right) \log{\left(a + b x \right)}}{b^{7}} + x^{2} \left(\frac{A}{2 b^{4}} - \frac{2 B a}{b^{5}}\right) + x \left(- \frac{4 A a}{b^{5}} + \frac{10 B a^{2}}{b^{6}}\right) + \frac{47 A a^{5} b - 74 B a^{6} + x^{2} \left(60 A a^{3} b^{3} - 90 B a^{4} b^{2}\right) + x \left(105 A a^{4} b^{2} - 162 B a^{5} b\right)}{6 a^{3} b^{7} + 18 a^{2} b^{8} x + 18 a b^{9} x^{2} + 6 b^{10} x^{3}}"," ",0,"B*x**3/(3*b**4) - 10*a**2*(-A*b + 2*B*a)*log(a + b*x)/b**7 + x**2*(A/(2*b**4) - 2*B*a/b**5) + x*(-4*A*a/b**5 + 10*B*a**2/b**6) + (47*A*a**5*b - 74*B*a**6 + x**2*(60*A*a**3*b**3 - 90*B*a**4*b**2) + x*(105*A*a**4*b**2 - 162*B*a**5*b))/(6*a**3*b**7 + 18*a**2*b**8*x + 18*a*b**9*x**2 + 6*b**10*x**3)","A",0
634,1,144,0,1.148366," ","integrate(x**4*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B x^{2}}{2 b^{4}} + \frac{2 a \left(- 2 A b + 5 B a\right) \log{\left(a + b x \right)}}{b^{6}} + x \left(\frac{A}{b^{4}} - \frac{4 B a}{b^{5}}\right) + \frac{- 26 A a^{4} b + 47 B a^{5} + x^{2} \left(- 36 A a^{2} b^{3} + 60 B a^{3} b^{2}\right) + x \left(- 60 A a^{3} b^{2} + 105 B a^{4} b\right)}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}}"," ",0,"B*x**2/(2*b**4) + 2*a*(-2*A*b + 5*B*a)*log(a + b*x)/b**6 + x*(A/b**4 - 4*B*a/b**5) + (-26*A*a**4*b + 47*B*a**5 + x**2*(-36*A*a**2*b**3 + 60*B*a**3*b**2) + x*(-60*A*a**3*b**2 + 105*B*a**4*b))/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3)","A",0
635,1,119,0,0.957125," ","integrate(x**3*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B x}{b^{4}} + \frac{11 A a^{3} b - 26 B a^{4} + x^{2} \left(18 A a b^{3} - 36 B a^{2} b^{2}\right) + x \left(27 A a^{2} b^{2} - 60 B a^{3} b\right)}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{\left(- A b + 4 B a\right) \log{\left(a + b x \right)}}{b^{5}}"," ",0,"B*x/b**4 + (11*A*a**3*b - 26*B*a**4 + x**2*(18*A*a*b**3 - 36*B*a**2*b**2) + x*(27*A*a**2*b**2 - 60*B*a**3*b))/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - (-A*b + 4*B*a)*log(a + b*x)/b**5","A",0
636,1,100,0,0.657271," ","integrate(x**2*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B \log{\left(a + b x \right)}}{b^{4}} + \frac{- 2 A a^{2} b + 11 B a^{3} + x^{2} \left(- 6 A b^{3} + 18 B a b^{2}\right) + x \left(- 6 A a b^{2} + 27 B a^{2} b\right)}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}}"," ",0,"B*log(a + b*x)/b**4 + (-2*A*a**2*b + 11*B*a**3 + x**2*(-6*A*b**3 + 18*B*a*b**2) + x*(-6*A*a*b**2 + 27*B*a**2*b))/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3)","A",0
637,1,75,0,0.445203," ","integrate(x*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- A a b - 2 B a^{2} - 6 B b^{2} x^{2} + x \left(- 3 A b^{2} - 6 B a b\right)}{6 a^{3} b^{3} + 18 a^{2} b^{4} x + 18 a b^{5} x^{2} + 6 b^{6} x^{3}}"," ",0,"(-A*a*b - 2*B*a**2 - 6*B*b**2*x**2 + x*(-3*A*b**2 - 6*B*a*b))/(6*a**3*b**3 + 18*a**2*b**4*x + 18*a*b**5*x**2 + 6*b**6*x**3)","A",0
638,1,53,0,0.354940," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 2 A b - B a - 3 B b x}{6 a^{3} b^{2} + 18 a^{2} b^{3} x + 18 a b^{4} x^{2} + 6 b^{5} x^{3}}"," ",0,"(-2*A*b - B*a - 3*B*b*x)/(6*a**3*b**2 + 18*a**2*b**3*x + 18*a*b**4*x**2 + 6*b**5*x**3)","A",0
639,1,90,0,0.527071," ","integrate((B*x+A)/x/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{A \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{4}} + \frac{11 A a^{2} b + 15 A a b^{2} x + 6 A b^{3} x^{2} - 2 B a^{3}}{6 a^{6} b + 18 a^{5} b^{2} x + 18 a^{4} b^{3} x^{2} + 6 a^{3} b^{4} x^{3}}"," ",0,"A*(log(x) - log(a/b + x))/a**4 + (11*A*a**2*b + 15*A*a*b**2*x + 6*A*b**3*x**2 - 2*B*a**3)/(6*a**6*b + 18*a**5*b**2*x + 18*a**4*b**3*x**2 + 6*a**3*b**4*x**3)","A",0
640,1,204,0,0.756912," ","integrate((B*x+A)/x**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 6 A a^{3} + x^{3} \left(- 24 A b^{3} + 6 B a b^{2}\right) + x^{2} \left(- 60 A a b^{2} + 15 B a^{2} b\right) + x \left(- 44 A a^{2} b + 11 B a^{3}\right)}{6 a^{7} x + 18 a^{6} b x^{2} + 18 a^{5} b^{2} x^{3} + 6 a^{4} b^{3} x^{4}} + \frac{\left(- 4 A b + B a\right) \log{\left(x + \frac{- 4 A a b + B a^{2} - a \left(- 4 A b + B a\right)}{- 8 A b^{2} + 2 B a b} \right)}}{a^{5}} - \frac{\left(- 4 A b + B a\right) \log{\left(x + \frac{- 4 A a b + B a^{2} + a \left(- 4 A b + B a\right)}{- 8 A b^{2} + 2 B a b} \right)}}{a^{5}}"," ",0,"(-6*A*a**3 + x**3*(-24*A*b**3 + 6*B*a*b**2) + x**2*(-60*A*a*b**2 + 15*B*a**2*b) + x*(-44*A*a**2*b + 11*B*a**3))/(6*a**7*x + 18*a**6*b*x**2 + 18*a**5*b**2*x**3 + 6*a**4*b**3*x**4) + (-4*A*b + B*a)*log(x + (-4*A*a*b + B*a**2 - a*(-4*A*b + B*a))/(-8*A*b**2 + 2*B*a*b))/a**5 - (-4*A*b + B*a)*log(x + (-4*A*a*b + B*a**2 + a*(-4*A*b + B*a))/(-8*A*b**2 + 2*B*a*b))/a**5","B",0
641,1,264,0,0.881596," ","integrate((B*x+A)/x**3/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 3 A a^{4} + x^{4} \left(60 A b^{4} - 24 B a b^{3}\right) + x^{3} \left(150 A a b^{3} - 60 B a^{2} b^{2}\right) + x^{2} \left(110 A a^{2} b^{2} - 44 B a^{3} b\right) + x \left(15 A a^{3} b - 6 B a^{4}\right)}{6 a^{8} x^{2} + 18 a^{7} b x^{3} + 18 a^{6} b^{2} x^{4} + 6 a^{5} b^{3} x^{5}} - \frac{2 b \left(- 5 A b + 2 B a\right) \log{\left(x + \frac{- 10 A a b^{2} + 4 B a^{2} b - 2 a b \left(- 5 A b + 2 B a\right)}{- 20 A b^{3} + 8 B a b^{2}} \right)}}{a^{6}} + \frac{2 b \left(- 5 A b + 2 B a\right) \log{\left(x + \frac{- 10 A a b^{2} + 4 B a^{2} b + 2 a b \left(- 5 A b + 2 B a\right)}{- 20 A b^{3} + 8 B a b^{2}} \right)}}{a^{6}}"," ",0,"(-3*A*a**4 + x**4*(60*A*b**4 - 24*B*a*b**3) + x**3*(150*A*a*b**3 - 60*B*a**2*b**2) + x**2*(110*A*a**2*b**2 - 44*B*a**3*b) + x*(15*A*a**3*b - 6*B*a**4))/(6*a**8*x**2 + 18*a**7*b*x**3 + 18*a**6*b**2*x**4 + 6*a**5*b**3*x**5) - 2*b*(-5*A*b + 2*B*a)*log(x + (-10*A*a*b**2 + 4*B*a**2*b - 2*a*b*(-5*A*b + 2*B*a))/(-20*A*b**3 + 8*B*a*b**2))/a**6 + 2*b*(-5*A*b + 2*B*a)*log(x + (-10*A*a*b**2 + 4*B*a**2*b + 2*a*b*(-5*A*b + 2*B*a))/(-20*A*b**3 + 8*B*a*b**2))/a**6","B",0
642,1,291,0,0.943361," ","integrate((B*x+A)/x**4/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 2 A a^{5} + x^{5} \left(- 120 A b^{5} + 60 B a b^{4}\right) + x^{4} \left(- 300 A a b^{4} + 150 B a^{2} b^{3}\right) + x^{3} \left(- 220 A a^{2} b^{3} + 110 B a^{3} b^{2}\right) + x^{2} \left(- 30 A a^{3} b^{2} + 15 B a^{4} b\right) + x \left(6 A a^{4} b - 3 B a^{5}\right)}{6 a^{9} x^{3} + 18 a^{8} b x^{4} + 18 a^{7} b^{2} x^{5} + 6 a^{6} b^{3} x^{6}} + \frac{10 b^{2} \left(- 2 A b + B a\right) \log{\left(x + \frac{- 20 A a b^{3} + 10 B a^{2} b^{2} - 10 a b^{2} \left(- 2 A b + B a\right)}{- 40 A b^{4} + 20 B a b^{3}} \right)}}{a^{7}} - \frac{10 b^{2} \left(- 2 A b + B a\right) \log{\left(x + \frac{- 20 A a b^{3} + 10 B a^{2} b^{2} + 10 a b^{2} \left(- 2 A b + B a\right)}{- 40 A b^{4} + 20 B a b^{3}} \right)}}{a^{7}}"," ",0,"(-2*A*a**5 + x**5*(-120*A*b**5 + 60*B*a*b**4) + x**4*(-300*A*a*b**4 + 150*B*a**2*b**3) + x**3*(-220*A*a**2*b**3 + 110*B*a**3*b**2) + x**2*(-30*A*a**3*b**2 + 15*B*a**4*b) + x*(6*A*a**4*b - 3*B*a**5))/(6*a**9*x**3 + 18*a**8*b*x**4 + 18*a**7*b**2*x**5 + 6*a**6*b**3*x**6) + 10*b**2*(-2*A*b + B*a)*log(x + (-20*A*a*b**3 + 10*B*a**2*b**2 - 10*a*b**2*(-2*A*b + B*a))/(-40*A*b**4 + 20*B*a*b**3))/a**7 - 10*b**2*(-2*A*b + B*a)*log(x + (-20*A*a*b**3 + 10*B*a**2*b**2 + 10*a*b**2*(-2*A*b + B*a))/(-40*A*b**4 + 20*B*a*b**3))/a**7","A",0
643,1,216,0,2.752698," ","integrate(x**6*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{B x^{2}}{2 b^{6}} + \frac{3 a \left(- 2 A b + 7 B a\right) \log{\left(a + b x \right)}}{b^{8}} + x \left(\frac{A}{b^{6}} - \frac{6 B a}{b^{7}}\right) + \frac{- 174 A a^{6} b + 459 B a^{7} + x^{4} \left(- 300 A a^{2} b^{5} + 700 B a^{3} b^{4}\right) + x^{3} \left(- 1000 A a^{3} b^{4} + 2450 B a^{4} b^{3}\right) + x^{2} \left(- 1300 A a^{4} b^{3} + 3290 B a^{5} b^{2}\right) + x \left(- 770 A a^{5} b^{2} + 1995 B a^{6} b\right)}{20 a^{5} b^{8} + 100 a^{4} b^{9} x + 200 a^{3} b^{10} x^{2} + 200 a^{2} b^{11} x^{3} + 100 a b^{12} x^{4} + 20 b^{13} x^{5}}"," ",0,"B*x**2/(2*b**6) + 3*a*(-2*A*b + 7*B*a)*log(a + b*x)/b**8 + x*(A/b**6 - 6*B*a/b**7) + (-174*A*a**6*b + 459*B*a**7 + x**4*(-300*A*a**2*b**5 + 700*B*a**3*b**4) + x**3*(-1000*A*a**3*b**4 + 2450*B*a**4*b**3) + x**2*(-1300*A*a**4*b**3 + 3290*B*a**5*b**2) + x*(-770*A*a**5*b**2 + 1995*B*a**6*b))/(20*a**5*b**8 + 100*a**4*b**9*x + 200*a**3*b**10*x**2 + 200*a**2*b**11*x**3 + 100*a*b**12*x**4 + 20*b**13*x**5)","A",0
644,1,190,0,2.483654," ","integrate(x**5*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{B x}{b^{6}} + \frac{137 A a^{5} b - 522 B a^{6} + x^{4} \left(300 A a b^{5} - 900 B a^{2} b^{4}\right) + x^{3} \left(900 A a^{2} b^{4} - 3000 B a^{3} b^{3}\right) + x^{2} \left(1100 A a^{3} b^{3} - 3900 B a^{4} b^{2}\right) + x \left(625 A a^{4} b^{2} - 2310 B a^{5} b\right)}{60 a^{5} b^{7} + 300 a^{4} b^{8} x + 600 a^{3} b^{9} x^{2} + 600 a^{2} b^{10} x^{3} + 300 a b^{11} x^{4} + 60 b^{12} x^{5}} - \frac{\left(- A b + 6 B a\right) \log{\left(a + b x \right)}}{b^{7}}"," ",0,"B*x/b**6 + (137*A*a**5*b - 522*B*a**6 + x**4*(300*A*a*b**5 - 900*B*a**2*b**4) + x**3*(900*A*a**2*b**4 - 3000*B*a**3*b**3) + x**2*(1100*A*a**3*b**3 - 3900*B*a**4*b**2) + x*(625*A*a**4*b**2 - 2310*B*a**5*b))/(60*a**5*b**7 + 300*a**4*b**8*x + 600*a**3*b**9*x**2 + 600*a**2*b**10*x**3 + 300*a*b**11*x**4 + 60*b**12*x**5) - (-A*b + 6*B*a)*log(a + b*x)/b**7","A",0
645,1,172,0,1.952996," ","integrate(x**4*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{B \log{\left(a + b x \right)}}{b^{6}} + \frac{- 12 A a^{4} b + 137 B a^{5} + x^{4} \left(- 60 A b^{5} + 300 B a b^{4}\right) + x^{3} \left(- 120 A a b^{4} + 900 B a^{2} b^{3}\right) + x^{2} \left(- 120 A a^{2} b^{3} + 1100 B a^{3} b^{2}\right) + x \left(- 60 A a^{3} b^{2} + 625 B a^{4} b\right)}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}}"," ",0,"B*log(a + b*x)/b**6 + (-12*A*a**4*b + 137*B*a**5 + x**4*(-60*A*b**5 + 300*B*a*b**4) + x**3*(-120*A*a*b**4 + 900*B*a**2*b**3) + x**2*(-120*A*a**2*b**3 + 1100*B*a**3*b**2) + x*(-60*A*a**3*b**2 + 625*B*a**4*b))/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5)","A",0
646,1,150,0,1.474001," ","integrate(x**3*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- A a^{3} b - 4 B a^{4} - 20 B b^{4} x^{4} + x^{3} \left(- 10 A b^{4} - 40 B a b^{3}\right) + x^{2} \left(- 10 A a b^{3} - 40 B a^{2} b^{2}\right) + x \left(- 5 A a^{2} b^{2} - 20 B a^{3} b\right)}{20 a^{5} b^{5} + 100 a^{4} b^{6} x + 200 a^{3} b^{7} x^{2} + 200 a^{2} b^{8} x^{3} + 100 a b^{9} x^{4} + 20 b^{10} x^{5}}"," ",0,"(-A*a**3*b - 4*B*a**4 - 20*B*b**4*x**4 + x**3*(-10*A*b**4 - 40*B*a*b**3) + x**2*(-10*A*a*b**3 - 40*B*a**2*b**2) + x*(-5*A*a**2*b**2 - 20*B*a**3*b))/(20*a**5*b**5 + 100*a**4*b**6*x + 200*a**3*b**7*x**2 + 200*a**2*b**8*x**3 + 100*a*b**9*x**4 + 20*b**10*x**5)","B",0
647,1,126,0,1.009006," ","integrate(x**2*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- 2 A a^{2} b - 3 B a^{3} - 30 B b^{3} x^{3} + x^{2} \left(- 20 A b^{3} - 30 B a b^{2}\right) + x \left(- 10 A a b^{2} - 15 B a^{2} b\right)}{60 a^{5} b^{4} + 300 a^{4} b^{5} x + 600 a^{3} b^{6} x^{2} + 600 a^{2} b^{7} x^{3} + 300 a b^{8} x^{4} + 60 b^{9} x^{5}}"," ",0,"(-2*A*a**2*b - 3*B*a**3 - 30*B*b**3*x**3 + x**2*(-20*A*b**3 - 30*B*a*b**2) + x*(-10*A*a*b**2 - 15*B*a**2*b))/(60*a**5*b**4 + 300*a**4*b**5*x + 600*a**3*b**6*x**2 + 600*a**2*b**7*x**3 + 300*a*b**8*x**4 + 60*b**9*x**5)","A",0
648,1,100,0,0.680530," ","integrate(x*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- 3 A a b - 2 B a^{2} - 20 B b^{2} x^{2} + x \left(- 15 A b^{2} - 10 B a b\right)}{60 a^{5} b^{3} + 300 a^{4} b^{4} x + 600 a^{3} b^{5} x^{2} + 600 a^{2} b^{6} x^{3} + 300 a b^{7} x^{4} + 60 b^{8} x^{5}}"," ",0,"(-3*A*a*b - 2*B*a**2 - 20*B*b**2*x**2 + x*(-15*A*b**2 - 10*B*a*b))/(60*a**5*b**3 + 300*a**4*b**4*x + 600*a**3*b**5*x**2 + 600*a**2*b**6*x**3 + 300*a*b**7*x**4 + 60*b**8*x**5)","A",0
649,1,76,0,0.541012," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- 4 A b - B a - 5 B b x}{20 a^{5} b^{2} + 100 a^{4} b^{3} x + 200 a^{3} b^{4} x^{2} + 200 a^{2} b^{5} x^{3} + 100 a b^{6} x^{4} + 20 b^{7} x^{5}}"," ",0,"(-4*A*b - B*a - 5*B*b*x)/(20*a**5*b**2 + 100*a**4*b**3*x + 200*a**3*b**4*x**2 + 200*a**2*b**5*x**3 + 100*a*b**6*x**4 + 20*b**7*x**5)","B",0
650,1,141,0,0.766050," ","integrate((B*x+A)/x/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{A \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{6}} + \frac{137 A a^{4} b + 385 A a^{3} b^{2} x + 470 A a^{2} b^{3} x^{2} + 270 A a b^{4} x^{3} + 60 A b^{5} x^{4} - 12 B a^{5}}{60 a^{10} b + 300 a^{9} b^{2} x + 600 a^{8} b^{3} x^{2} + 600 a^{7} b^{4} x^{3} + 300 a^{6} b^{5} x^{4} + 60 a^{5} b^{6} x^{5}}"," ",0,"A*(log(x) - log(a/b + x))/a**6 + (137*A*a**4*b + 385*A*a**3*b**2*x + 470*A*a**2*b**3*x**2 + 270*A*a*b**4*x**3 + 60*A*b**5*x**4 - 12*B*a**5)/(60*a**10*b + 300*a**9*b**2*x + 600*a**8*b**3*x**2 + 600*a**7*b**4*x**3 + 300*a**6*b**5*x**4 + 60*a**5*b**6*x**5)","A",0
651,1,275,0,1.062994," ","integrate((B*x+A)/x**2/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- 60 A a^{5} + x^{5} \left(- 360 A b^{5} + 60 B a b^{4}\right) + x^{4} \left(- 1620 A a b^{4} + 270 B a^{2} b^{3}\right) + x^{3} \left(- 2820 A a^{2} b^{3} + 470 B a^{3} b^{2}\right) + x^{2} \left(- 2310 A a^{3} b^{2} + 385 B a^{4} b\right) + x \left(- 822 A a^{4} b + 137 B a^{5}\right)}{60 a^{11} x + 300 a^{10} b x^{2} + 600 a^{9} b^{2} x^{3} + 600 a^{8} b^{3} x^{4} + 300 a^{7} b^{4} x^{5} + 60 a^{6} b^{5} x^{6}} + \frac{\left(- 6 A b + B a\right) \log{\left(x + \frac{- 6 A a b + B a^{2} - a \left(- 6 A b + B a\right)}{- 12 A b^{2} + 2 B a b} \right)}}{a^{7}} - \frac{\left(- 6 A b + B a\right) \log{\left(x + \frac{- 6 A a b + B a^{2} + a \left(- 6 A b + B a\right)}{- 12 A b^{2} + 2 B a b} \right)}}{a^{7}}"," ",0,"(-60*A*a**5 + x**5*(-360*A*b**5 + 60*B*a*b**4) + x**4*(-1620*A*a*b**4 + 270*B*a**2*b**3) + x**3*(-2820*A*a**2*b**3 + 470*B*a**3*b**2) + x**2*(-2310*A*a**3*b**2 + 385*B*a**4*b) + x*(-822*A*a**4*b + 137*B*a**5))/(60*a**11*x + 300*a**10*b*x**2 + 600*a**9*b**2*x**3 + 600*a**8*b**3*x**4 + 300*a**7*b**4*x**5 + 60*a**6*b**5*x**6) + (-6*A*b + B*a)*log(x + (-6*A*a*b + B*a**2 - a*(-6*A*b + B*a))/(-12*A*b**2 + 2*B*a*b))/a**7 - (-6*A*b + B*a)*log(x + (-6*A*a*b + B*a**2 + a*(-6*A*b + B*a))/(-12*A*b**2 + 2*B*a*b))/a**7","B",0
652,1,335,0,1.189418," ","integrate((B*x+A)/x**3/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- 10 A a^{6} + x^{6} \left(420 A b^{6} - 120 B a b^{5}\right) + x^{5} \left(1890 A a b^{5} - 540 B a^{2} b^{4}\right) + x^{4} \left(3290 A a^{2} b^{4} - 940 B a^{3} b^{3}\right) + x^{3} \left(2695 A a^{3} b^{3} - 770 B a^{4} b^{2}\right) + x^{2} \left(959 A a^{4} b^{2} - 274 B a^{5} b\right) + x \left(70 A a^{5} b - 20 B a^{6}\right)}{20 a^{12} x^{2} + 100 a^{11} b x^{3} + 200 a^{10} b^{2} x^{4} + 200 a^{9} b^{3} x^{5} + 100 a^{8} b^{4} x^{6} + 20 a^{7} b^{5} x^{7}} - \frac{3 b \left(- 7 A b + 2 B a\right) \log{\left(x + \frac{- 21 A a b^{2} + 6 B a^{2} b - 3 a b \left(- 7 A b + 2 B a\right)}{- 42 A b^{3} + 12 B a b^{2}} \right)}}{a^{8}} + \frac{3 b \left(- 7 A b + 2 B a\right) \log{\left(x + \frac{- 21 A a b^{2} + 6 B a^{2} b + 3 a b \left(- 7 A b + 2 B a\right)}{- 42 A b^{3} + 12 B a b^{2}} \right)}}{a^{8}}"," ",0,"(-10*A*a**6 + x**6*(420*A*b**6 - 120*B*a*b**5) + x**5*(1890*A*a*b**5 - 540*B*a**2*b**4) + x**4*(3290*A*a**2*b**4 - 940*B*a**3*b**3) + x**3*(2695*A*a**3*b**3 - 770*B*a**4*b**2) + x**2*(959*A*a**4*b**2 - 274*B*a**5*b) + x*(70*A*a**5*b - 20*B*a**6))/(20*a**12*x**2 + 100*a**11*b*x**3 + 200*a**10*b**2*x**4 + 200*a**9*b**3*x**5 + 100*a**8*b**4*x**6 + 20*a**7*b**5*x**7) - 3*b*(-7*A*b + 2*B*a)*log(x + (-21*A*a*b**2 + 6*B*a**2*b - 3*a*b*(-7*A*b + 2*B*a))/(-42*A*b**3 + 12*B*a*b**2))/a**8 + 3*b*(-7*A*b + 2*B*a)*log(x + (-21*A*a*b**2 + 6*B*a**2*b + 3*a*b*(-7*A*b + 2*B*a))/(-42*A*b**3 + 12*B*a*b**2))/a**8","A",0
653,1,29,0,0.098460," ","integrate(x**4*(B*x+A)*((b*x+a)**2)**(1/2),x)","\frac{A a x^{5}}{5} + \frac{B b x^{7}}{7} + x^{6} \left(\frac{A b}{6} + \frac{B a}{6}\right)"," ",0,"A*a*x**5/5 + B*b*x**7/7 + x**6*(A*b/6 + B*a/6)","A",0
654,1,29,0,0.098950," ","integrate(x**3*(B*x+A)*((b*x+a)**2)**(1/2),x)","\frac{A a x^{4}}{4} + \frac{B b x^{6}}{6} + x^{5} \left(\frac{A b}{5} + \frac{B a}{5}\right)"," ",0,"A*a*x**4/4 + B*b*x**6/6 + x**5*(A*b/5 + B*a/5)","A",0
655,1,29,0,0.097646," ","integrate(x**2*(B*x+A)*((b*x+a)**2)**(1/2),x)","\frac{A a x^{3}}{3} + \frac{B b x^{5}}{5} + x^{4} \left(\frac{A b}{4} + \frac{B a}{4}\right)"," ",0,"A*a*x**3/3 + B*b*x**5/5 + x**4*(A*b/4 + B*a/4)","A",0
656,1,29,0,0.097641," ","integrate(x*(B*x+A)*((b*x+a)**2)**(1/2),x)","\frac{A a x^{2}}{2} + \frac{B b x^{4}}{4} + x^{3} \left(\frac{A b}{3} + \frac{B a}{3}\right)"," ",0,"A*a*x**2/2 + B*b*x**4/4 + x**3*(A*b/3 + B*a/3)","A",0
657,1,26,0,0.095939," ","integrate((B*x+A)*((b*x+a)**2)**(1/2),x)","A a x + \frac{B b x^{3}}{3} + x^{2} \left(\frac{A b}{2} + \frac{B a}{2}\right)"," ",0,"A*a*x + B*b*x**3/3 + x**2*(A*b/2 + B*a/2)","A",0
658,1,22,0,0.131148," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x,x)","A a \log{\left(x \right)} + \frac{B b x^{2}}{2} + x \left(A b + B a\right)"," ",0,"A*a*log(x) + B*b*x**2/2 + x*(A*b + B*a)","A",0
659,1,19,0,0.169502," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**2,x)","- \frac{A a}{x} + B b x + \left(A b + B a\right) \log{\left(x \right)}"," ",0,"-A*a/x + B*b*x + (A*b + B*a)*log(x)","A",0
660,1,27,0,0.250960," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**3,x)","B b \log{\left(x \right)} + \frac{- A a + x \left(- 2 A b - 2 B a\right)}{2 x^{2}}"," ",0,"B*b*log(x) + (-A*a + x*(-2*A*b - 2*B*a))/(2*x**2)","A",0
661,1,31,0,0.297618," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**4,x)","\frac{- 2 A a - 6 B b x^{2} + x \left(- 3 A b - 3 B a\right)}{6 x^{3}}"," ",0,"(-2*A*a - 6*B*b*x**2 + x*(-3*A*b - 3*B*a))/(6*x**3)","A",0
662,1,31,0,0.366394," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**5,x)","\frac{- 3 A a - 6 B b x^{2} + x \left(- 4 A b - 4 B a\right)}{12 x^{4}}"," ",0,"(-3*A*a - 6*B*b*x**2 + x*(-4*A*b - 4*B*a))/(12*x**4)","A",0
663,1,31,0,0.425455," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**6,x)","\frac{- 12 A a - 20 B b x^{2} + x \left(- 15 A b - 15 B a\right)}{60 x^{5}}"," ",0,"(-12*A*a - 20*B*b*x**2 + x*(-15*A*b - 15*B*a))/(60*x**5)","A",0
664,1,31,0,0.511341," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**7,x)","\frac{- 10 A a - 15 B b x^{2} + x \left(- 12 A b - 12 B a\right)}{60 x^{6}}"," ",0,"(-10*A*a - 15*B*b*x**2 + x*(-12*A*b - 12*B*a))/(60*x**6)","A",0
665,0,0,0,0.000000," ","integrate(x**5*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{5} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
666,0,0,0,0.000000," ","integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{4} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
667,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{3} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
668,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{2} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
669,0,0,0,0.000000," ","integrate(x*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
670,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
671,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x, x)","F",0
672,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**2,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**2, x)","F",0
673,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**3,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**3, x)","F",0
674,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**4,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**4, x)","F",0
675,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**5,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**5, x)","F",0
676,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**6,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**6, x)","F",0
677,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**7,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**7, x)","F",0
678,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**8,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**8, x)","F",0
679,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**9,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**9, x)","F",0
680,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**10,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{10}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**10, x)","F",0
681,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**11,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{11}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**11, x)","F",0
682,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**12,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{12}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**12, x)","F",0
683,0,0,0,0.000000," ","integrate(x**6*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{6} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**6*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
684,0,0,0,0.000000," ","integrate(x**5*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{5} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**5*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
685,0,0,0,0.000000," ","integrate(x**4*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{4} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**4*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
686,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{3} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**3*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
687,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x^{2} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
688,0,0,0,0.000000," ","integrate(x*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int x \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
689,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
690,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x, x)","F",0
691,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**2,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**2, x)","F",0
692,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**3,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**3, x)","F",0
693,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**4,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**4, x)","F",0
694,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**5,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**5, x)","F",0
695,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**6,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**6, x)","F",0
696,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**7,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**7, x)","F",0
697,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**8,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{8}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**8, x)","F",0
698,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**9,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{9}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**9, x)","F",0
699,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**10,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{10}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**10, x)","F",0
700,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**11,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{11}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**11, x)","F",0
701,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**12,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{12}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**12, x)","F",0
702,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**13,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{13}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**13, x)","F",0
703,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**14,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{14}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**14, x)","F",0
704,1,109,0,0.290291," ","integrate(x**4*(B*x+A)/((b*x+a)**2)**(1/2),x)","\frac{B x^{5}}{5 b} - \frac{a^{4} \left(- A b + B a\right) \log{\left(a + b x \right)}}{b^{6}} + x^{4} \left(\frac{A}{4 b} - \frac{B a}{4 b^{2}}\right) + x^{3} \left(- \frac{A a}{3 b^{2}} + \frac{B a^{2}}{3 b^{3}}\right) + x^{2} \left(\frac{A a^{2}}{2 b^{3}} - \frac{B a^{3}}{2 b^{4}}\right) + x \left(- \frac{A a^{3}}{b^{4}} + \frac{B a^{4}}{b^{5}}\right)"," ",0,"B*x**5/(5*b) - a**4*(-A*b + B*a)*log(a + b*x)/b**6 + x**4*(A/(4*b) - B*a/(4*b**2)) + x**3*(-A*a/(3*b**2) + B*a**2/(3*b**3)) + x**2*(A*a**2/(2*b**3) - B*a**3/(2*b**4)) + x*(-A*a**3/b**4 + B*a**4/b**5)","A",0
705,1,85,0,0.265079," ","integrate(x**3*(B*x+A)/((b*x+a)**2)**(1/2),x)","\frac{B x^{4}}{4 b} + \frac{a^{3} \left(- A b + B a\right) \log{\left(a + b x \right)}}{b^{5}} + x^{3} \left(\frac{A}{3 b} - \frac{B a}{3 b^{2}}\right) + x^{2} \left(- \frac{A a}{2 b^{2}} + \frac{B a^{2}}{2 b^{3}}\right) + x \left(\frac{A a^{2}}{b^{3}} - \frac{B a^{3}}{b^{4}}\right)"," ",0,"B*x**4/(4*b) + a**3*(-A*b + B*a)*log(a + b*x)/b**5 + x**3*(A/(3*b) - B*a/(3*b**2)) + x**2*(-A*a/(2*b**2) + B*a**2/(2*b**3)) + x*(A*a**2/b**3 - B*a**3/b**4)","A",0
706,1,61,0,0.240504," ","integrate(x**2*(B*x+A)/((b*x+a)**2)**(1/2),x)","\frac{B x^{3}}{3 b} - \frac{a^{2} \left(- A b + B a\right) \log{\left(a + b x \right)}}{b^{4}} + x^{2} \left(\frac{A}{2 b} - \frac{B a}{2 b^{2}}\right) + x \left(- \frac{A a}{b^{2}} + \frac{B a^{2}}{b^{3}}\right)"," ",0,"B*x**3/(3*b) - a**2*(-A*b + B*a)*log(a + b*x)/b**4 + x**2*(A/(2*b) - B*a/(2*b**2)) + x*(-A*a/b**2 + B*a**2/b**3)","A",0
707,1,37,0,0.209318," ","integrate(x*(B*x+A)/((b*x+a)**2)**(1/2),x)","\frac{B x^{2}}{2 b} + \frac{a \left(- A b + B a\right) \log{\left(a + b x \right)}}{b^{3}} + x \left(\frac{A}{b} - \frac{B a}{b^{2}}\right)"," ",0,"B*x**2/(2*b) + a*(-A*b + B*a)*log(a + b*x)/b**3 + x*(A/b - B*a/b**2)","A",0
708,1,20,0,0.179767," ","integrate((B*x+A)/((b*x+a)**2)**(1/2),x)","\frac{B x}{b} - \frac{\left(- A b + B a\right) \log{\left(a + b x \right)}}{b^{2}}"," ",0,"B*x/b - (-A*b + B*a)*log(a + b*x)/b**2","A",0
709,1,41,0,0.436296," ","integrate((B*x+A)/x/((b*x+a)**2)**(1/2),x)","\frac{A \log{\left(x \right)}}{a} + \frac{\left(- A b + B a\right) \log{\left(x + \frac{- A a + \frac{a \left(- A b + B a\right)}{b}}{- 2 A b + B a} \right)}}{a b}"," ",0,"A*log(x)/a + (-A*b + B*a)*log(x + (-A*a + a*(-A*b + B*a)/b)/(-2*A*b + B*a))/(a*b)","A",0
710,1,95,0,0.398477," ","integrate((B*x+A)/x**2/((b*x+a)**2)**(1/2),x)","- \frac{A}{a x} + \frac{\left(- A b + B a\right) \log{\left(x + \frac{- A a b + B a^{2} - a \left(- A b + B a\right)}{- 2 A b^{2} + 2 B a b} \right)}}{a^{2}} - \frac{\left(- A b + B a\right) \log{\left(x + \frac{- A a b + B a^{2} + a \left(- A b + B a\right)}{- 2 A b^{2} + 2 B a b} \right)}}{a^{2}}"," ",0,"-A/(a*x) + (-A*b + B*a)*log(x + (-A*a*b + B*a**2 - a*(-A*b + B*a))/(-2*A*b**2 + 2*B*a*b))/a**2 - (-A*b + B*a)*log(x + (-A*a*b + B*a**2 + a*(-A*b + B*a))/(-2*A*b**2 + 2*B*a*b))/a**2","A",0
711,1,131,0,0.476626," ","integrate((B*x+A)/x**3/((b*x+a)**2)**(1/2),x)","\frac{- A a + x \left(2 A b - 2 B a\right)}{2 a^{2} x^{2}} - \frac{b \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{2} + B a^{2} b - a b \left(- A b + B a\right)}{- 2 A b^{3} + 2 B a b^{2}} \right)}}{a^{3}} + \frac{b \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{2} + B a^{2} b + a b \left(- A b + B a\right)}{- 2 A b^{3} + 2 B a b^{2}} \right)}}{a^{3}}"," ",0,"(-A*a + x*(2*A*b - 2*B*a))/(2*a**2*x**2) - b*(-A*b + B*a)*log(x + (-A*a*b**2 + B*a**2*b - a*b*(-A*b + B*a))/(-2*A*b**3 + 2*B*a*b**2))/a**3 + b*(-A*b + B*a)*log(x + (-A*a*b**2 + B*a**2*b + a*b*(-A*b + B*a))/(-2*A*b**3 + 2*B*a*b**2))/a**3","A",0
712,1,165,0,0.526673," ","integrate((B*x+A)/x**4/((b*x+a)**2)**(1/2),x)","\frac{- 2 A a^{2} + x^{2} \left(- 6 A b^{2} + 6 B a b\right) + x \left(3 A a b - 3 B a^{2}\right)}{6 a^{3} x^{3}} + \frac{b^{2} \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{3} + B a^{2} b^{2} - a b^{2} \left(- A b + B a\right)}{- 2 A b^{4} + 2 B a b^{3}} \right)}}{a^{4}} - \frac{b^{2} \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{3} + B a^{2} b^{2} + a b^{2} \left(- A b + B a\right)}{- 2 A b^{4} + 2 B a b^{3}} \right)}}{a^{4}}"," ",0,"(-2*A*a**2 + x**2*(-6*A*b**2 + 6*B*a*b) + x*(3*A*a*b - 3*B*a**2))/(6*a**3*x**3) + b**2*(-A*b + B*a)*log(x + (-A*a*b**3 + B*a**2*b**2 - a*b**2*(-A*b + B*a))/(-2*A*b**4 + 2*B*a*b**3))/a**4 - b**2*(-A*b + B*a)*log(x + (-A*a*b**3 + B*a**2*b**2 + a*b**2*(-A*b + B*a))/(-2*A*b**4 + 2*B*a*b**3))/a**4","A",0
713,1,189,0,0.594062," ","integrate((B*x+A)/x**5/((b*x+a)**2)**(1/2),x)","\frac{- 3 A a^{3} + x^{3} \left(12 A b^{3} - 12 B a b^{2}\right) + x^{2} \left(- 6 A a b^{2} + 6 B a^{2} b\right) + x \left(4 A a^{2} b - 4 B a^{3}\right)}{12 a^{4} x^{4}} - \frac{b^{3} \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{4} + B a^{2} b^{3} - a b^{3} \left(- A b + B a\right)}{- 2 A b^{5} + 2 B a b^{4}} \right)}}{a^{5}} + \frac{b^{3} \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{4} + B a^{2} b^{3} + a b^{3} \left(- A b + B a\right)}{- 2 A b^{5} + 2 B a b^{4}} \right)}}{a^{5}}"," ",0,"(-3*A*a**3 + x**3*(12*A*b**3 - 12*B*a*b**2) + x**2*(-6*A*a*b**2 + 6*B*a**2*b) + x*(4*A*a**2*b - 4*B*a**3))/(12*a**4*x**4) - b**3*(-A*b + B*a)*log(x + (-A*a*b**4 + B*a**2*b**3 - a*b**3*(-A*b + B*a))/(-2*A*b**5 + 2*B*a*b**4))/a**5 + b**3*(-A*b + B*a)*log(x + (-A*a*b**4 + B*a**2*b**3 + a*b**3*(-A*b + B*a))/(-2*A*b**5 + 2*B*a*b**4))/a**5","A",0
714,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*(A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
715,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
716,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
717,0,0,0,0.000000," ","integrate(x*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{x \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
718,0,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
719,0,0,0,0.000000," ","integrate((B*x+A)/x/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{x \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*((a + b*x)**2)**(3/2)), x)","F",0
720,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{x^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**2*((a + b*x)**2)**(3/2)), x)","F",0
721,0,0,0,0.000000," ","integrate((B*x+A)/x**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{x^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**3*((a + b*x)**2)**(3/2)), x)","F",0
722,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*(A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
723,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
724,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
725,0,0,0,0.000000," ","integrate(x*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{x \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
726,0,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{A + B x}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
727,0,0,0,0.000000," ","integrate((B*x+A)/x/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{A + B x}{x \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*((a + b*x)**2)**(5/2)), x)","F",0
728,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{A + B x}{x^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**2*((a + b*x)**2)**(5/2)), x)","F",0
729,1,80,0,8.079636," ","integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a b x^{\frac{11}{2}}}{11} + \frac{2 A b^{2} x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a b x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**2*x**(9/2)/9 + 4*A*a*b*x**(11/2)/11 + 2*A*b**2*x**(13/2)/13 + 2*B*a**2*x**(11/2)/11 + 4*B*a*b*x**(13/2)/13 + 2*B*b**2*x**(15/2)/15","A",0
730,1,80,0,3.979480," ","integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{4 A a b x^{\frac{9}{2}}}{9} + \frac{2 A b^{2} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} x^{\frac{9}{2}}}{9} + \frac{4 B a b x^{\frac{11}{2}}}{11} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13}"," ",0,"2*A*a**2*x**(7/2)/7 + 4*A*a*b*x**(9/2)/9 + 2*A*b**2*x**(11/2)/11 + 2*B*a**2*x**(9/2)/9 + 4*B*a*b*x**(11/2)/11 + 2*B*b**2*x**(13/2)/13","A",0
731,1,80,0,1.773646," ","integrate(x**(3/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\frac{2 A a^{2} x^{\frac{5}{2}}}{5} + \frac{4 A a b x^{\frac{7}{2}}}{7} + \frac{2 A b^{2} x^{\frac{9}{2}}}{9} + \frac{2 B a^{2} x^{\frac{7}{2}}}{7} + \frac{4 B a b x^{\frac{9}{2}}}{9} + \frac{2 B b^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*A*a**2*x**(5/2)/5 + 4*A*a*b*x**(7/2)/7 + 2*A*b**2*x**(9/2)/9 + 2*B*a**2*x**(7/2)/7 + 4*B*a*b*x**(9/2)/9 + 2*B*b**2*x**(11/2)/11","A",0
732,1,66,0,2.899990," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)*x**(1/2),x)","\frac{2 A a^{2} x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{9}{2}}}{9} + \frac{2 x^{\frac{7}{2}} \left(A b^{2} + 2 B a b\right)}{7} + \frac{2 x^{\frac{5}{2}} \left(2 A a b + B a^{2}\right)}{5}"," ",0,"2*A*a**2*x**(3/2)/3 + 2*B*b**2*x**(9/2)/9 + 2*x**(7/2)*(A*b**2 + 2*B*a*b)/7 + 2*x**(5/2)*(2*A*a*b + B*a**2)/5","A",0
733,1,78,0,0.463423," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**(1/2),x)","2 A a^{2} \sqrt{x} + \frac{4 A a b x^{\frac{3}{2}}}{3} + \frac{2 A b^{2} x^{\frac{5}{2}}}{5} + \frac{2 B a^{2} x^{\frac{3}{2}}}{3} + \frac{4 B a b x^{\frac{5}{2}}}{5} + \frac{2 B b^{2} x^{\frac{7}{2}}}{7}"," ",0,"2*A*a**2*sqrt(x) + 4*A*a*b*x**(3/2)/3 + 2*A*b**2*x**(5/2)/5 + 2*B*a**2*x**(3/2)/3 + 4*B*a*b*x**(5/2)/5 + 2*B*b**2*x**(7/2)/7","A",0
734,1,75,0,0.664549," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**(3/2),x)","- \frac{2 A a^{2}}{\sqrt{x}} + 4 A a b \sqrt{x} + \frac{2 A b^{2} x^{\frac{3}{2}}}{3} + 2 B a^{2} \sqrt{x} + \frac{4 B a b x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**2/sqrt(x) + 4*A*a*b*sqrt(x) + 2*A*b**2*x**(3/2)/3 + 2*B*a**2*sqrt(x) + 4*B*a*b*x**(3/2)/3 + 2*B*b**2*x**(5/2)/5","A",0
735,1,73,0,0.802531," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**(5/2),x)","- \frac{2 A a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 A a b}{\sqrt{x}} + 2 A b^{2} \sqrt{x} - \frac{2 B a^{2}}{\sqrt{x}} + 4 B a b \sqrt{x} + \frac{2 B b^{2} x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a**2/(3*x**(3/2)) - 4*A*a*b/sqrt(x) + 2*A*b**2*sqrt(x) - 2*B*a**2/sqrt(x) + 4*B*a*b*sqrt(x) + 2*B*b**2*x**(3/2)/3","A",0
736,1,75,0,1.472366," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**(7/2),x)","- \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a b}{3 x^{\frac{3}{2}}} - \frac{2 A b^{2}}{\sqrt{x}} - \frac{2 B a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 B a b}{\sqrt{x}} + 2 B b^{2} \sqrt{x}"," ",0,"-2*A*a**2/(5*x**(5/2)) - 4*A*a*b/(3*x**(3/2)) - 2*A*b**2/sqrt(x) - 2*B*a**2/(3*x**(3/2)) - 4*B*a*b/sqrt(x) + 2*B*b**2*sqrt(x)","A",0
737,1,80,0,3.067446," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**(9/2),x)","- \frac{2 A a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 A a b}{5 x^{\frac{5}{2}}} - \frac{2 A b^{2}}{3 x^{\frac{3}{2}}} - \frac{2 B a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 B a b}{3 x^{\frac{3}{2}}} - \frac{2 B b^{2}}{\sqrt{x}}"," ",0,"-2*A*a**2/(7*x**(7/2)) - 4*A*a*b/(5*x**(5/2)) - 2*A*b**2/(3*x**(3/2)) - 2*B*a**2/(5*x**(5/2)) - 4*B*a*b/(3*x**(3/2)) - 2*B*b**2/sqrt(x)","A",0
738,1,148,0,15.901027," ","integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{2 A a^{4} x^{\frac{9}{2}}}{9} + \frac{8 A a^{3} b x^{\frac{11}{2}}}{11} + \frac{12 A a^{2} b^{2} x^{\frac{13}{2}}}{13} + \frac{8 A a b^{3} x^{\frac{15}{2}}}{15} + \frac{2 A b^{4} x^{\frac{17}{2}}}{17} + \frac{2 B a^{4} x^{\frac{11}{2}}}{11} + \frac{8 B a^{3} b x^{\frac{13}{2}}}{13} + \frac{4 B a^{2} b^{2} x^{\frac{15}{2}}}{5} + \frac{8 B a b^{3} x^{\frac{17}{2}}}{17} + \frac{2 B b^{4} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**4*x**(9/2)/9 + 8*A*a**3*b*x**(11/2)/11 + 12*A*a**2*b**2*x**(13/2)/13 + 8*A*a*b**3*x**(15/2)/15 + 2*A*b**4*x**(17/2)/17 + 2*B*a**4*x**(11/2)/11 + 8*B*a**3*b*x**(13/2)/13 + 4*B*a**2*b**2*x**(15/2)/5 + 8*B*a*b**3*x**(17/2)/17 + 2*B*b**4*x**(19/2)/19","A",0
739,1,148,0,8.746375," ","integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{2 A a^{4} x^{\frac{7}{2}}}{7} + \frac{8 A a^{3} b x^{\frac{9}{2}}}{9} + \frac{12 A a^{2} b^{2} x^{\frac{11}{2}}}{11} + \frac{8 A a b^{3} x^{\frac{13}{2}}}{13} + \frac{2 A b^{4} x^{\frac{15}{2}}}{15} + \frac{2 B a^{4} x^{\frac{9}{2}}}{9} + \frac{8 B a^{3} b x^{\frac{11}{2}}}{11} + \frac{12 B a^{2} b^{2} x^{\frac{13}{2}}}{13} + \frac{8 B a b^{3} x^{\frac{15}{2}}}{15} + \frac{2 B b^{4} x^{\frac{17}{2}}}{17}"," ",0,"2*A*a**4*x**(7/2)/7 + 8*A*a**3*b*x**(9/2)/9 + 12*A*a**2*b**2*x**(11/2)/11 + 8*A*a*b**3*x**(13/2)/13 + 2*A*b**4*x**(15/2)/15 + 2*B*a**4*x**(9/2)/9 + 8*B*a**3*b*x**(11/2)/11 + 12*B*a**2*b**2*x**(13/2)/13 + 8*B*a*b**3*x**(15/2)/15 + 2*B*b**4*x**(17/2)/17","A",0
740,1,148,0,4.299250," ","integrate(x**(3/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{2 A a^{4} x^{\frac{5}{2}}}{5} + \frac{8 A a^{3} b x^{\frac{7}{2}}}{7} + \frac{4 A a^{2} b^{2} x^{\frac{9}{2}}}{3} + \frac{8 A a b^{3} x^{\frac{11}{2}}}{11} + \frac{2 A b^{4} x^{\frac{13}{2}}}{13} + \frac{2 B a^{4} x^{\frac{7}{2}}}{7} + \frac{8 B a^{3} b x^{\frac{9}{2}}}{9} + \frac{12 B a^{2} b^{2} x^{\frac{11}{2}}}{11} + \frac{8 B a b^{3} x^{\frac{13}{2}}}{13} + \frac{2 B b^{4} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**4*x**(5/2)/5 + 8*A*a**3*b*x**(7/2)/7 + 4*A*a**2*b**2*x**(9/2)/3 + 8*A*a*b**3*x**(11/2)/11 + 2*A*b**4*x**(13/2)/13 + 2*B*a**4*x**(7/2)/7 + 8*B*a**3*b*x**(9/2)/9 + 12*B*a**2*b**2*x**(11/2)/11 + 8*B*a*b**3*x**(13/2)/13 + 2*B*b**4*x**(15/2)/15","A",0
741,1,124,0,4.383006," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2*x**(1/2),x)","\frac{2 A a^{4} x^{\frac{3}{2}}}{3} + \frac{2 B b^{4} x^{\frac{13}{2}}}{13} + \frac{2 x^{\frac{11}{2}} \left(A b^{4} + 4 B a b^{3}\right)}{11} + \frac{2 x^{\frac{9}{2}} \left(4 A a b^{3} + 6 B a^{2} b^{2}\right)}{9} + \frac{2 x^{\frac{7}{2}} \left(6 A a^{2} b^{2} + 4 B a^{3} b\right)}{7} + \frac{2 x^{\frac{5}{2}} \left(4 A a^{3} b + B a^{4}\right)}{5}"," ",0,"2*A*a**4*x**(3/2)/3 + 2*B*b**4*x**(13/2)/13 + 2*x**(11/2)*(A*b**4 + 4*B*a*b**3)/11 + 2*x**(9/2)*(4*A*a*b**3 + 6*B*a**2*b**2)/9 + 2*x**(7/2)*(6*A*a**2*b**2 + 4*B*a**3*b)/7 + 2*x**(5/2)*(4*A*a**3*b + B*a**4)/5","A",0
742,1,146,0,1.583458," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(1/2),x)","2 A a^{4} \sqrt{x} + \frac{8 A a^{3} b x^{\frac{3}{2}}}{3} + \frac{12 A a^{2} b^{2} x^{\frac{5}{2}}}{5} + \frac{8 A a b^{3} x^{\frac{7}{2}}}{7} + \frac{2 A b^{4} x^{\frac{9}{2}}}{9} + \frac{2 B a^{4} x^{\frac{3}{2}}}{3} + \frac{8 B a^{3} b x^{\frac{5}{2}}}{5} + \frac{12 B a^{2} b^{2} x^{\frac{7}{2}}}{7} + \frac{8 B a b^{3} x^{\frac{9}{2}}}{9} + \frac{2 B b^{4} x^{\frac{11}{2}}}{11}"," ",0,"2*A*a**4*sqrt(x) + 8*A*a**3*b*x**(3/2)/3 + 12*A*a**2*b**2*x**(5/2)/5 + 8*A*a*b**3*x**(7/2)/7 + 2*A*b**4*x**(9/2)/9 + 2*B*a**4*x**(3/2)/3 + 8*B*a**3*b*x**(5/2)/5 + 12*B*a**2*b**2*x**(7/2)/7 + 8*B*a*b**3*x**(9/2)/9 + 2*B*b**4*x**(11/2)/11","A",0
743,1,141,0,1.799037," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(3/2),x)","- \frac{2 A a^{4}}{\sqrt{x}} + 8 A a^{3} b \sqrt{x} + 4 A a^{2} b^{2} x^{\frac{3}{2}} + \frac{8 A a b^{3} x^{\frac{5}{2}}}{5} + \frac{2 A b^{4} x^{\frac{7}{2}}}{7} + 2 B a^{4} \sqrt{x} + \frac{8 B a^{3} b x^{\frac{3}{2}}}{3} + \frac{12 B a^{2} b^{2} x^{\frac{5}{2}}}{5} + \frac{8 B a b^{3} x^{\frac{7}{2}}}{7} + \frac{2 B b^{4} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**4/sqrt(x) + 8*A*a**3*b*sqrt(x) + 4*A*a**2*b**2*x**(3/2) + 8*A*a*b**3*x**(5/2)/5 + 2*A*b**4*x**(7/2)/7 + 2*B*a**4*sqrt(x) + 8*B*a**3*b*x**(3/2)/3 + 12*B*a**2*b**2*x**(5/2)/5 + 8*B*a*b**3*x**(7/2)/7 + 2*B*b**4*x**(9/2)/9","A",0
744,1,139,0,2.156172," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(5/2),x)","- \frac{2 A a^{4}}{3 x^{\frac{3}{2}}} - \frac{8 A a^{3} b}{\sqrt{x}} + 12 A a^{2} b^{2} \sqrt{x} + \frac{8 A a b^{3} x^{\frac{3}{2}}}{3} + \frac{2 A b^{4} x^{\frac{5}{2}}}{5} - \frac{2 B a^{4}}{\sqrt{x}} + 8 B a^{3} b \sqrt{x} + 4 B a^{2} b^{2} x^{\frac{3}{2}} + \frac{8 B a b^{3} x^{\frac{5}{2}}}{5} + \frac{2 B b^{4} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**4/(3*x**(3/2)) - 8*A*a**3*b/sqrt(x) + 12*A*a**2*b**2*sqrt(x) + 8*A*a*b**3*x**(3/2)/3 + 2*A*b**4*x**(5/2)/5 - 2*B*a**4/sqrt(x) + 8*B*a**3*b*sqrt(x) + 4*B*a**2*b**2*x**(3/2) + 8*B*a*b**3*x**(5/2)/5 + 2*B*b**4*x**(7/2)/7","A",0
745,1,141,0,3.137360," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(7/2),x)","- \frac{2 A a^{4}}{5 x^{\frac{5}{2}}} - \frac{8 A a^{3} b}{3 x^{\frac{3}{2}}} - \frac{12 A a^{2} b^{2}}{\sqrt{x}} + 8 A a b^{3} \sqrt{x} + \frac{2 A b^{4} x^{\frac{3}{2}}}{3} - \frac{2 B a^{4}}{3 x^{\frac{3}{2}}} - \frac{8 B a^{3} b}{\sqrt{x}} + 12 B a^{2} b^{2} \sqrt{x} + \frac{8 B a b^{3} x^{\frac{3}{2}}}{3} + \frac{2 B b^{4} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**4/(5*x**(5/2)) - 8*A*a**3*b/(3*x**(3/2)) - 12*A*a**2*b**2/sqrt(x) + 8*A*a*b**3*sqrt(x) + 2*A*b**4*x**(3/2)/3 - 2*B*a**4/(3*x**(3/2)) - 8*B*a**3*b/sqrt(x) + 12*B*a**2*b**2*sqrt(x) + 8*B*a*b**3*x**(3/2)/3 + 2*B*b**4*x**(5/2)/5","A",0
746,1,139,0,4.102551," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(9/2),x)","- \frac{2 A a^{4}}{7 x^{\frac{7}{2}}} - \frac{8 A a^{3} b}{5 x^{\frac{5}{2}}} - \frac{4 A a^{2} b^{2}}{x^{\frac{3}{2}}} - \frac{8 A a b^{3}}{\sqrt{x}} + 2 A b^{4} \sqrt{x} - \frac{2 B a^{4}}{5 x^{\frac{5}{2}}} - \frac{8 B a^{3} b}{3 x^{\frac{3}{2}}} - \frac{12 B a^{2} b^{2}}{\sqrt{x}} + 8 B a b^{3} \sqrt{x} + \frac{2 B b^{4} x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a**4/(7*x**(7/2)) - 8*A*a**3*b/(5*x**(5/2)) - 4*A*a**2*b**2/x**(3/2) - 8*A*a*b**3/sqrt(x) + 2*A*b**4*sqrt(x) - 2*B*a**4/(5*x**(5/2)) - 8*B*a**3*b/(3*x**(3/2)) - 12*B*a**2*b**2/sqrt(x) + 8*B*a*b**3*sqrt(x) + 2*B*b**4*x**(3/2)/3","A",0
747,1,214,0,28.781855," ","integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{2 A a^{6} x^{\frac{9}{2}}}{9} + \frac{12 A a^{5} b x^{\frac{11}{2}}}{11} + \frac{30 A a^{4} b^{2} x^{\frac{13}{2}}}{13} + \frac{8 A a^{3} b^{3} x^{\frac{15}{2}}}{3} + \frac{30 A a^{2} b^{4} x^{\frac{17}{2}}}{17} + \frac{12 A a b^{5} x^{\frac{19}{2}}}{19} + \frac{2 A b^{6} x^{\frac{21}{2}}}{21} + \frac{2 B a^{6} x^{\frac{11}{2}}}{11} + \frac{12 B a^{5} b x^{\frac{13}{2}}}{13} + 2 B a^{4} b^{2} x^{\frac{15}{2}} + \frac{40 B a^{3} b^{3} x^{\frac{17}{2}}}{17} + \frac{30 B a^{2} b^{4} x^{\frac{19}{2}}}{19} + \frac{4 B a b^{5} x^{\frac{21}{2}}}{7} + \frac{2 B b^{6} x^{\frac{23}{2}}}{23}"," ",0,"2*A*a**6*x**(9/2)/9 + 12*A*a**5*b*x**(11/2)/11 + 30*A*a**4*b**2*x**(13/2)/13 + 8*A*a**3*b**3*x**(15/2)/3 + 30*A*a**2*b**4*x**(17/2)/17 + 12*A*a*b**5*x**(19/2)/19 + 2*A*b**6*x**(21/2)/21 + 2*B*a**6*x**(11/2)/11 + 12*B*a**5*b*x**(13/2)/13 + 2*B*a**4*b**2*x**(15/2) + 40*B*a**3*b**3*x**(17/2)/17 + 30*B*a**2*b**4*x**(19/2)/19 + 4*B*a*b**5*x**(21/2)/7 + 2*B*b**6*x**(23/2)/23","A",0
748,1,214,0,19.548400," ","integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{2 A a^{6} x^{\frac{7}{2}}}{7} + \frac{4 A a^{5} b x^{\frac{9}{2}}}{3} + \frac{30 A a^{4} b^{2} x^{\frac{11}{2}}}{11} + \frac{40 A a^{3} b^{3} x^{\frac{13}{2}}}{13} + 2 A a^{2} b^{4} x^{\frac{15}{2}} + \frac{12 A a b^{5} x^{\frac{17}{2}}}{17} + \frac{2 A b^{6} x^{\frac{19}{2}}}{19} + \frac{2 B a^{6} x^{\frac{9}{2}}}{9} + \frac{12 B a^{5} b x^{\frac{11}{2}}}{11} + \frac{30 B a^{4} b^{2} x^{\frac{13}{2}}}{13} + \frac{8 B a^{3} b^{3} x^{\frac{15}{2}}}{3} + \frac{30 B a^{2} b^{4} x^{\frac{17}{2}}}{17} + \frac{12 B a b^{5} x^{\frac{19}{2}}}{19} + \frac{2 B b^{6} x^{\frac{21}{2}}}{21}"," ",0,"2*A*a**6*x**(7/2)/7 + 4*A*a**5*b*x**(9/2)/3 + 30*A*a**4*b**2*x**(11/2)/11 + 40*A*a**3*b**3*x**(13/2)/13 + 2*A*a**2*b**4*x**(15/2) + 12*A*a*b**5*x**(17/2)/17 + 2*A*b**6*x**(19/2)/19 + 2*B*a**6*x**(9/2)/9 + 12*B*a**5*b*x**(11/2)/11 + 30*B*a**4*b**2*x**(13/2)/13 + 8*B*a**3*b**3*x**(15/2)/3 + 30*B*a**2*b**4*x**(17/2)/17 + 12*B*a*b**5*x**(19/2)/19 + 2*B*b**6*x**(21/2)/21","A",0
749,1,214,0,10.106553," ","integrate(x**(3/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{2 A a^{6} x^{\frac{5}{2}}}{5} + \frac{12 A a^{5} b x^{\frac{7}{2}}}{7} + \frac{10 A a^{4} b^{2} x^{\frac{9}{2}}}{3} + \frac{40 A a^{3} b^{3} x^{\frac{11}{2}}}{11} + \frac{30 A a^{2} b^{4} x^{\frac{13}{2}}}{13} + \frac{4 A a b^{5} x^{\frac{15}{2}}}{5} + \frac{2 A b^{6} x^{\frac{17}{2}}}{17} + \frac{2 B a^{6} x^{\frac{7}{2}}}{7} + \frac{4 B a^{5} b x^{\frac{9}{2}}}{3} + \frac{30 B a^{4} b^{2} x^{\frac{11}{2}}}{11} + \frac{40 B a^{3} b^{3} x^{\frac{13}{2}}}{13} + 2 B a^{2} b^{4} x^{\frac{15}{2}} + \frac{12 B a b^{5} x^{\frac{17}{2}}}{17} + \frac{2 B b^{6} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**6*x**(5/2)/5 + 12*A*a**5*b*x**(7/2)/7 + 10*A*a**4*b**2*x**(9/2)/3 + 40*A*a**3*b**3*x**(11/2)/11 + 30*A*a**2*b**4*x**(13/2)/13 + 4*A*a*b**5*x**(15/2)/5 + 2*A*b**6*x**(17/2)/17 + 2*B*a**6*x**(7/2)/7 + 4*B*a**5*b*x**(9/2)/3 + 30*B*a**4*b**2*x**(11/2)/11 + 40*B*a**3*b**3*x**(13/2)/13 + 2*B*a**2*b**4*x**(15/2) + 12*B*a*b**5*x**(17/2)/17 + 2*B*b**6*x**(19/2)/19","A",0
750,1,182,0,5.907732," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3*x**(1/2),x)","\frac{2 A a^{6} x^{\frac{3}{2}}}{3} + \frac{2 B b^{6} x^{\frac{17}{2}}}{17} + \frac{2 x^{\frac{15}{2}} \left(A b^{6} + 6 B a b^{5}\right)}{15} + \frac{2 x^{\frac{13}{2}} \left(6 A a b^{5} + 15 B a^{2} b^{4}\right)}{13} + \frac{2 x^{\frac{11}{2}} \left(15 A a^{2} b^{4} + 20 B a^{3} b^{3}\right)}{11} + \frac{2 x^{\frac{9}{2}} \left(20 A a^{3} b^{3} + 15 B a^{4} b^{2}\right)}{9} + \frac{2 x^{\frac{7}{2}} \left(15 A a^{4} b^{2} + 6 B a^{5} b\right)}{7} + \frac{2 x^{\frac{5}{2}} \left(6 A a^{5} b + B a^{6}\right)}{5}"," ",0,"2*A*a**6*x**(3/2)/3 + 2*B*b**6*x**(17/2)/17 + 2*x**(15/2)*(A*b**6 + 6*B*a*b**5)/15 + 2*x**(13/2)*(6*A*a*b**5 + 15*B*a**2*b**4)/13 + 2*x**(11/2)*(15*A*a**2*b**4 + 20*B*a**3*b**3)/11 + 2*x**(9/2)*(20*A*a**3*b**3 + 15*B*a**4*b**2)/9 + 2*x**(7/2)*(15*A*a**4*b**2 + 6*B*a**5*b)/7 + 2*x**(5/2)*(6*A*a**5*b + B*a**6)/5","A",0
751,1,211,0,4.109933," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**(1/2),x)","2 A a^{6} \sqrt{x} + 4 A a^{5} b x^{\frac{3}{2}} + 6 A a^{4} b^{2} x^{\frac{5}{2}} + \frac{40 A a^{3} b^{3} x^{\frac{7}{2}}}{7} + \frac{10 A a^{2} b^{4} x^{\frac{9}{2}}}{3} + \frac{12 A a b^{5} x^{\frac{11}{2}}}{11} + \frac{2 A b^{6} x^{\frac{13}{2}}}{13} + \frac{2 B a^{6} x^{\frac{3}{2}}}{3} + \frac{12 B a^{5} b x^{\frac{5}{2}}}{5} + \frac{30 B a^{4} b^{2} x^{\frac{7}{2}}}{7} + \frac{40 B a^{3} b^{3} x^{\frac{9}{2}}}{9} + \frac{30 B a^{2} b^{4} x^{\frac{11}{2}}}{11} + \frac{12 B a b^{5} x^{\frac{13}{2}}}{13} + \frac{2 B b^{6} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**6*sqrt(x) + 4*A*a**5*b*x**(3/2) + 6*A*a**4*b**2*x**(5/2) + 40*A*a**3*b**3*x**(7/2)/7 + 10*A*a**2*b**4*x**(9/2)/3 + 12*A*a*b**5*x**(11/2)/11 + 2*A*b**6*x**(13/2)/13 + 2*B*a**6*x**(3/2)/3 + 12*B*a**5*b*x**(5/2)/5 + 30*B*a**4*b**2*x**(7/2)/7 + 40*B*a**3*b**3*x**(9/2)/9 + 30*B*a**2*b**4*x**(11/2)/11 + 12*B*a*b**5*x**(13/2)/13 + 2*B*b**6*x**(15/2)/15","A",0
752,1,204,0,4.601112," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**(3/2),x)","- \frac{2 A a^{6}}{\sqrt{x}} + 12 A a^{5} b \sqrt{x} + 10 A a^{4} b^{2} x^{\frac{3}{2}} + 8 A a^{3} b^{3} x^{\frac{5}{2}} + \frac{30 A a^{2} b^{4} x^{\frac{7}{2}}}{7} + \frac{4 A a b^{5} x^{\frac{9}{2}}}{3} + \frac{2 A b^{6} x^{\frac{11}{2}}}{11} + 2 B a^{6} \sqrt{x} + 4 B a^{5} b x^{\frac{3}{2}} + 6 B a^{4} b^{2} x^{\frac{5}{2}} + \frac{40 B a^{3} b^{3} x^{\frac{7}{2}}}{7} + \frac{10 B a^{2} b^{4} x^{\frac{9}{2}}}{3} + \frac{12 B a b^{5} x^{\frac{11}{2}}}{11} + \frac{2 B b^{6} x^{\frac{13}{2}}}{13}"," ",0,"-2*A*a**6/sqrt(x) + 12*A*a**5*b*sqrt(x) + 10*A*a**4*b**2*x**(3/2) + 8*A*a**3*b**3*x**(5/2) + 30*A*a**2*b**4*x**(7/2)/7 + 4*A*a*b**5*x**(9/2)/3 + 2*A*b**6*x**(11/2)/11 + 2*B*a**6*sqrt(x) + 4*B*a**5*b*x**(3/2) + 6*B*a**4*b**2*x**(5/2) + 40*B*a**3*b**3*x**(7/2)/7 + 10*B*a**2*b**4*x**(9/2)/3 + 12*B*a*b**5*x**(11/2)/11 + 2*B*b**6*x**(13/2)/13","A",0
753,1,204,0,5.441106," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**(5/2),x)","- \frac{2 A a^{6}}{3 x^{\frac{3}{2}}} - \frac{12 A a^{5} b}{\sqrt{x}} + 30 A a^{4} b^{2} \sqrt{x} + \frac{40 A a^{3} b^{3} x^{\frac{3}{2}}}{3} + 6 A a^{2} b^{4} x^{\frac{5}{2}} + \frac{12 A a b^{5} x^{\frac{7}{2}}}{7} + \frac{2 A b^{6} x^{\frac{9}{2}}}{9} - \frac{2 B a^{6}}{\sqrt{x}} + 12 B a^{5} b \sqrt{x} + 10 B a^{4} b^{2} x^{\frac{3}{2}} + 8 B a^{3} b^{3} x^{\frac{5}{2}} + \frac{30 B a^{2} b^{4} x^{\frac{7}{2}}}{7} + \frac{4 B a b^{5} x^{\frac{9}{2}}}{3} + \frac{2 B b^{6} x^{\frac{11}{2}}}{11}"," ",0,"-2*A*a**6/(3*x**(3/2)) - 12*A*a**5*b/sqrt(x) + 30*A*a**4*b**2*sqrt(x) + 40*A*a**3*b**3*x**(3/2)/3 + 6*A*a**2*b**4*x**(5/2) + 12*A*a*b**5*x**(7/2)/7 + 2*A*b**6*x**(9/2)/9 - 2*B*a**6/sqrt(x) + 12*B*a**5*b*sqrt(x) + 10*B*a**4*b**2*x**(3/2) + 8*B*a**3*b**3*x**(5/2) + 30*B*a**2*b**4*x**(7/2)/7 + 4*B*a*b**5*x**(9/2)/3 + 2*B*b**6*x**(11/2)/11","A",0
754,1,204,0,7.323077," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**(7/2),x)","- \frac{2 A a^{6}}{5 x^{\frac{5}{2}}} - \frac{4 A a^{5} b}{x^{\frac{3}{2}}} - \frac{30 A a^{4} b^{2}}{\sqrt{x}} + 40 A a^{3} b^{3} \sqrt{x} + 10 A a^{2} b^{4} x^{\frac{3}{2}} + \frac{12 A a b^{5} x^{\frac{5}{2}}}{5} + \frac{2 A b^{6} x^{\frac{7}{2}}}{7} - \frac{2 B a^{6}}{3 x^{\frac{3}{2}}} - \frac{12 B a^{5} b}{\sqrt{x}} + 30 B a^{4} b^{2} \sqrt{x} + \frac{40 B a^{3} b^{3} x^{\frac{3}{2}}}{3} + 6 B a^{2} b^{4} x^{\frac{5}{2}} + \frac{12 B a b^{5} x^{\frac{7}{2}}}{7} + \frac{2 B b^{6} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**6/(5*x**(5/2)) - 4*A*a**5*b/x**(3/2) - 30*A*a**4*b**2/sqrt(x) + 40*A*a**3*b**3*sqrt(x) + 10*A*a**2*b**4*x**(3/2) + 12*A*a*b**5*x**(5/2)/5 + 2*A*b**6*x**(7/2)/7 - 2*B*a**6/(3*x**(3/2)) - 12*B*a**5*b/sqrt(x) + 30*B*a**4*b**2*sqrt(x) + 40*B*a**3*b**3*x**(3/2)/3 + 6*B*a**2*b**4*x**(5/2) + 12*B*a*b**5*x**(7/2)/7 + 2*B*b**6*x**(9/2)/9","A",0
755,1,202,0,9.614680," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**(9/2),x)","- \frac{2 A a^{6}}{7 x^{\frac{7}{2}}} - \frac{12 A a^{5} b}{5 x^{\frac{5}{2}}} - \frac{10 A a^{4} b^{2}}{x^{\frac{3}{2}}} - \frac{40 A a^{3} b^{3}}{\sqrt{x}} + 30 A a^{2} b^{4} \sqrt{x} + 4 A a b^{5} x^{\frac{3}{2}} + \frac{2 A b^{6} x^{\frac{5}{2}}}{5} - \frac{2 B a^{6}}{5 x^{\frac{5}{2}}} - \frac{4 B a^{5} b}{x^{\frac{3}{2}}} - \frac{30 B a^{4} b^{2}}{\sqrt{x}} + 40 B a^{3} b^{3} \sqrt{x} + 10 B a^{2} b^{4} x^{\frac{3}{2}} + \frac{12 B a b^{5} x^{\frac{5}{2}}}{5} + \frac{2 B b^{6} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**6/(7*x**(7/2)) - 12*A*a**5*b/(5*x**(5/2)) - 10*A*a**4*b**2/x**(3/2) - 40*A*a**3*b**3/sqrt(x) + 30*A*a**2*b**4*sqrt(x) + 4*A*a*b**5*x**(3/2) + 2*A*b**6*x**(5/2)/5 - 2*B*a**6/(5*x**(5/2)) - 4*B*a**5*b/x**(3/2) - 30*B*a**4*b**2/sqrt(x) + 40*B*a**3*b**3*sqrt(x) + 10*B*a**2*b**4*x**(3/2) + 12*B*a*b**5*x**(5/2)/5 + 2*B*b**6*x**(7/2)/7","A",0
756,1,204,0,12.624548," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x**(11/2),x)","- \frac{2 A a^{6}}{9 x^{\frac{9}{2}}} - \frac{12 A a^{5} b}{7 x^{\frac{7}{2}}} - \frac{6 A a^{4} b^{2}}{x^{\frac{5}{2}}} - \frac{40 A a^{3} b^{3}}{3 x^{\frac{3}{2}}} - \frac{30 A a^{2} b^{4}}{\sqrt{x}} + 12 A a b^{5} \sqrt{x} + \frac{2 A b^{6} x^{\frac{3}{2}}}{3} - \frac{2 B a^{6}}{7 x^{\frac{7}{2}}} - \frac{12 B a^{5} b}{5 x^{\frac{5}{2}}} - \frac{10 B a^{4} b^{2}}{x^{\frac{3}{2}}} - \frac{40 B a^{3} b^{3}}{\sqrt{x}} + 30 B a^{2} b^{4} \sqrt{x} + 4 B a b^{5} x^{\frac{3}{2}} + \frac{2 B b^{6} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**6/(9*x**(9/2)) - 12*A*a**5*b/(7*x**(7/2)) - 6*A*a**4*b**2/x**(5/2) - 40*A*a**3*b**3/(3*x**(3/2)) - 30*A*a**2*b**4/sqrt(x) + 12*A*a*b**5*sqrt(x) + 2*A*b**6*x**(3/2)/3 - 2*B*a**6/(7*x**(7/2)) - 12*B*a**5*b/(5*x**(5/2)) - 10*B*a**4*b**2/x**(3/2) - 40*B*a**3*b**3/sqrt(x) + 30*B*a**2*b**4*sqrt(x) + 4*B*a*b**5*x**(3/2) + 2*B*b**6*x**(5/2)/5","A",0
757,1,1197,0,153.513591," ","integrate(x**(7/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{9}{2}}}{9} + \frac{2 B x^{\frac{11}{2}}}{11}}{a^{2}} & \text{for}\: b = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}}{b^{2}} & \text{for}\: a = 0 \\\frac{1470 i A a^{\frac{7}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{980 i A a^{\frac{5}{2}} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{196 i A a^{\frac{3}{2}} b^{4} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{84 i A \sqrt{a} b^{5} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{735 A a^{4} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{735 A a^{4} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{735 A a^{3} b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{735 A a^{3} b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{1890 i B a^{\frac{9}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{1260 i B a^{\frac{7}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{252 i B a^{\frac{5}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{108 i B a^{\frac{3}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{60 i B \sqrt{a} b^{5} x^{\frac{9}{2}} \sqrt{\frac{1}{b}}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{945 B a^{5} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{945 B a^{5} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} + \frac{945 B a^{4} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} - \frac{945 B a^{4} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{210 i a^{\frac{3}{2}} b^{6} \sqrt{\frac{1}{b}} + 210 i \sqrt{a} b^{7} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*x**(5/2)/5 + 2*B*x**(7/2)/7), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(9/2)/9 + 2*B*x**(11/2)/11)/a**2, Eq(b, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(7/2)/7)/b**2, Eq(a, 0)), (1470*I*A*a**(7/2)*b**2*sqrt(x)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 980*I*A*a**(5/2)*b**3*x**(3/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 196*I*A*a**(3/2)*b**4*x**(5/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 84*I*A*sqrt(a)*b**5*x**(7/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 735*A*a**4*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 735*A*a**4*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 735*A*a**3*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 735*A*a**3*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 1890*I*B*a**(9/2)*b*sqrt(x)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 1260*I*B*a**(7/2)*b**2*x**(3/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 252*I*B*a**(5/2)*b**3*x**(5/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 108*I*B*a**(3/2)*b**4*x**(7/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 60*I*B*sqrt(a)*b**5*x**(9/2)*sqrt(1/b)/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 945*B*a**5*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 945*B*a**5*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) + 945*B*a**4*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)) - 945*B*a**4*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(210*I*a**(3/2)*b**6*sqrt(1/b) + 210*I*sqrt(a)*b**7*x*sqrt(1/b)), True))","A",0
758,1,1068,0,52.862163," ","integrate(x**(5/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{7}{2}}}{7} + \frac{2 B x^{\frac{9}{2}}}{9}}{a^{2}} & \text{for}\: b = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{b^{2}} & \text{for}\: a = 0 \\- \frac{150 i A a^{\frac{5}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} - \frac{100 i A a^{\frac{3}{2}} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{20 i A \sqrt{a} b^{4} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{75 A a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} - \frac{75 A a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{75 A a^{2} b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} - \frac{75 A a^{2} b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{210 i B a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{140 i B a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} - \frac{28 i B a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{12 i B \sqrt{a} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} - \frac{105 B a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{105 B a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} - \frac{105 B a^{3} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} + \frac{105 B a^{3} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{3}{2}} b^{5} \sqrt{\frac{1}{b}} + 30 i \sqrt{a} b^{6} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*x**(3/2)/3 + 2*B*x**(5/2)/5), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(7/2)/7 + 2*B*x**(9/2)/9)/a**2, Eq(b, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/b**2, Eq(a, 0)), (-150*I*A*a**(5/2)*b**2*sqrt(x)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) - 100*I*A*a**(3/2)*b**3*x**(3/2)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 20*I*A*sqrt(a)*b**4*x**(5/2)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 75*A*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) - 75*A*a**3*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 75*A*a**2*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) - 75*A*a**2*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 210*I*B*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 140*I*B*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) - 28*I*B*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 12*I*B*sqrt(a)*b**4*x**(7/2)*sqrt(1/b)/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) - 105*B*a**4*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 105*B*a**4*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) - 105*B*a**3*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)) + 105*B*a**3*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(3/2)*b**5*sqrt(1/b) + 30*I*sqrt(a)*b**6*x*sqrt(1/b)), True))","A",0
759,1,932,0,14.338495," ","integrate(x**(3/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}}{a^{2}} & \text{for}\: b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{b^{2}} & \text{for}\: a = 0 \\\frac{18 i A a^{\frac{3}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{12 i A \sqrt{a} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{9 A a^{2} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{9 A a^{2} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{9 A a b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{9 A a b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{30 i B a^{\frac{5}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{20 i B a^{\frac{3}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{4 i B \sqrt{a} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{15 B a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{15 B a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{15 B a^{2} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{15 B a^{2} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*sqrt(x) + 2*B*x**(3/2)/3), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(7/2)/7)/a**2, Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/b**2, Eq(a, 0)), (18*I*A*a**(3/2)*b**2*sqrt(x)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 12*I*A*sqrt(a)*b**3*x**(3/2)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 9*A*a**2*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 9*A*a**2*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 9*A*a*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 9*A*a*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 30*I*B*a**(5/2)*b*sqrt(x)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 20*I*B*a**(3/2)*b**2*x**(3/2)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 4*I*B*sqrt(a)*b**3*x**(5/2)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 15*B*a**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 15*B*a**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 15*B*a**2*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 15*B*a**2*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)), True))","A",0
760,1,782,0,10.573417," ","integrate((B*x+A)*x**(1/2)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{a^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{b^{2}} & \text{for}\: a = 0 \\- \frac{2 i A \sqrt{a} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{A a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{A a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{A b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{A b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{6 i B a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{4 i B \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{3 B a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{3 B a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{3 B a b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{3 B a b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*sqrt(x)), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/a**2, Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/b**2, Eq(a, 0)), (-2*I*A*sqrt(a)*b**2*sqrt(x)*sqrt(1/b)/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + A*a*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) - A*a*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + A*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) - A*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 6*I*B*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 4*I*B*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) - 3*B*a**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 3*B*a**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) - 3*B*a*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 3*B*a*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)), True))","A",0
761,1,716,0,8.356635," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{a^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{b^{2}} & \text{for}\: a = 0 \\\frac{2 i A \sqrt{a} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} + \frac{A a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} - \frac{A a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} + \frac{A b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} - \frac{A b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} - \frac{2 i B a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} + \frac{B a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} - \frac{B a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} + \frac{B a b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} - \frac{B a b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{3} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) - 2*B/sqrt(x)), Eq(a, 0) & Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/a**2, Eq(b, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/b**2, Eq(a, 0)), (2*I*A*sqrt(a)*b**2*sqrt(x)*sqrt(1/b)/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) + A*a*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) - A*a*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) + A*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) - A*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) - 2*I*B*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) + B*a**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) - B*a**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) + B*a*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)) - B*a*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b**2*sqrt(1/b) + 2*I*a**(3/2)*b**3*x*sqrt(1/b)), True))","A",0
762,1,884,0,19.074021," ","integrate((B*x+A)/x**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{a^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{b^{2}} & \text{for}\: a = 0 \\- \frac{4 i A a^{\frac{3}{2}} b \sqrt{\frac{1}{b}}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{6 i A \sqrt{a} b^{2} x \sqrt{\frac{1}{b}}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{3 A a b \sqrt{x} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{3 A a b \sqrt{x} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{3 A b^{2} x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{3 A b^{2} x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{2 i B a^{\frac{3}{2}} b x \sqrt{\frac{1}{b}}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{B a^{2} \sqrt{x} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{B a^{2} \sqrt{x} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{B a b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{B a b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2))), Eq(a, 0) & Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/a**2, Eq(b, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/b**2, Eq(a, 0)), (-4*I*A*a**(3/2)*b*sqrt(1/b)/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) - 6*I*A*sqrt(a)*b**2*x*sqrt(1/b)/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) - 3*A*a*b*sqrt(x)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) + 3*A*a*b*sqrt(x)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) - 3*A*b**2*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) + 3*A*b**2*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) + 2*I*B*a**(3/2)*b*x*sqrt(1/b)/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) + B*a**2*sqrt(x)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) - B*a**2*sqrt(x)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) + B*a*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)) - B*a*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*b*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)), True))","A",0
763,1,983,0,53.229291," ","integrate((B*x+A)/x**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{b^{2}} & \text{for}\: a = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{a^{2}} & \text{for}\: b = 0 \\- \frac{4 i A a^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{20 i A a^{\frac{3}{2}} b x \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{30 i A \sqrt{a} b^{2} x^{2} \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 A a b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 A a b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 A b^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 A b^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{12 i B a^{\frac{5}{2}} x \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{18 i B a^{\frac{3}{2}} b x^{2} \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{9 B a^{2} x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{9 B a^{2} x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{9 B a b x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{9 B a b x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2))), Eq(a, 0) & Eq(b, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/b**2, Eq(a, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/a**2, Eq(b, 0)), (-4*I*A*a**(5/2)*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 20*I*A*a**(3/2)*b*x*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 30*I*A*sqrt(a)*b**2*x**2*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 15*A*a*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 15*A*a*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 15*A*b**2*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 15*A*b**2*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 12*I*B*a**(5/2)*x*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 18*I*B*a**(3/2)*b*x**2*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 9*B*a**2*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 9*B*a**2*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 9*B*a*b*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 9*B*a*b*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)), True))","A",0
764,1,1127,0,155.212962," ","integrate((B*x+A)/x**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{a^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{b^{2}} & \text{for}\: a = 0 \\- \frac{12 i A a^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{28 i A a^{\frac{5}{2}} b x \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{140 i A a^{\frac{3}{2}} b^{2} x^{2} \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{210 i A \sqrt{a} b^{3} x^{3} \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 A a b^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 A a b^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 A b^{3} x^{\frac{7}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 A b^{3} x^{\frac{7}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{20 i B a^{\frac{7}{2}} x \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{100 i B a^{\frac{5}{2}} b x^{2} \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{150 i B a^{\frac{3}{2}} b^{2} x^{3} \sqrt{\frac{1}{b}}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{75 B a^{2} b x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{75 B a^{2} b x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{75 B a b^{2} x^{\frac{7}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{75 B a b^{2} x^{\frac{7}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{30 i a^{\frac{11}{2}} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 30 i a^{\frac{9}{2}} b x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(a, 0) & Eq(b, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/a**2, Eq(b, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/b**2, Eq(a, 0)), (-12*I*A*a**(7/2)*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 28*I*A*a**(5/2)*b*x*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 140*I*A*a**(3/2)*b**2*x**2*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 210*I*A*sqrt(a)*b**3*x**3*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 105*A*a*b**2*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 105*A*a*b**2*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 105*A*b**3*x**(7/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 105*A*b**3*x**(7/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 20*I*B*a**(7/2)*x*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 100*I*B*a**(5/2)*b*x**2*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 150*I*B*a**(3/2)*b**2*x**3*sqrt(1/b)/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 75*B*a**2*b*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 75*B*a**2*b*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) + 75*B*a*b**2*x**(7/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)) - 75*B*a*b**2*x**(7/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(30*I*a**(11/2)*x**(5/2)*sqrt(1/b) + 30*I*a**(9/2)*b*x**(7/2)*sqrt(1/b)), True))","A",0
765,-1,0,0,0.000000," ","integrate((B*x+A)/x**(9/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,1,2649,0,151.180162," ","integrate(x**(5/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{b^{4}} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{7}{2}}}{7} + \frac{2 B x^{\frac{9}{2}}}{9}}{a^{4}} & \text{for}\: b = 0 \\- \frac{30 i A a^{\frac{5}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{80 i A a^{\frac{3}{2}} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{66 i A \sqrt{a} b^{4} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{15 A a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{15 A a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{45 A a^{2} b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{45 A a^{2} b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{45 A a b^{3} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{45 A a b^{3} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{15 A b^{4} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{15 A b^{4} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{210 i B a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{560 i B a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{462 i B a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{96 i B \sqrt{a} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{105 B a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{105 B a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{315 B a^{3} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{315 B a^{3} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{315 B a^{2} b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{315 B a^{2} b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} - \frac{105 B a b^{3} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} + \frac{105 B a b^{3} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{7}{2}} b^{5} \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{3}{2}} b^{7} x^{2} \sqrt{\frac{1}{b}} + 48 i \sqrt{a} b^{8} x^{3} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*sqrt(x)), Eq(a, 0) & Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/b**4, Eq(a, 0)), ((2*A*x**(7/2)/7 + 2*B*x**(9/2)/9)/a**4, Eq(b, 0)), (-30*I*A*a**(5/2)*b**2*sqrt(x)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 80*I*A*a**(3/2)*b**3*x**(3/2)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 66*I*A*sqrt(a)*b**4*x**(5/2)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 15*A*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 15*A*a**3*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 45*A*a**2*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 45*A*a**2*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 45*A*a*b**3*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 45*A*a*b**3*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 15*A*b**4*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 15*A*b**4*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 210*I*B*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 560*I*B*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 462*I*B*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 96*I*B*sqrt(a)*b**4*x**(7/2)*sqrt(1/b)/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 105*B*a**4*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 105*B*a**4*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 315*B*a**3*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 315*B*a**3*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 315*B*a**2*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 315*B*a**2*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) - 105*B*a*b**3*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)) + 105*B*a*b**3*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(7/2)*b**5*sqrt(1/b) + 144*I*a**(5/2)*b**6*x*sqrt(1/b) + 144*I*a**(3/2)*b**7*x**2*sqrt(1/b) + 48*I*sqrt(a)*b**8*x**3*sqrt(1/b)), True))","A",0
768,1,2547,0,84.208290," ","integrate(x**(3/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{7}{2}}}{7}}{a^{4}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} - \frac{2 B}{\sqrt{x}}}{b^{4}} & \text{for}\: a = 0 \\- \frac{6 i A a^{\frac{5}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{16 i A a^{\frac{3}{2}} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{6 i A \sqrt{a} b^{4} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 A a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 A a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 A a^{2} b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 A a^{2} b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 A a b^{3} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 A a b^{3} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 A b^{4} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 A b^{4} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{30 i B a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{80 i B a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{66 i B a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{15 B a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{15 B a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{45 B a^{3} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{45 B a^{3} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{45 B a^{2} b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{45 B a^{2} b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} + \frac{15 B a b^{3} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} - \frac{15 B a b^{3} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{9}{2}} b^{4} \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{5}{2}} b^{6} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} x^{3} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) - 2*B/sqrt(x)), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(7/2)/7)/a**4, Eq(b, 0)), ((-2*A/(3*x**(3/2)) - 2*B/sqrt(x))/b**4, Eq(a, 0)), (-6*I*A*a**(5/2)*b**2*sqrt(x)*sqrt(1/b)/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 16*I*A*a**(3/2)*b**3*x**(3/2)*sqrt(1/b)/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 6*I*A*sqrt(a)*b**4*x**(5/2)*sqrt(1/b)/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 3*A*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 3*A*a**3*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 9*A*a**2*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 9*A*a**2*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 9*A*a*b**3*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 9*A*a*b**3*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 3*A*b**4*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 3*A*b**4*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 30*I*B*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 80*I*B*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 66*I*B*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 15*B*a**4*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 15*B*a**4*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 45*B*a**3*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 45*B*a**3*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 45*B*a**2*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 45*B*a**2*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) + 15*B*a*b**3*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)) - 15*B*a*b**3*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(9/2)*b**4*sqrt(1/b) + 144*I*a**(7/2)*b**5*x*sqrt(1/b) + 144*I*a**(5/2)*b**6*x**2*sqrt(1/b) + 48*I*a**(3/2)*b**7*x**3*sqrt(1/b)), True))","A",0
769,1,2550,0,49.696442," ","integrate((B*x+A)*x**(1/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{5 x^{\frac{5}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{b^{4}} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{5}{2}}}{5}}{a^{4}} & \text{for}\: b = 0 \\- \frac{6 i A a^{\frac{5}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{16 i A a^{\frac{3}{2}} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{6 i A \sqrt{a} b^{4} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 A a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 A a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 A a^{2} b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 A a^{2} b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 A a b^{3} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 A a b^{3} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 A b^{4} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 A b^{4} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{6 i B a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{16 i B a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{6 i B a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 B a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 B a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 B a^{3} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 B a^{3} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 B a^{2} b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 B a^{2} b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 B a b^{3} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 B a b^{3} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{11}{2}} b^{3} \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{7}{2}} b^{5} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{6} x^{3} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2))), Eq(a, 0) & Eq(b, 0)), ((-2*A/(5*x**(5/2)) - 2*B/(3*x**(3/2)))/b**4, Eq(a, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(5/2)/5)/a**4, Eq(b, 0)), (-6*I*A*a**(5/2)*b**2*sqrt(x)*sqrt(1/b)/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 16*I*A*a**(3/2)*b**3*x**(3/2)*sqrt(1/b)/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 6*I*A*sqrt(a)*b**4*x**(5/2)*sqrt(1/b)/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 3*A*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 3*A*a**3*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 9*A*a**2*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 9*A*a**2*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 9*A*a*b**3*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 9*A*a*b**3*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 3*A*b**4*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 3*A*b**4*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 6*I*B*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 16*I*B*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 6*I*B*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 3*B*a**4*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 3*B*a**4*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 9*B*a**3*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 9*B*a**3*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 9*B*a**2*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 9*B*a**2*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) + 3*B*a*b**3*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)) - 3*B*a*b**3*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(11/2)*b**3*sqrt(1/b) + 144*I*a**(9/2)*b**4*x*sqrt(1/b) + 144*I*a**(7/2)*b**5*x**2*sqrt(1/b) + 48*I*a**(5/2)*b**6*x**3*sqrt(1/b)), True))","A",0
770,1,2548,0,70.820856," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{3}{2}}}{3}}{a^{4}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{5 x^{\frac{5}{2}}}}{b^{4}} & \text{for}\: a = 0 \\\frac{66 i A a^{\frac{5}{2}} b^{2} \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{80 i A a^{\frac{3}{2}} b^{3} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{30 i A \sqrt{a} b^{4} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{15 A a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{15 A a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{45 A a^{2} b^{2} x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{45 A a^{2} b^{2} x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{45 A a b^{3} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{45 A a b^{3} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{15 A b^{4} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{15 A b^{4} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{6 i B a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{16 i B a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{6 i B a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 B a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 B a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 B a^{3} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 B a^{3} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{9 B a^{2} b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{9 B a^{2} b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} + \frac{3 B a b^{3} x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} - \frac{3 B a b^{3} x^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{13}{2}} b^{2} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x \sqrt{\frac{1}{b}} + 144 i a^{\frac{9}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{5} x^{3} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2))), Eq(a, 0) & Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(3/2)/3)/a**4, Eq(b, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(5*x**(5/2)))/b**4, Eq(a, 0)), (66*I*A*a**(5/2)*b**2*sqrt(x)*sqrt(1/b)/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 80*I*A*a**(3/2)*b**3*x**(3/2)*sqrt(1/b)/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 30*I*A*sqrt(a)*b**4*x**(5/2)*sqrt(1/b)/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 15*A*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 15*A*a**3*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 45*A*a**2*b**2*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 45*A*a**2*b**2*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 45*A*a*b**3*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 45*A*a*b**3*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 15*A*b**4*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 15*A*b**4*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 6*I*B*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 16*I*B*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 6*I*B*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 3*B*a**4*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 3*B*a**4*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 9*B*a**3*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 9*B*a**3*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 9*B*a**2*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 9*B*a**2*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) + 3*B*a*b**3*x**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)) - 3*B*a*b**3*x**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(13/2)*b**2*sqrt(1/b) + 144*I*a**(11/2)*b**3*x*sqrt(1/b) + 144*I*a**(9/2)*b**4*x**2*sqrt(1/b) + 48*I*a**(7/2)*b**5*x**3*sqrt(1/b)), True))","A",0
771,1,2917,0,144.727873," ","integrate((B*x+A)/x**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + 2 B \sqrt{x}}{a^{4}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{9 x^{\frac{9}{2}}} - \frac{2 B}{7 x^{\frac{7}{2}}}}{b^{4}} & \text{for}\: a = 0 \\- \frac{96 i A a^{\frac{7}{2}} b \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{462 i A a^{\frac{5}{2}} b^{2} x \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{560 i A a^{\frac{3}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{210 i A \sqrt{a} b^{4} x^{3} \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 A a^{3} b \sqrt{x} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 A a^{3} b \sqrt{x} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{315 A a^{2} b^{2} x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{315 A a^{2} b^{2} x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{315 A a b^{3} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{315 A a b^{3} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 A b^{4} x^{\frac{7}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 A b^{4} x^{\frac{7}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{66 i B a^{\frac{7}{2}} b x \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{80 i B a^{\frac{5}{2}} b^{2} x^{2} \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{30 i B a^{\frac{3}{2}} b^{3} x^{3} \sqrt{\frac{1}{b}}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{15 B a^{4} \sqrt{x} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{15 B a^{4} \sqrt{x} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{45 B a^{3} b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{45 B a^{3} b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{45 B a^{2} b^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{45 B a^{2} b^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{15 B a b^{3} x^{\frac{7}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{15 B a b^{3} x^{\frac{7}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{48 i a^{\frac{15}{2}} b \sqrt{x} \sqrt{\frac{1}{b}} + 144 i a^{\frac{13}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 144 i a^{\frac{11}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{9}{2}} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2))), Eq(a, 0) & Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*sqrt(x))/a**4, Eq(b, 0)), ((-2*A/(9*x**(9/2)) - 2*B/(7*x**(7/2)))/b**4, Eq(a, 0)), (-96*I*A*a**(7/2)*b*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 462*I*A*a**(5/2)*b**2*x*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 560*I*A*a**(3/2)*b**3*x**2*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 210*I*A*sqrt(a)*b**4*x**3*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 105*A*a**3*b*sqrt(x)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 105*A*a**3*b*sqrt(x)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 315*A*a**2*b**2*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 315*A*a**2*b**2*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 315*A*a*b**3*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 315*A*a*b**3*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 105*A*b**4*x**(7/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 105*A*b**4*x**(7/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 66*I*B*a**(7/2)*b*x*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 80*I*B*a**(5/2)*b**2*x**2*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 30*I*B*a**(3/2)*b**3*x**3*sqrt(1/b)/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 15*B*a**4*sqrt(x)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 15*B*a**4*sqrt(x)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 45*B*a**3*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 45*B*a**3*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 45*B*a**2*b**2*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 45*B*a**2*b**2*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) + 15*B*a*b**3*x**(7/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)) - 15*B*a*b**3*x**(7/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(48*I*a**(15/2)*b*sqrt(x)*sqrt(1/b) + 144*I*a**(13/2)*b**2*x**(3/2)*sqrt(1/b) + 144*I*a**(11/2)*b**3*x**(5/2)*sqrt(1/b) + 48*I*a**(9/2)*b**4*x**(7/2)*sqrt(1/b)), True))","A",0
772,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,-1,0,0,0.000000," ","integrate(x**(11/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
774,-1,0,0,0.000000," ","integrate(x**(9/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
775,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
776,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
777,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,-1,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
781,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
782,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
783,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
784,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
785,-1,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
786,0,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{\left(a + b x\right)^{2}}}{\sqrt{x}}\, dx"," ",0,"Integral((A + B*x)*sqrt((a + b*x)**2)/sqrt(x), x)","F",0
787,-1,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
788,-1,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
789,-1,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
790,-1,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/x**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
791,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
792,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
793,0,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int x^{\frac{3}{2}} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**(3/2)*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
794,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)*x**(1/2),x)","\int \sqrt{x} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
795,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**(1/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\sqrt{x}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/sqrt(x), x)","F",0
796,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**(3/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**(3/2), x)","F",0
797,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**(5/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**(5/2), x)","F",0
798,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**(7/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**(7/2), x)","F",0
799,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**(9/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/x**(9/2), x)","F",0
800,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
802,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)*x**(1/2),x)","\int \sqrt{x} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
804,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**(1/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\sqrt{x}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/sqrt(x), x)","F",0
805,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**(3/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**(3/2), x)","F",0
806,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**(5/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**(5/2), x)","F",0
807,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**(7/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**(7/2), x)","F",0
808,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**(9/2),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/x**(9/2), x)","F",0
809,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
812,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{\sqrt{x} \left(A + B x\right)}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)/sqrt((a + b*x)**2), x)","F",0
813,0,0,0,0.000000," ","integrate((B*x+A)/x**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{A + B x}{\sqrt{x} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x)*sqrt((a + b*x)**2)), x)","F",0
814,0,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{A + B x}{x^{\frac{3}{2}} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**(3/2)*sqrt((a + b*x)**2)), x)","F",0
815,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate((B*x+A)/x**(7/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate((B*x+A)/x**(9/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\sqrt{x} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
822,0,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2)/x**(1/2),x)","\int \frac{A + B x}{\sqrt{x} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x)*((a + b*x)**2)**(3/2)), x)","F",0
823,0,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{x^{\frac{3}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**(3/2)*((a + b*x)**2)**(3/2)), x)","F",0
824,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,-1,0,0,0.000000," ","integrate((B*x+A)/x**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,-1,0,0,0.000000," ","integrate(x**(11/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,-1,0,0,0.000000," ","integrate(x**(9/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\sqrt{x} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
832,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2)/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate((B*x+A)/x**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,1,7745,0,5.082251," ","integrate(x**m*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3,x)","\begin{cases} - \frac{A a^{6}}{7 x^{7}} - \frac{A a^{5} b}{x^{6}} - \frac{3 A a^{4} b^{2}}{x^{5}} - \frac{5 A a^{3} b^{3}}{x^{4}} - \frac{5 A a^{2} b^{4}}{x^{3}} - \frac{3 A a b^{5}}{x^{2}} - \frac{A b^{6}}{x} - \frac{B a^{6}}{6 x^{6}} - \frac{6 B a^{5} b}{5 x^{5}} - \frac{15 B a^{4} b^{2}}{4 x^{4}} - \frac{20 B a^{3} b^{3}}{3 x^{3}} - \frac{15 B a^{2} b^{4}}{2 x^{2}} - \frac{6 B a b^{5}}{x} + B b^{6} \log{\left(x \right)} & \text{for}\: m = -8 \\- \frac{A a^{6}}{6 x^{6}} - \frac{6 A a^{5} b}{5 x^{5}} - \frac{15 A a^{4} b^{2}}{4 x^{4}} - \frac{20 A a^{3} b^{3}}{3 x^{3}} - \frac{15 A a^{2} b^{4}}{2 x^{2}} - \frac{6 A a b^{5}}{x} + A b^{6} \log{\left(x \right)} - \frac{B a^{6}}{5 x^{5}} - \frac{3 B a^{5} b}{2 x^{4}} - \frac{5 B a^{4} b^{2}}{x^{3}} - \frac{10 B a^{3} b^{3}}{x^{2}} - \frac{15 B a^{2} b^{4}}{x} + 6 B a b^{5} \log{\left(x \right)} + B b^{6} x & \text{for}\: m = -7 \\- \frac{A a^{6}}{5 x^{5}} - \frac{3 A a^{5} b}{2 x^{4}} - \frac{5 A a^{4} b^{2}}{x^{3}} - \frac{10 A a^{3} b^{3}}{x^{2}} - \frac{15 A a^{2} b^{4}}{x} + 6 A a b^{5} \log{\left(x \right)} + A b^{6} x - \frac{B a^{6}}{4 x^{4}} - \frac{2 B a^{5} b}{x^{3}} - \frac{15 B a^{4} b^{2}}{2 x^{2}} - \frac{20 B a^{3} b^{3}}{x} + 15 B a^{2} b^{4} \log{\left(x \right)} + 6 B a b^{5} x + \frac{B b^{6} x^{2}}{2} & \text{for}\: m = -6 \\- \frac{A a^{6}}{4 x^{4}} - \frac{2 A a^{5} b}{x^{3}} - \frac{15 A a^{4} b^{2}}{2 x^{2}} - \frac{20 A a^{3} b^{3}}{x} + 15 A a^{2} b^{4} \log{\left(x \right)} + 6 A a b^{5} x + \frac{A b^{6} x^{2}}{2} - \frac{B a^{6}}{3 x^{3}} - \frac{3 B a^{5} b}{x^{2}} - \frac{15 B a^{4} b^{2}}{x} + 20 B a^{3} b^{3} \log{\left(x \right)} + 15 B a^{2} b^{4} x + 3 B a b^{5} x^{2} + \frac{B b^{6} x^{3}}{3} & \text{for}\: m = -5 \\- \frac{A a^{6}}{3 x^{3}} - \frac{3 A a^{5} b}{x^{2}} - \frac{15 A a^{4} b^{2}}{x} + 20 A a^{3} b^{3} \log{\left(x \right)} + 15 A a^{2} b^{4} x + 3 A a b^{5} x^{2} + \frac{A b^{6} x^{3}}{3} - \frac{B a^{6}}{2 x^{2}} - \frac{6 B a^{5} b}{x} + 15 B a^{4} b^{2} \log{\left(x \right)} + 20 B a^{3} b^{3} x + \frac{15 B a^{2} b^{4} x^{2}}{2} + 2 B a b^{5} x^{3} + \frac{B b^{6} x^{4}}{4} & \text{for}\: m = -4 \\- \frac{A a^{6}}{2 x^{2}} - \frac{6 A a^{5} b}{x} + 15 A a^{4} b^{2} \log{\left(x \right)} + 20 A a^{3} b^{3} x + \frac{15 A a^{2} b^{4} x^{2}}{2} + 2 A a b^{5} x^{3} + \frac{A b^{6} x^{4}}{4} - \frac{B a^{6}}{x} + 6 B a^{5} b \log{\left(x \right)} + 15 B a^{4} b^{2} x + 10 B a^{3} b^{3} x^{2} + 5 B a^{2} b^{4} x^{3} + \frac{3 B a b^{5} x^{4}}{2} + \frac{B b^{6} x^{5}}{5} & \text{for}\: m = -3 \\- \frac{A a^{6}}{x} + 6 A a^{5} b \log{\left(x \right)} + 15 A a^{4} b^{2} x + 10 A a^{3} b^{3} x^{2} + 5 A a^{2} b^{4} x^{3} + \frac{3 A a b^{5} x^{4}}{2} + \frac{A b^{6} x^{5}}{5} + B a^{6} \log{\left(x \right)} + 6 B a^{5} b x + \frac{15 B a^{4} b^{2} x^{2}}{2} + \frac{20 B a^{3} b^{3} x^{3}}{3} + \frac{15 B a^{2} b^{4} x^{4}}{4} + \frac{6 B a b^{5} x^{5}}{5} + \frac{B b^{6} x^{6}}{6} & \text{for}\: m = -2 \\A a^{6} \log{\left(x \right)} + 6 A a^{5} b x + \frac{15 A a^{4} b^{2} x^{2}}{2} + \frac{20 A a^{3} b^{3} x^{3}}{3} + \frac{15 A a^{2} b^{4} x^{4}}{4} + \frac{6 A a b^{5} x^{5}}{5} + \frac{A b^{6} x^{6}}{6} + B a^{6} x + 3 B a^{5} b x^{2} + 5 B a^{4} b^{2} x^{3} + 5 B a^{3} b^{3} x^{4} + 3 B a^{2} b^{4} x^{5} + B a b^{5} x^{6} + \frac{B b^{6} x^{7}}{7} & \text{for}\: m = -1 \\\frac{A a^{6} m^{7} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35 A a^{6} m^{6} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{511 A a^{6} m^{5} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{4025 A a^{6} m^{4} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{18424 A a^{6} m^{3} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{48860 A a^{6} m^{2} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69264 A a^{6} m x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a^{6} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6 A a^{5} b m^{7} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{204 A a^{5} b m^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2868 A a^{5} b m^{5} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{21480 A a^{5} b m^{4} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{91734 A a^{5} b m^{3} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{220236 A a^{5} b m^{2} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{268272 A a^{5} b m x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{120960 A a^{5} b x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15 A a^{4} b^{2} m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{495 A a^{4} b^{2} m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6705 A a^{4} b^{2} m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{47925 A a^{4} b^{2} m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{192960 A a^{4} b^{2} m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{430380 A a^{4} b^{2} m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{480720 A a^{4} b^{2} m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{201600 A a^{4} b^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20 A a^{3} b^{3} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{640 A a^{3} b^{3} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{8360 A a^{3} b^{3} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{57280 A a^{3} b^{3} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{219860 A a^{3} b^{3} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{466240 A a^{3} b^{3} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{497520 A a^{3} b^{3} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{201600 A a^{3} b^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15 A a^{2} b^{4} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{465 A a^{2} b^{4} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5865 A a^{2} b^{4} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{38715 A a^{2} b^{4} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{143160 A a^{2} b^{4} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{293460 A a^{2} b^{4} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{304560 A a^{2} b^{4} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{120960 A a^{2} b^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6 A a b^{5} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{180 A a b^{5} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2196 A a b^{5} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14040 A a b^{5} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{50454 A a b^{5} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{100980 A a b^{5} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{102864 A a b^{5} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a b^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{A b^{6} m^{7} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{29 A b^{6} m^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{343 A b^{6} m^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2135 A b^{6} m^{4} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7504 A b^{6} m^{3} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14756 A b^{6} m^{2} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14832 A b^{6} m x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5760 A b^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B a^{6} m^{7} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{34 B a^{6} m^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{478 B a^{6} m^{5} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3580 B a^{6} m^{4} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15289 B a^{6} m^{3} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{36706 B a^{6} m^{2} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{44712 B a^{6} m x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 B a^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6 B a^{5} b m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{198 B a^{5} b m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2682 B a^{5} b m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{19170 B a^{5} b m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{77184 B a^{5} b m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{172152 B a^{5} b m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{192288 B a^{5} b m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{80640 B a^{5} b x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15 B a^{4} b^{2} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{480 B a^{4} b^{2} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6270 B a^{4} b^{2} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{42960 B a^{4} b^{2} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{164895 B a^{4} b^{2} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{349680 B a^{4} b^{2} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{373140 B a^{4} b^{2} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{151200 B a^{4} b^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20 B a^{3} b^{3} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{620 B a^{3} b^{3} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7820 B a^{3} b^{3} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{51620 B a^{3} b^{3} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{190880 B a^{3} b^{3} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{391280 B a^{3} b^{3} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{406080 B a^{3} b^{3} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{161280 B a^{3} b^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15 B a^{2} b^{4} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{450 B a^{2} b^{4} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5490 B a^{2} b^{4} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35100 B a^{2} b^{4} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{126135 B a^{2} b^{4} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{252450 B a^{2} b^{4} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{257160 B a^{2} b^{4} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{100800 B a^{2} b^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6 B a b^{5} m^{7} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{174 B a b^{5} m^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2058 B a b^{5} m^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{12810 B a b^{5} m^{4} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{45024 B a b^{5} m^{3} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{88536 B a b^{5} m^{2} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{88992 B a b^{5} m x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{34560 B a b^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B b^{6} m^{7} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28 B b^{6} m^{6} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{322 B b^{6} m^{5} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1960 B b^{6} m^{4} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6769 B b^{6} m^{3} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13132 B b^{6} m^{2} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13068 B b^{6} m x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5040 B b^{6} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**6/(7*x**7) - A*a**5*b/x**6 - 3*A*a**4*b**2/x**5 - 5*A*a**3*b**3/x**4 - 5*A*a**2*b**4/x**3 - 3*A*a*b**5/x**2 - A*b**6/x - B*a**6/(6*x**6) - 6*B*a**5*b/(5*x**5) - 15*B*a**4*b**2/(4*x**4) - 20*B*a**3*b**3/(3*x**3) - 15*B*a**2*b**4/(2*x**2) - 6*B*a*b**5/x + B*b**6*log(x), Eq(m, -8)), (-A*a**6/(6*x**6) - 6*A*a**5*b/(5*x**5) - 15*A*a**4*b**2/(4*x**4) - 20*A*a**3*b**3/(3*x**3) - 15*A*a**2*b**4/(2*x**2) - 6*A*a*b**5/x + A*b**6*log(x) - B*a**6/(5*x**5) - 3*B*a**5*b/(2*x**4) - 5*B*a**4*b**2/x**3 - 10*B*a**3*b**3/x**2 - 15*B*a**2*b**4/x + 6*B*a*b**5*log(x) + B*b**6*x, Eq(m, -7)), (-A*a**6/(5*x**5) - 3*A*a**5*b/(2*x**4) - 5*A*a**4*b**2/x**3 - 10*A*a**3*b**3/x**2 - 15*A*a**2*b**4/x + 6*A*a*b**5*log(x) + A*b**6*x - B*a**6/(4*x**4) - 2*B*a**5*b/x**3 - 15*B*a**4*b**2/(2*x**2) - 20*B*a**3*b**3/x + 15*B*a**2*b**4*log(x) + 6*B*a*b**5*x + B*b**6*x**2/2, Eq(m, -6)), (-A*a**6/(4*x**4) - 2*A*a**5*b/x**3 - 15*A*a**4*b**2/(2*x**2) - 20*A*a**3*b**3/x + 15*A*a**2*b**4*log(x) + 6*A*a*b**5*x + A*b**6*x**2/2 - B*a**6/(3*x**3) - 3*B*a**5*b/x**2 - 15*B*a**4*b**2/x + 20*B*a**3*b**3*log(x) + 15*B*a**2*b**4*x + 3*B*a*b**5*x**2 + B*b**6*x**3/3, Eq(m, -5)), (-A*a**6/(3*x**3) - 3*A*a**5*b/x**2 - 15*A*a**4*b**2/x + 20*A*a**3*b**3*log(x) + 15*A*a**2*b**4*x + 3*A*a*b**5*x**2 + A*b**6*x**3/3 - B*a**6/(2*x**2) - 6*B*a**5*b/x + 15*B*a**4*b**2*log(x) + 20*B*a**3*b**3*x + 15*B*a**2*b**4*x**2/2 + 2*B*a*b**5*x**3 + B*b**6*x**4/4, Eq(m, -4)), (-A*a**6/(2*x**2) - 6*A*a**5*b/x + 15*A*a**4*b**2*log(x) + 20*A*a**3*b**3*x + 15*A*a**2*b**4*x**2/2 + 2*A*a*b**5*x**3 + A*b**6*x**4/4 - B*a**6/x + 6*B*a**5*b*log(x) + 15*B*a**4*b**2*x + 10*B*a**3*b**3*x**2 + 5*B*a**2*b**4*x**3 + 3*B*a*b**5*x**4/2 + B*b**6*x**5/5, Eq(m, -3)), (-A*a**6/x + 6*A*a**5*b*log(x) + 15*A*a**4*b**2*x + 10*A*a**3*b**3*x**2 + 5*A*a**2*b**4*x**3 + 3*A*a*b**5*x**4/2 + A*b**6*x**5/5 + B*a**6*log(x) + 6*B*a**5*b*x + 15*B*a**4*b**2*x**2/2 + 20*B*a**3*b**3*x**3/3 + 15*B*a**2*b**4*x**4/4 + 6*B*a*b**5*x**5/5 + B*b**6*x**6/6, Eq(m, -2)), (A*a**6*log(x) + 6*A*a**5*b*x + 15*A*a**4*b**2*x**2/2 + 20*A*a**3*b**3*x**3/3 + 15*A*a**2*b**4*x**4/4 + 6*A*a*b**5*x**5/5 + A*b**6*x**6/6 + B*a**6*x + 3*B*a**5*b*x**2 + 5*B*a**4*b**2*x**3 + 5*B*a**3*b**3*x**4 + 3*B*a**2*b**4*x**5 + B*a*b**5*x**6 + B*b**6*x**7/7, Eq(m, -1)), (A*a**6*m**7*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35*A*a**6*m**6*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 511*A*a**6*m**5*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 4025*A*a**6*m**4*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 18424*A*a**6*m**3*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 48860*A*a**6*m**2*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69264*A*a**6*m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a**6*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6*A*a**5*b*m**7*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 204*A*a**5*b*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2868*A*a**5*b*m**5*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 21480*A*a**5*b*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 91734*A*a**5*b*m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 220236*A*a**5*b*m**2*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 268272*A*a**5*b*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 120960*A*a**5*b*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15*A*a**4*b**2*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 495*A*a**4*b**2*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6705*A*a**4*b**2*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 47925*A*a**4*b**2*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 192960*A*a**4*b**2*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 430380*A*a**4*b**2*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 480720*A*a**4*b**2*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 201600*A*a**4*b**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20*A*a**3*b**3*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 640*A*a**3*b**3*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 8360*A*a**3*b**3*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 57280*A*a**3*b**3*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 219860*A*a**3*b**3*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 466240*A*a**3*b**3*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 497520*A*a**3*b**3*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 201600*A*a**3*b**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15*A*a**2*b**4*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 465*A*a**2*b**4*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5865*A*a**2*b**4*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 38715*A*a**2*b**4*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 143160*A*a**2*b**4*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 293460*A*a**2*b**4*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 304560*A*a**2*b**4*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 120960*A*a**2*b**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6*A*a*b**5*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 180*A*a*b**5*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2196*A*a*b**5*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14040*A*a*b**5*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 50454*A*a*b**5*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 100980*A*a*b**5*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 102864*A*a*b**5*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a*b**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + A*b**6*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 29*A*b**6*m**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 343*A*b**6*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2135*A*b**6*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7504*A*b**6*m**3*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14756*A*b**6*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14832*A*b**6*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5760*A*b**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*a**6*m**7*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 34*B*a**6*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 478*B*a**6*m**5*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3580*B*a**6*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15289*B*a**6*m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 36706*B*a**6*m**2*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 44712*B*a**6*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*B*a**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6*B*a**5*b*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 198*B*a**5*b*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2682*B*a**5*b*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 19170*B*a**5*b*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 77184*B*a**5*b*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 172152*B*a**5*b*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 192288*B*a**5*b*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 80640*B*a**5*b*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15*B*a**4*b**2*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 480*B*a**4*b**2*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6270*B*a**4*b**2*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 42960*B*a**4*b**2*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 164895*B*a**4*b**2*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 349680*B*a**4*b**2*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 373140*B*a**4*b**2*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 151200*B*a**4*b**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20*B*a**3*b**3*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 620*B*a**3*b**3*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7820*B*a**3*b**3*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 51620*B*a**3*b**3*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 190880*B*a**3*b**3*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 391280*B*a**3*b**3*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 406080*B*a**3*b**3*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 161280*B*a**3*b**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15*B*a**2*b**4*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 450*B*a**2*b**4*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5490*B*a**2*b**4*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35100*B*a**2*b**4*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 126135*B*a**2*b**4*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 252450*B*a**2*b**4*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 257160*B*a**2*b**4*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 100800*B*a**2*b**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6*B*a*b**5*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 174*B*a*b**5*m**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2058*B*a*b**5*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 12810*B*a*b**5*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 45024*B*a*b**5*m**3*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 88536*B*a*b**5*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 88992*B*a*b**5*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 34560*B*a*b**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*b**6*m**7*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28*B*b**6*m**6*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 322*B*b**6*m**5*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1960*B*b**6*m**4*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6769*B*b**6*m**3*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13132*B*b**6*m**2*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13068*B*b**6*m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5040*B*b**6*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320), True))","A",0
837,1,3417,0,2.544346," ","integrate(x**m*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} - \frac{A a^{4}}{5 x^{5}} - \frac{A a^{3} b}{x^{4}} - \frac{2 A a^{2} b^{2}}{x^{3}} - \frac{2 A a b^{3}}{x^{2}} - \frac{A b^{4}}{x} - \frac{B a^{4}}{4 x^{4}} - \frac{4 B a^{3} b}{3 x^{3}} - \frac{3 B a^{2} b^{2}}{x^{2}} - \frac{4 B a b^{3}}{x} + B b^{4} \log{\left(x \right)} & \text{for}\: m = -6 \\- \frac{A a^{4}}{4 x^{4}} - \frac{4 A a^{3} b}{3 x^{3}} - \frac{3 A a^{2} b^{2}}{x^{2}} - \frac{4 A a b^{3}}{x} + A b^{4} \log{\left(x \right)} - \frac{B a^{4}}{3 x^{3}} - \frac{2 B a^{3} b}{x^{2}} - \frac{6 B a^{2} b^{2}}{x} + 4 B a b^{3} \log{\left(x \right)} + B b^{4} x & \text{for}\: m = -5 \\- \frac{A a^{4}}{3 x^{3}} - \frac{2 A a^{3} b}{x^{2}} - \frac{6 A a^{2} b^{2}}{x} + 4 A a b^{3} \log{\left(x \right)} + A b^{4} x - \frac{B a^{4}}{2 x^{2}} - \frac{4 B a^{3} b}{x} + 6 B a^{2} b^{2} \log{\left(x \right)} + 4 B a b^{3} x + \frac{B b^{4} x^{2}}{2} & \text{for}\: m = -4 \\- \frac{A a^{4}}{2 x^{2}} - \frac{4 A a^{3} b}{x} + 6 A a^{2} b^{2} \log{\left(x \right)} + 4 A a b^{3} x + \frac{A b^{4} x^{2}}{2} - \frac{B a^{4}}{x} + 4 B a^{3} b \log{\left(x \right)} + 6 B a^{2} b^{2} x + 2 B a b^{3} x^{2} + \frac{B b^{4} x^{3}}{3} & \text{for}\: m = -3 \\- \frac{A a^{4}}{x} + 4 A a^{3} b \log{\left(x \right)} + 6 A a^{2} b^{2} x + 2 A a b^{3} x^{2} + \frac{A b^{4} x^{3}}{3} + B a^{4} \log{\left(x \right)} + 4 B a^{3} b x + 3 B a^{2} b^{2} x^{2} + \frac{4 B a b^{3} x^{3}}{3} + \frac{B b^{4} x^{4}}{4} & \text{for}\: m = -2 \\A a^{4} \log{\left(x \right)} + 4 A a^{3} b x + 3 A a^{2} b^{2} x^{2} + \frac{4 A a b^{3} x^{3}}{3} + \frac{A b^{4} x^{4}}{4} + B a^{4} x + 2 B a^{3} b x^{2} + 2 B a^{2} b^{2} x^{3} + B a b^{3} x^{4} + \frac{B b^{4} x^{5}}{5} & \text{for}\: m = -1 \\\frac{A a^{4} m^{5} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{20 A a^{4} m^{4} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{155 A a^{4} m^{3} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{580 A a^{4} m^{2} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1044 A a^{4} m x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{720 A a^{4} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{4 A a^{3} b m^{5} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{76 A a^{3} b m^{4} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{548 A a^{3} b m^{3} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1844 A a^{3} b m^{2} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2808 A a^{3} b m x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1440 A a^{3} b x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{6 A a^{2} b^{2} m^{5} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{108 A a^{2} b^{2} m^{4} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{726 A a^{2} b^{2} m^{3} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2232 A a^{2} b^{2} m^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{3048 A a^{2} b^{2} m x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1440 A a^{2} b^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{4 A a b^{3} m^{5} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{68 A a b^{3} m^{4} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{428 A a b^{3} m^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1228 A a b^{3} m^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1584 A a b^{3} m x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{720 A a b^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{A b^{4} m^{5} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{16 A b^{4} m^{4} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{95 A b^{4} m^{3} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{260 A b^{4} m^{2} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{324 A b^{4} m x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{144 A b^{4} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B a^{4} m^{5} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{19 B a^{4} m^{4} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{137 B a^{4} m^{3} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{461 B a^{4} m^{2} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{702 B a^{4} m x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{360 B a^{4} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{4 B a^{3} b m^{5} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{72 B a^{3} b m^{4} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{484 B a^{3} b m^{3} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1488 B a^{3} b m^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2032 B a^{3} b m x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{960 B a^{3} b x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{6 B a^{2} b^{2} m^{5} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{102 B a^{2} b^{2} m^{4} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{642 B a^{2} b^{2} m^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1842 B a^{2} b^{2} m^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2376 B a^{2} b^{2} m x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1080 B a^{2} b^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{4 B a b^{3} m^{5} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{64 B a b^{3} m^{4} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{380 B a b^{3} m^{3} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1040 B a b^{3} m^{2} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1296 B a b^{3} m x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{576 B a b^{3} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B b^{4} m^{5} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{15 B b^{4} m^{4} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{85 B b^{4} m^{3} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{225 B b^{4} m^{2} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{274 B b^{4} m x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{120 B b^{4} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**4/(5*x**5) - A*a**3*b/x**4 - 2*A*a**2*b**2/x**3 - 2*A*a*b**3/x**2 - A*b**4/x - B*a**4/(4*x**4) - 4*B*a**3*b/(3*x**3) - 3*B*a**2*b**2/x**2 - 4*B*a*b**3/x + B*b**4*log(x), Eq(m, -6)), (-A*a**4/(4*x**4) - 4*A*a**3*b/(3*x**3) - 3*A*a**2*b**2/x**2 - 4*A*a*b**3/x + A*b**4*log(x) - B*a**4/(3*x**3) - 2*B*a**3*b/x**2 - 6*B*a**2*b**2/x + 4*B*a*b**3*log(x) + B*b**4*x, Eq(m, -5)), (-A*a**4/(3*x**3) - 2*A*a**3*b/x**2 - 6*A*a**2*b**2/x + 4*A*a*b**3*log(x) + A*b**4*x - B*a**4/(2*x**2) - 4*B*a**3*b/x + 6*B*a**2*b**2*log(x) + 4*B*a*b**3*x + B*b**4*x**2/2, Eq(m, -4)), (-A*a**4/(2*x**2) - 4*A*a**3*b/x + 6*A*a**2*b**2*log(x) + 4*A*a*b**3*x + A*b**4*x**2/2 - B*a**4/x + 4*B*a**3*b*log(x) + 6*B*a**2*b**2*x + 2*B*a*b**3*x**2 + B*b**4*x**3/3, Eq(m, -3)), (-A*a**4/x + 4*A*a**3*b*log(x) + 6*A*a**2*b**2*x + 2*A*a*b**3*x**2 + A*b**4*x**3/3 + B*a**4*log(x) + 4*B*a**3*b*x + 3*B*a**2*b**2*x**2 + 4*B*a*b**3*x**3/3 + B*b**4*x**4/4, Eq(m, -2)), (A*a**4*log(x) + 4*A*a**3*b*x + 3*A*a**2*b**2*x**2 + 4*A*a*b**3*x**3/3 + A*b**4*x**4/4 + B*a**4*x + 2*B*a**3*b*x**2 + 2*B*a**2*b**2*x**3 + B*a*b**3*x**4 + B*b**4*x**5/5, Eq(m, -1)), (A*a**4*m**5*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 20*A*a**4*m**4*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 155*A*a**4*m**3*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 580*A*a**4*m**2*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1044*A*a**4*m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 720*A*a**4*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 4*A*a**3*b*m**5*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 76*A*a**3*b*m**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 548*A*a**3*b*m**3*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1844*A*a**3*b*m**2*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2808*A*a**3*b*m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1440*A*a**3*b*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 6*A*a**2*b**2*m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 108*A*a**2*b**2*m**4*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 726*A*a**2*b**2*m**3*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2232*A*a**2*b**2*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 3048*A*a**2*b**2*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1440*A*a**2*b**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 4*A*a*b**3*m**5*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 68*A*a*b**3*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 428*A*a*b**3*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1228*A*a*b**3*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1584*A*a*b**3*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 720*A*a*b**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + A*b**4*m**5*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 16*A*b**4*m**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 95*A*b**4*m**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 260*A*b**4*m**2*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 324*A*b**4*m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 144*A*b**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*a**4*m**5*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 19*B*a**4*m**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 137*B*a**4*m**3*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 461*B*a**4*m**2*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 702*B*a**4*m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 360*B*a**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 4*B*a**3*b*m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 72*B*a**3*b*m**4*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 484*B*a**3*b*m**3*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1488*B*a**3*b*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2032*B*a**3*b*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 960*B*a**3*b*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 6*B*a**2*b**2*m**5*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 102*B*a**2*b**2*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 642*B*a**2*b**2*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1842*B*a**2*b**2*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2376*B*a**2*b**2*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1080*B*a**2*b**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 4*B*a*b**3*m**5*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 64*B*a*b**3*m**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 380*B*a*b**3*m**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1040*B*a*b**3*m**2*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1296*B*a*b**3*m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 576*B*a*b**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*b**4*m**5*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 15*B*b**4*m**4*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 85*B*b**4*m**3*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 225*B*b**4*m**2*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 274*B*b**4*m*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 120*B*b**4*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720), True))","A",0
838,1,1020,0,1.132720," ","integrate(x**m*(B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} - \frac{A a^{2}}{3 x^{3}} - \frac{A a b}{x^{2}} - \frac{A b^{2}}{x} - \frac{B a^{2}}{2 x^{2}} - \frac{2 B a b}{x} + B b^{2} \log{\left(x \right)} & \text{for}\: m = -4 \\- \frac{A a^{2}}{2 x^{2}} - \frac{2 A a b}{x} + A b^{2} \log{\left(x \right)} - \frac{B a^{2}}{x} + 2 B a b \log{\left(x \right)} + B b^{2} x & \text{for}\: m = -3 \\- \frac{A a^{2}}{x} + 2 A a b \log{\left(x \right)} + A b^{2} x + B a^{2} \log{\left(x \right)} + 2 B a b x + \frac{B b^{2} x^{2}}{2} & \text{for}\: m = -2 \\A a^{2} \log{\left(x \right)} + 2 A a b x + \frac{A b^{2} x^{2}}{2} + B a^{2} x + B a b x^{2} + \frac{B b^{2} x^{3}}{3} & \text{for}\: m = -1 \\\frac{A a^{2} m^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{9 A a^{2} m^{2} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{26 A a^{2} m x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 A a^{2} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{2 A a b m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{16 A a b m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{38 A a b m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 A a b x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{A b^{2} m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{7 A b^{2} m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{14 A b^{2} m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 A b^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B a^{2} m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 B a^{2} m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{19 B a^{2} m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{12 B a^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{2 B a b m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{14 B a b m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{28 B a b m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{16 B a b x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B b^{2} m^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 B b^{2} m^{2} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{11 B b^{2} m x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 B b^{2} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**2/(3*x**3) - A*a*b/x**2 - A*b**2/x - B*a**2/(2*x**2) - 2*B*a*b/x + B*b**2*log(x), Eq(m, -4)), (-A*a**2/(2*x**2) - 2*A*a*b/x + A*b**2*log(x) - B*a**2/x + 2*B*a*b*log(x) + B*b**2*x, Eq(m, -3)), (-A*a**2/x + 2*A*a*b*log(x) + A*b**2*x + B*a**2*log(x) + 2*B*a*b*x + B*b**2*x**2/2, Eq(m, -2)), (A*a**2*log(x) + 2*A*a*b*x + A*b**2*x**2/2 + B*a**2*x + B*a*b*x**2 + B*b**2*x**3/3, Eq(m, -1)), (A*a**2*m**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 9*A*a**2*m**2*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 26*A*a**2*m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*A*a**2*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 2*A*a*b*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 16*A*a*b*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 38*A*a*b*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*A*a*b*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + A*b**2*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 7*A*b**2*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 14*A*b**2*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*A*b**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*a**2*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*B*a**2*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 19*B*a**2*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 12*B*a**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 2*B*a*b*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 14*B*a*b*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 28*B*a*b*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 16*B*a*b*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*b**2*m**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*B*b**2*m**2*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 11*B*b**2*m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*B*b**2*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24), True))","A",0
839,0,0,0,0.000000," ","integrate(x**m*(B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{x^{m} \left(A + B x\right)}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**m*(A + B*x)/(a + b*x)**2, x)","F",0
840,0,0,0,0.000000," ","integrate(x**m*(B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\int \frac{x^{m} \left(A + B x\right)}{\left(a + b x\right)^{4}}\, dx"," ",0,"Integral(x**m*(A + B*x)/(a + b*x)**4, x)","F",0
841,-1,0,0,0.000000," ","integrate(x**m*(1+x)*(x**2+2*x+1)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,-1,0,0,0.000000," ","integrate(x**m*(e*x+d)*(x**2+2*x+1)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
843,1,42,0,0.070404," ","integrate(x**3*(B*x+A)*(c*x**2+b*x+a),x)","\frac{A a x^{4}}{4} + \frac{B c x^{7}}{7} + x^{6} \left(\frac{A c}{6} + \frac{B b}{6}\right) + x^{5} \left(\frac{A b}{5} + \frac{B a}{5}\right)"," ",0,"A*a*x**4/4 + B*c*x**7/7 + x**6*(A*c/6 + B*b/6) + x**5*(A*b/5 + B*a/5)","A",0
844,1,42,0,0.069208," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a),x)","\frac{A a x^{3}}{3} + \frac{B c x^{6}}{6} + x^{5} \left(\frac{A c}{5} + \frac{B b}{5}\right) + x^{4} \left(\frac{A b}{4} + \frac{B a}{4}\right)"," ",0,"A*a*x**3/3 + B*c*x**6/6 + x**5*(A*c/5 + B*b/5) + x**4*(A*b/4 + B*a/4)","A",0
845,1,42,0,0.069416," ","integrate(x*(B*x+A)*(c*x**2+b*x+a),x)","\frac{A a x^{2}}{2} + \frac{B c x^{5}}{5} + x^{4} \left(\frac{A c}{4} + \frac{B b}{4}\right) + x^{3} \left(\frac{A b}{3} + \frac{B a}{3}\right)"," ",0,"A*a*x**2/2 + B*c*x**5/5 + x**4*(A*c/4 + B*b/4) + x**3*(A*b/3 + B*a/3)","A",0
846,1,39,0,0.067813," ","integrate((B*x+A)*(c*x**2+b*x+a),x)","A a x + \frac{B c x^{4}}{4} + x^{3} \left(\frac{A c}{3} + \frac{B b}{3}\right) + x^{2} \left(\frac{A b}{2} + \frac{B a}{2}\right)"," ",0,"A*a*x + B*c*x**4/4 + x**3*(A*c/3 + B*b/3) + x**2*(A*b/2 + B*a/2)","A",0
847,1,36,0,0.130482," ","integrate((B*x+A)*(c*x**2+b*x+a)/x,x)","A a \log{\left(x \right)} + \frac{B c x^{3}}{3} + x^{2} \left(\frac{A c}{2} + \frac{B b}{2}\right) + x \left(A b + B a\right)"," ",0,"A*a*log(x) + B*c*x**3/3 + x**2*(A*c/2 + B*b/2) + x*(A*b + B*a)","A",0
848,1,31,0,0.168102," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**2,x)","- \frac{A a}{x} + \frac{B c x^{2}}{2} + x \left(A c + B b\right) + \left(A b + B a\right) \log{\left(x \right)}"," ",0,"-A*a/x + B*c*x**2/2 + x*(A*c + B*b) + (A*b + B*a)*log(x)","A",0
849,1,36,0,0.312253," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**3,x)","B c x + \left(A c + B b\right) \log{\left(x \right)} + \frac{- A a + x \left(- 2 A b - 2 B a\right)}{2 x^{2}}"," ",0,"B*c*x + (A*c + B*b)*log(x) + (-A*a + x*(-2*A*b - 2*B*a))/(2*x**2)","A",0
850,1,44,0,0.576766," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**4,x)","B c \log{\left(x \right)} + \frac{- 2 A a + x^{2} \left(- 6 A c - 6 B b\right) + x \left(- 3 A b - 3 B a\right)}{6 x^{3}}"," ",0,"B*c*log(x) + (-2*A*a + x**2*(-6*A*c - 6*B*b) + x*(-3*A*b - 3*B*a))/(6*x**3)","A",0
851,1,46,0,1.035546," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**5,x)","\frac{- 3 A a - 12 B c x^{3} + x^{2} \left(- 6 A c - 6 B b\right) + x \left(- 4 A b - 4 B a\right)}{12 x^{4}}"," ",0,"(-3*A*a - 12*B*c*x**3 + x**2*(-6*A*c - 6*B*b) + x*(-4*A*b - 4*B*a))/(12*x**4)","A",0
852,1,46,0,1.700601," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**6,x)","\frac{- 12 A a - 30 B c x^{3} + x^{2} \left(- 20 A c - 20 B b\right) + x \left(- 15 A b - 15 B a\right)}{60 x^{5}}"," ",0,"(-12*A*a - 30*B*c*x**3 + x**2*(-20*A*c - 20*B*b) + x*(-15*A*b - 15*B*a))/(60*x**5)","A",0
853,1,46,0,2.674931," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**7,x)","\frac{- 10 A a - 20 B c x^{3} + x^{2} \left(- 15 A c - 15 B b\right) + x \left(- 12 A b - 12 B a\right)}{60 x^{6}}"," ",0,"(-10*A*a - 20*B*c*x**3 + x**2*(-15*A*c - 15*B*b) + x*(-12*A*b - 12*B*a))/(60*x**6)","A",0
854,1,46,0,3.868473," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**8,x)","\frac{- 60 A a - 105 B c x^{3} + x^{2} \left(- 84 A c - 84 B b\right) + x \left(- 70 A b - 70 B a\right)}{420 x^{7}}"," ",0,"(-60*A*a - 105*B*c*x**3 + x**2*(-84*A*c - 84*B*b) + x*(-70*A*b - 70*B*a))/(420*x**7)","A",0
855,1,105,0,0.087493," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**2,x)","\frac{A a^{2} x^{3}}{3} + \frac{B c^{2} x^{8}}{8} + x^{7} \left(\frac{A c^{2}}{7} + \frac{2 B b c}{7}\right) + x^{6} \left(\frac{A b c}{3} + \frac{B a c}{3} + \frac{B b^{2}}{6}\right) + x^{5} \left(\frac{2 A a c}{5} + \frac{A b^{2}}{5} + \frac{2 B a b}{5}\right) + x^{4} \left(\frac{A a b}{2} + \frac{B a^{2}}{4}\right)"," ",0,"A*a**2*x**3/3 + B*c**2*x**8/8 + x**7*(A*c**2/7 + 2*B*b*c/7) + x**6*(A*b*c/3 + B*a*c/3 + B*b**2/6) + x**5*(2*A*a*c/5 + A*b**2/5 + 2*B*a*b/5) + x**4*(A*a*b/2 + B*a**2/4)","A",0
856,1,105,0,0.085607," ","integrate(x*(B*x+A)*(c*x**2+b*x+a)**2,x)","\frac{A a^{2} x^{2}}{2} + \frac{B c^{2} x^{7}}{7} + x^{6} \left(\frac{A c^{2}}{6} + \frac{B b c}{3}\right) + x^{5} \left(\frac{2 A b c}{5} + \frac{2 B a c}{5} + \frac{B b^{2}}{5}\right) + x^{4} \left(\frac{A a c}{2} + \frac{A b^{2}}{4} + \frac{B a b}{2}\right) + x^{3} \left(\frac{2 A a b}{3} + \frac{B a^{2}}{3}\right)"," ",0,"A*a**2*x**2/2 + B*c**2*x**7/7 + x**6*(A*c**2/6 + B*b*c/3) + x**5*(2*A*b*c/5 + 2*B*a*c/5 + B*b**2/5) + x**4*(A*a*c/2 + A*b**2/4 + B*a*b/2) + x**3*(2*A*a*b/3 + B*a**2/3)","A",0
857,1,100,0,0.089260," ","integrate((B*x+A)*(c*x**2+b*x+a)**2,x)","A a^{2} x + \frac{B c^{2} x^{6}}{6} + x^{5} \left(\frac{A c^{2}}{5} + \frac{2 B b c}{5}\right) + x^{4} \left(\frac{A b c}{2} + \frac{B a c}{2} + \frac{B b^{2}}{4}\right) + x^{3} \left(\frac{2 A a c}{3} + \frac{A b^{2}}{3} + \frac{2 B a b}{3}\right) + x^{2} \left(A a b + \frac{B a^{2}}{2}\right)"," ",0,"A*a**2*x + B*c**2*x**6/6 + x**5*(A*c**2/5 + 2*B*b*c/5) + x**4*(A*b*c/2 + B*a*c/2 + B*b**2/4) + x**3*(2*A*a*c/3 + A*b**2/3 + 2*B*a*b/3) + x**2*(A*a*b + B*a**2/2)","A",0
858,1,95,0,0.208523," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x,x)","A a^{2} \log{\left(x \right)} + \frac{B c^{2} x^{5}}{5} + x^{4} \left(\frac{A c^{2}}{4} + \frac{B b c}{2}\right) + x^{3} \left(\frac{2 A b c}{3} + \frac{2 B a c}{3} + \frac{B b^{2}}{3}\right) + x^{2} \left(A a c + \frac{A b^{2}}{2} + B a b\right) + x \left(2 A a b + B a^{2}\right)"," ",0,"A*a**2*log(x) + B*c**2*x**5/5 + x**4*(A*c**2/4 + B*b*c/2) + x**3*(2*A*b*c/3 + 2*B*a*c/3 + B*b**2/3) + x**2*(A*a*c + A*b**2/2 + B*a*b) + x*(2*A*a*b + B*a**2)","A",0
859,1,88,0,0.256949," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**2,x)","- \frac{A a^{2}}{x} + \frac{B c^{2} x^{4}}{4} + a \left(2 A b + B a\right) \log{\left(x \right)} + x^{3} \left(\frac{A c^{2}}{3} + \frac{2 B b c}{3}\right) + x^{2} \left(A b c + B a c + \frac{B b^{2}}{2}\right) + x \left(2 A a c + A b^{2} + 2 B a b\right)"," ",0,"-A*a**2/x + B*c**2*x**4/4 + a*(2*A*b + B*a)*log(x) + x**3*(A*c**2/3 + 2*B*b*c/3) + x**2*(A*b*c + B*a*c + B*b**2/2) + x*(2*A*a*c + A*b**2 + 2*B*a*b)","A",0
860,1,94,0,0.441161," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**3,x)","\frac{B c^{2} x^{3}}{3} + x^{2} \left(\frac{A c^{2}}{2} + B b c\right) + x \left(2 A b c + 2 B a c + B b^{2}\right) + \left(2 A a c + A b^{2} + 2 B a b\right) \log{\left(x \right)} + \frac{- A a^{2} + x \left(- 4 A a b - 2 B a^{2}\right)}{2 x^{2}}"," ",0,"B*c**2*x**3/3 + x**2*(A*c**2/2 + B*b*c) + x*(2*A*b*c + 2*B*a*c + B*b**2) + (2*A*a*c + A*b**2 + 2*B*a*b)*log(x) + (-A*a**2 + x*(-4*A*a*b - 2*B*a**2))/(2*x**2)","A",0
861,1,99,0,1.074150," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**4,x)","\frac{B c^{2} x^{2}}{2} + x \left(A c^{2} + 2 B b c\right) + \left(2 A b c + 2 B a c + B b^{2}\right) \log{\left(x \right)} + \frac{- 2 A a^{2} + x^{2} \left(- 12 A a c - 6 A b^{2} - 12 B a b\right) + x \left(- 6 A a b - 3 B a^{2}\right)}{6 x^{3}}"," ",0,"B*c**2*x**2/2 + x*(A*c**2 + 2*B*b*c) + (2*A*b*c + 2*B*a*c + B*b**2)*log(x) + (-2*A*a**2 + x**2*(-12*A*a*c - 6*A*b**2 - 12*B*a*b) + x*(-6*A*a*b - 3*B*a**2))/(6*x**3)","A",0
862,1,99,0,3.049388," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**5,x)","B c^{2} x + c \left(A c + 2 B b\right) \log{\left(x \right)} + \frac{- 3 A a^{2} + x^{3} \left(- 24 A b c - 24 B a c - 12 B b^{2}\right) + x^{2} \left(- 12 A a c - 6 A b^{2} - 12 B a b\right) + x \left(- 8 A a b - 4 B a^{2}\right)}{12 x^{4}}"," ",0,"B*c**2*x + c*(A*c + 2*B*b)*log(x) + (-3*A*a**2 + x**3*(-24*A*b*c - 24*B*a*c - 12*B*b**2) + x**2*(-12*A*a*c - 6*A*b**2 - 12*B*a*b) + x*(-8*A*a*b - 4*B*a**2))/(12*x**4)","A",0
863,1,105,0,7.106082," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**6,x)","B c^{2} \log{\left(x \right)} + \frac{- 12 A a^{2} + x^{4} \left(- 60 A c^{2} - 120 B b c\right) + x^{3} \left(- 60 A b c - 60 B a c - 30 B b^{2}\right) + x^{2} \left(- 40 A a c - 20 A b^{2} - 40 B a b\right) + x \left(- 30 A a b - 15 B a^{2}\right)}{60 x^{5}}"," ",0,"B*c**2*log(x) + (-12*A*a**2 + x**4*(-60*A*c**2 - 120*B*b*c) + x**3*(-60*A*b*c - 60*B*a*c - 30*B*b**2) + x**2*(-40*A*a*c - 20*A*b**2 - 40*B*a*b) + x*(-30*A*a*b - 15*B*a**2))/(60*x**5)","A",0
864,1,107,0,14.089062," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**7,x)","\frac{- 10 A a^{2} - 60 B c^{2} x^{5} + x^{4} \left(- 30 A c^{2} - 60 B b c\right) + x^{3} \left(- 40 A b c - 40 B a c - 20 B b^{2}\right) + x^{2} \left(- 30 A a c - 15 A b^{2} - 30 B a b\right) + x \left(- 24 A a b - 12 B a^{2}\right)}{60 x^{6}}"," ",0,"(-10*A*a**2 - 60*B*c**2*x**5 + x**4*(-30*A*c**2 - 60*B*b*c) + x**3*(-40*A*b*c - 40*B*a*c - 20*B*b**2) + x**2*(-30*A*a*c - 15*A*b**2 - 30*B*a*b) + x*(-24*A*a*b - 12*B*a**2))/(60*x**6)","A",0
865,1,107,0,24.022430," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**8,x)","\frac{- 60 A a^{2} - 210 B c^{2} x^{5} + x^{4} \left(- 140 A c^{2} - 280 B b c\right) + x^{3} \left(- 210 A b c - 210 B a c - 105 B b^{2}\right) + x^{2} \left(- 168 A a c - 84 A b^{2} - 168 B a b\right) + x \left(- 140 A a b - 70 B a^{2}\right)}{420 x^{7}}"," ",0,"(-60*A*a**2 - 210*B*c**2*x**5 + x**4*(-140*A*c**2 - 280*B*b*c) + x**3*(-210*A*b*c - 210*B*a*c - 105*B*b**2) + x**2*(-168*A*a*c - 84*A*b**2 - 168*B*a*b) + x*(-140*A*a*b - 70*B*a**2))/(420*x**7)","A",0
866,1,107,0,41.522599," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**9,x)","\frac{- 105 A a^{2} - 280 B c^{2} x^{5} + x^{4} \left(- 210 A c^{2} - 420 B b c\right) + x^{3} \left(- 336 A b c - 336 B a c - 168 B b^{2}\right) + x^{2} \left(- 280 A a c - 140 A b^{2} - 280 B a b\right) + x \left(- 240 A a b - 120 B a^{2}\right)}{840 x^{8}}"," ",0,"(-105*A*a**2 - 280*B*c**2*x**5 + x**4*(-210*A*c**2 - 420*B*b*c) + x**3*(-336*A*b*c - 336*B*a*c - 168*B*b**2) + x**2*(-280*A*a*c - 140*A*b**2 - 280*B*a*b) + x*(-240*A*a*b - 120*B*a**2))/(840*x**8)","A",0
867,1,201,0,0.105477," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**3,x)","\frac{A a^{3} x^{3}}{3} + \frac{B c^{3} x^{10}}{10} + x^{9} \left(\frac{A c^{3}}{9} + \frac{B b c^{2}}{3}\right) + x^{8} \left(\frac{3 A b c^{2}}{8} + \frac{3 B a c^{2}}{8} + \frac{3 B b^{2} c}{8}\right) + x^{7} \left(\frac{3 A a c^{2}}{7} + \frac{3 A b^{2} c}{7} + \frac{6 B a b c}{7} + \frac{B b^{3}}{7}\right) + x^{6} \left(A a b c + \frac{A b^{3}}{6} + \frac{B a^{2} c}{2} + \frac{B a b^{2}}{2}\right) + x^{5} \left(\frac{3 A a^{2} c}{5} + \frac{3 A a b^{2}}{5} + \frac{3 B a^{2} b}{5}\right) + x^{4} \left(\frac{3 A a^{2} b}{4} + \frac{B a^{3}}{4}\right)"," ",0,"A*a**3*x**3/3 + B*c**3*x**10/10 + x**9*(A*c**3/9 + B*b*c**2/3) + x**8*(3*A*b*c**2/8 + 3*B*a*c**2/8 + 3*B*b**2*c/8) + x**7*(3*A*a*c**2/7 + 3*A*b**2*c/7 + 6*B*a*b*c/7 + B*b**3/7) + x**6*(A*a*b*c + A*b**3/6 + B*a**2*c/2 + B*a*b**2/2) + x**5*(3*A*a**2*c/5 + 3*A*a*b**2/5 + 3*B*a**2*b/5) + x**4*(3*A*a**2*b/4 + B*a**3/4)","A",0
868,1,199,0,0.102592," ","integrate(x*(B*x+A)*(c*x**2+b*x+a)**3,x)","\frac{A a^{3} x^{2}}{2} + \frac{B c^{3} x^{9}}{9} + x^{8} \left(\frac{A c^{3}}{8} + \frac{3 B b c^{2}}{8}\right) + x^{7} \left(\frac{3 A b c^{2}}{7} + \frac{3 B a c^{2}}{7} + \frac{3 B b^{2} c}{7}\right) + x^{6} \left(\frac{A a c^{2}}{2} + \frac{A b^{2} c}{2} + B a b c + \frac{B b^{3}}{6}\right) + x^{5} \left(\frac{6 A a b c}{5} + \frac{A b^{3}}{5} + \frac{3 B a^{2} c}{5} + \frac{3 B a b^{2}}{5}\right) + x^{4} \left(\frac{3 A a^{2} c}{4} + \frac{3 A a b^{2}}{4} + \frac{3 B a^{2} b}{4}\right) + x^{3} \left(A a^{2} b + \frac{B a^{3}}{3}\right)"," ",0,"A*a**3*x**2/2 + B*c**3*x**9/9 + x**8*(A*c**3/8 + 3*B*b*c**2/8) + x**7*(3*A*b*c**2/7 + 3*B*a*c**2/7 + 3*B*b**2*c/7) + x**6*(A*a*c**2/2 + A*b**2*c/2 + B*a*b*c + B*b**3/6) + x**5*(6*A*a*b*c/5 + A*b**3/5 + 3*B*a**2*c/5 + 3*B*a*b**2/5) + x**4*(3*A*a**2*c/4 + 3*A*a*b**2/4 + 3*B*a**2*b/4) + x**3*(A*a**2*b + B*a**3/3)","A",0
869,1,190,0,0.104814," ","integrate((B*x+A)*(c*x**2+b*x+a)**3,x)","A a^{3} x + \frac{B c^{3} x^{8}}{8} + x^{7} \left(\frac{A c^{3}}{7} + \frac{3 B b c^{2}}{7}\right) + x^{6} \left(\frac{A b c^{2}}{2} + \frac{B a c^{2}}{2} + \frac{B b^{2} c}{2}\right) + x^{5} \left(\frac{3 A a c^{2}}{5} + \frac{3 A b^{2} c}{5} + \frac{6 B a b c}{5} + \frac{B b^{3}}{5}\right) + x^{4} \left(\frac{3 A a b c}{2} + \frac{A b^{3}}{4} + \frac{3 B a^{2} c}{4} + \frac{3 B a b^{2}}{4}\right) + x^{3} \left(A a^{2} c + A a b^{2} + B a^{2} b\right) + x^{2} \left(\frac{3 A a^{2} b}{2} + \frac{B a^{3}}{2}\right)"," ",0,"A*a**3*x + B*c**3*x**8/8 + x**7*(A*c**3/7 + 3*B*b*c**2/7) + x**6*(A*b*c**2/2 + B*a*c**2/2 + B*b**2*c/2) + x**5*(3*A*a*c**2/5 + 3*A*b**2*c/5 + 6*B*a*b*c/5 + B*b**3/5) + x**4*(3*A*a*b*c/2 + A*b**3/4 + 3*B*a**2*c/4 + 3*B*a*b**2/4) + x**3*(A*a**2*c + A*a*b**2 + B*a**2*b) + x**2*(3*A*a**2*b/2 + B*a**3/2)","A",0
870,1,192,0,0.308577," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x,x)","A a^{3} \log{\left(x \right)} + \frac{B c^{3} x^{7}}{7} + x^{6} \left(\frac{A c^{3}}{6} + \frac{B b c^{2}}{2}\right) + x^{5} \left(\frac{3 A b c^{2}}{5} + \frac{3 B a c^{2}}{5} + \frac{3 B b^{2} c}{5}\right) + x^{4} \left(\frac{3 A a c^{2}}{4} + \frac{3 A b^{2} c}{4} + \frac{3 B a b c}{2} + \frac{B b^{3}}{4}\right) + x^{3} \left(2 A a b c + \frac{A b^{3}}{3} + B a^{2} c + B a b^{2}\right) + x^{2} \left(\frac{3 A a^{2} c}{2} + \frac{3 A a b^{2}}{2} + \frac{3 B a^{2} b}{2}\right) + x \left(3 A a^{2} b + B a^{3}\right)"," ",0,"A*a**3*log(x) + B*c**3*x**7/7 + x**6*(A*c**3/6 + B*b*c**2/2) + x**5*(3*A*b*c**2/5 + 3*B*a*c**2/5 + 3*B*b**2*c/5) + x**4*(3*A*a*c**2/4 + 3*A*b**2*c/4 + 3*B*a*b*c/2 + B*b**3/4) + x**3*(2*A*a*b*c + A*b**3/3 + B*a**2*c + B*a*b**2) + x**2*(3*A*a**2*c/2 + 3*A*a*b**2/2 + 3*B*a**2*b/2) + x*(3*A*a**2*b + B*a**3)","A",0
871,1,184,0,0.355878," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**2,x)","- \frac{A a^{3}}{x} + \frac{B c^{3} x^{6}}{6} + a^{2} \left(3 A b + B a\right) \log{\left(x \right)} + x^{5} \left(\frac{A c^{3}}{5} + \frac{3 B b c^{2}}{5}\right) + x^{4} \left(\frac{3 A b c^{2}}{4} + \frac{3 B a c^{2}}{4} + \frac{3 B b^{2} c}{4}\right) + x^{3} \left(A a c^{2} + A b^{2} c + 2 B a b c + \frac{B b^{3}}{3}\right) + x^{2} \left(3 A a b c + \frac{A b^{3}}{2} + \frac{3 B a^{2} c}{2} + \frac{3 B a b^{2}}{2}\right) + x \left(3 A a^{2} c + 3 A a b^{2} + 3 B a^{2} b\right)"," ",0,"-A*a**3/x + B*c**3*x**6/6 + a**2*(3*A*b + B*a)*log(x) + x**5*(A*c**3/5 + 3*B*b*c**2/5) + x**4*(3*A*b*c**2/4 + 3*B*a*c**2/4 + 3*B*b**2*c/4) + x**3*(A*a*c**2 + A*b**2*c + 2*B*a*b*c + B*b**3/3) + x**2*(3*A*a*b*c + A*b**3/2 + 3*B*a**2*c/2 + 3*B*a*b**2/2) + x*(3*A*a**2*c + 3*A*a*b**2 + 3*B*a**2*b)","A",0
872,1,175,0,0.601294," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**3,x)","\frac{B c^{3} x^{5}}{5} + 3 a \left(A a c + A b^{2} + B a b\right) \log{\left(x \right)} + x^{4} \left(\frac{A c^{3}}{4} + \frac{3 B b c^{2}}{4}\right) + x^{3} \left(A b c^{2} + B a c^{2} + B b^{2} c\right) + x^{2} \left(\frac{3 A a c^{2}}{2} + \frac{3 A b^{2} c}{2} + 3 B a b c + \frac{B b^{3}}{2}\right) + x \left(6 A a b c + A b^{3} + 3 B a^{2} c + 3 B a b^{2}\right) + \frac{- A a^{3} + x \left(- 6 A a^{2} b - 2 B a^{3}\right)}{2 x^{2}}"," ",0,"B*c**3*x**5/5 + 3*a*(A*a*c + A*b**2 + B*a*b)*log(x) + x**4*(A*c**3/4 + 3*B*b*c**2/4) + x**3*(A*b*c**2 + B*a*c**2 + B*b**2*c) + x**2*(3*A*a*c**2/2 + 3*A*b**2*c/2 + 3*B*a*b*c + B*b**3/2) + x*(6*A*a*b*c + A*b**3 + 3*B*a**2*c + 3*B*a*b**2) + (-A*a**3 + x*(-6*A*a**2*b - 2*B*a**3))/(2*x**2)","A",0
873,1,187,0,1.359673," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**4,x)","\frac{B c^{3} x^{4}}{4} + x^{3} \left(\frac{A c^{3}}{3} + B b c^{2}\right) + x^{2} \left(\frac{3 A b c^{2}}{2} + \frac{3 B a c^{2}}{2} + \frac{3 B b^{2} c}{2}\right) + x \left(3 A a c^{2} + 3 A b^{2} c + 6 B a b c + B b^{3}\right) + \left(6 A a b c + A b^{3} + 3 B a^{2} c + 3 B a b^{2}\right) \log{\left(x \right)} + \frac{- 2 A a^{3} + x^{2} \left(- 18 A a^{2} c - 18 A a b^{2} - 18 B a^{2} b\right) + x \left(- 9 A a^{2} b - 3 B a^{3}\right)}{6 x^{3}}"," ",0,"B*c**3*x**4/4 + x**3*(A*c**3/3 + B*b*c**2) + x**2*(3*A*b*c**2/2 + 3*B*a*c**2/2 + 3*B*b**2*c/2) + x*(3*A*a*c**2 + 3*A*b**2*c + 6*B*a*b*c + B*b**3) + (6*A*a*b*c + A*b**3 + 3*B*a**2*c + 3*B*a*b**2)*log(x) + (-2*A*a**3 + x**2*(-18*A*a**2*c - 18*A*a*b**2 - 18*B*a**2*b) + x*(-9*A*a**2*b - 3*B*a**3))/(6*x**3)","A",0
874,1,189,0,4.205881," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**5,x)","\frac{B c^{3} x^{3}}{3} + x^{2} \left(\frac{A c^{3}}{2} + \frac{3 B b c^{2}}{2}\right) + x \left(3 A b c^{2} + 3 B a c^{2} + 3 B b^{2} c\right) + \left(3 A a c^{2} + 3 A b^{2} c + 6 B a b c + B b^{3}\right) \log{\left(x \right)} + \frac{- 3 A a^{3} + x^{3} \left(- 72 A a b c - 12 A b^{3} - 36 B a^{2} c - 36 B a b^{2}\right) + x^{2} \left(- 18 A a^{2} c - 18 A a b^{2} - 18 B a^{2} b\right) + x \left(- 12 A a^{2} b - 4 B a^{3}\right)}{12 x^{4}}"," ",0,"B*c**3*x**3/3 + x**2*(A*c**3/2 + 3*B*b*c**2/2) + x*(3*A*b*c**2 + 3*B*a*c**2 + 3*B*b**2*c) + (3*A*a*c**2 + 3*A*b**2*c + 6*B*a*b*c + B*b**3)*log(x) + (-3*A*a**3 + x**3*(-72*A*a*b*c - 12*A*b**3 - 36*B*a**2*c - 36*B*a*b**2) + x**2*(-18*A*a**2*c - 18*A*a*b**2 - 18*B*a**2*b) + x*(-12*A*a**2*b - 4*B*a**3))/(12*x**4)","A",0
875,1,182,0,11.616939," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**6,x)","\frac{B c^{3} x^{2}}{2} + 3 c \left(A b c + B a c + B b^{2}\right) \log{\left(x \right)} + x \left(A c^{3} + 3 B b c^{2}\right) + \frac{- 4 A a^{3} + x^{4} \left(- 60 A a c^{2} - 60 A b^{2} c - 120 B a b c - 20 B b^{3}\right) + x^{3} \left(- 60 A a b c - 10 A b^{3} - 30 B a^{2} c - 30 B a b^{2}\right) + x^{2} \left(- 20 A a^{2} c - 20 A a b^{2} - 20 B a^{2} b\right) + x \left(- 15 A a^{2} b - 5 B a^{3}\right)}{20 x^{5}}"," ",0,"B*c**3*x**2/2 + 3*c*(A*b*c + B*a*c + B*b**2)*log(x) + x*(A*c**3 + 3*B*b*c**2) + (-4*A*a**3 + x**4*(-60*A*a*c**2 - 60*A*b**2*c - 120*B*a*b*c - 20*B*b**3) + x**3*(-60*A*a*b*c - 10*A*b**3 - 30*B*a**2*c - 30*B*a*b**2) + x**2*(-20*A*a**2*c - 20*A*a*b**2 - 20*B*a**2*b) + x*(-15*A*a**2*b - 5*B*a**3))/(20*x**5)","A",0
876,1,187,0,28.647430," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**7,x)","B c^{3} x + c^{2} \left(A c + 3 B b\right) \log{\left(x \right)} + \frac{- 10 A a^{3} + x^{5} \left(- 180 A b c^{2} - 180 B a c^{2} - 180 B b^{2} c\right) + x^{4} \left(- 90 A a c^{2} - 90 A b^{2} c - 180 B a b c - 30 B b^{3}\right) + x^{3} \left(- 120 A a b c - 20 A b^{3} - 60 B a^{2} c - 60 B a b^{2}\right) + x^{2} \left(- 45 A a^{2} c - 45 A a b^{2} - 45 B a^{2} b\right) + x \left(- 36 A a^{2} b - 12 B a^{3}\right)}{60 x^{6}}"," ",0,"B*c**3*x + c**2*(A*c + 3*B*b)*log(x) + (-10*A*a**3 + x**5*(-180*A*b*c**2 - 180*B*a*c**2 - 180*B*b**2*c) + x**4*(-90*A*a*c**2 - 90*A*b**2*c - 180*B*a*b*c - 30*B*b**3) + x**3*(-120*A*a*b*c - 20*A*b**3 - 60*B*a**2*c - 60*B*a*b**2) + x**2*(-45*A*a**2*c - 45*A*a*b**2 - 45*B*a**2*b) + x*(-36*A*a**2*b - 12*B*a**3))/(60*x**6)","A",0
877,1,194,0,57.144824," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**8,x)","B c^{3} \log{\left(x \right)} + \frac{- 60 A a^{3} + x^{6} \left(- 420 A c^{3} - 1260 B b c^{2}\right) + x^{5} \left(- 630 A b c^{2} - 630 B a c^{2} - 630 B b^{2} c\right) + x^{4} \left(- 420 A a c^{2} - 420 A b^{2} c - 840 B a b c - 140 B b^{3}\right) + x^{3} \left(- 630 A a b c - 105 A b^{3} - 315 B a^{2} c - 315 B a b^{2}\right) + x^{2} \left(- 252 A a^{2} c - 252 A a b^{2} - 252 B a^{2} b\right) + x \left(- 210 A a^{2} b - 70 B a^{3}\right)}{420 x^{7}}"," ",0,"B*c**3*log(x) + (-60*A*a**3 + x**6*(-420*A*c**3 - 1260*B*b*c**2) + x**5*(-630*A*b*c**2 - 630*B*a*c**2 - 630*B*b**2*c) + x**4*(-420*A*a*c**2 - 420*A*b**2*c - 840*B*a*b*c - 140*B*b**3) + x**3*(-630*A*a*b*c - 105*A*b**3 - 315*B*a**2*c - 315*B*a*b**2) + x**2*(-252*A*a**2*c - 252*A*a*b**2 - 252*B*a**2*b) + x*(-210*A*a**2*b - 70*B*a**3))/(420*x**7)","A",0
878,1,196,0,119.400248," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**9,x)","\frac{- 35 A a^{3} - 280 B c^{3} x^{7} + x^{6} \left(- 140 A c^{3} - 420 B b c^{2}\right) + x^{5} \left(- 280 A b c^{2} - 280 B a c^{2} - 280 B b^{2} c\right) + x^{4} \left(- 210 A a c^{2} - 210 A b^{2} c - 420 B a b c - 70 B b^{3}\right) + x^{3} \left(- 336 A a b c - 56 A b^{3} - 168 B a^{2} c - 168 B a b^{2}\right) + x^{2} \left(- 140 A a^{2} c - 140 A a b^{2} - 140 B a^{2} b\right) + x \left(- 120 A a^{2} b - 40 B a^{3}\right)}{280 x^{8}}"," ",0,"(-35*A*a**3 - 280*B*c**3*x**7 + x**6*(-140*A*c**3 - 420*B*b*c**2) + x**5*(-280*A*b*c**2 - 280*B*a*c**2 - 280*B*b**2*c) + x**4*(-210*A*a*c**2 - 210*A*b**2*c - 420*B*a*b*c - 70*B*b**3) + x**3*(-336*A*a*b*c - 56*A*b**3 - 168*B*a**2*c - 168*B*a*b**2) + x**2*(-140*A*a**2*c - 140*A*a*b**2 - 140*B*a**2*b) + x*(-120*A*a**2*b - 40*B*a**3))/(280*x**8)","A",0
879,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,1,1100,0,3.919081," ","integrate(x**4*(e*x+d)/(c*x**2+b*x+a),x)","x^{3} \left(- \frac{b e}{3 c^{2}} + \frac{d}{3 c}\right) + x^{2} \left(- \frac{a e}{2 c^{2}} + \frac{b^{2} e}{2 c^{3}} - \frac{b d}{2 c^{2}}\right) + x \left(\frac{2 a b e}{c^{3}} - \frac{a d}{c^{2}} - \frac{b^{3} e}{c^{4}} + \frac{b^{2} d}{c^{3}}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e - 3 a b^{2} c e + 2 a b c^{2} d + b^{4} e - b^{3} c d}{2 c^{5}}\right) \log{\left(x + \frac{2 a^{3} c^{2} e - 4 a^{2} b^{2} c e + 3 a^{2} b c^{2} d + a b^{4} e - a b^{3} c d - 4 a c^{5} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e - 3 a b^{2} c e + 2 a b c^{2} d + b^{4} e - b^{3} c d}{2 c^{5}}\right) + b^{2} c^{4} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e - 3 a b^{2} c e + 2 a b c^{2} d + b^{4} e - b^{3} c d}{2 c^{5}}\right)}{5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e - 3 a b^{2} c e + 2 a b c^{2} d + b^{4} e - b^{3} c d}{2 c^{5}}\right) \log{\left(x + \frac{2 a^{3} c^{2} e - 4 a^{2} b^{2} c e + 3 a^{2} b c^{2} d + a b^{4} e - a b^{3} c d - 4 a c^{5} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e - 3 a b^{2} c e + 2 a b c^{2} d + b^{4} e - b^{3} c d}{2 c^{5}}\right) + b^{2} c^{4} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e - 3 a b^{2} c e + 2 a b c^{2} d + b^{4} e - b^{3} c d}{2 c^{5}}\right)}{5 a^{2} b c^{2} e - 2 a^{2} c^{3} d - 5 a b^{3} c e + 4 a b^{2} c^{2} d + b^{5} e - b^{4} c d} \right)} + \frac{e x^{4}}{4 c}"," ",0,"x**3*(-b*e/(3*c**2) + d/(3*c)) + x**2*(-a*e/(2*c**2) + b**2*e/(2*c**3) - b*d/(2*c**2)) + x*(2*a*b*e/c**3 - a*d/c**2 - b**3*e/c**4 + b**2*d/c**3) + (-sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e - 3*a*b**2*c*e + 2*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**5))*log(x + (2*a**3*c**2*e - 4*a**2*b**2*c*e + 3*a**2*b*c**2*d + a*b**4*e - a*b**3*c*d - 4*a*c**5*(-sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e - 3*a*b**2*c*e + 2*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**5)) + b**2*c**4*(-sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e - 3*a*b**2*c*e + 2*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**5)))/(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)) + (sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e - 3*a*b**2*c*e + 2*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**5))*log(x + (2*a**3*c**2*e - 4*a**2*b**2*c*e + 3*a**2*b*c**2*d + a*b**4*e - a*b**3*c*d - 4*a*c**5*(sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e - 3*a*b**2*c*e + 2*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**5)) + b**2*c**4*(sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e - 3*a*b**2*c*e + 2*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**5)))/(5*a**2*b*c**2*e - 2*a**2*c**3*d - 5*a*b**3*c*e + 4*a*b**2*c**2*d + b**5*e - b**4*c*d)) + e*x**4/(4*c)","B",0
882,1,840,0,2.959800," ","integrate(x**3*(e*x+d)/(c*x**2+b*x+a),x)","x^{2} \left(- \frac{b e}{2 c^{2}} + \frac{d}{2 c}\right) + x \left(- \frac{a e}{c^{2}} + \frac{b^{2} e}{c^{3}} - \frac{b d}{c^{2}}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e - a c^{2} d - b^{3} e + b^{2} c d}{2 c^{4}}\right) \log{\left(x + \frac{- 3 a^{2} b c e + 2 a^{2} c^{2} d + a b^{3} e - a b^{2} c d + 4 a c^{4} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e - a c^{2} d - b^{3} e + b^{2} c d}{2 c^{4}}\right) - b^{2} c^{3} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e - a c^{2} d - b^{3} e + b^{2} c d}{2 c^{4}}\right)}{2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e - a c^{2} d - b^{3} e + b^{2} c d}{2 c^{4}}\right) \log{\left(x + \frac{- 3 a^{2} b c e + 2 a^{2} c^{2} d + a b^{3} e - a b^{2} c d + 4 a c^{4} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e - a c^{2} d - b^{3} e + b^{2} c d}{2 c^{4}}\right) - b^{2} c^{3} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e - a c^{2} d - b^{3} e + b^{2} c d}{2 c^{4}}\right)}{2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d} \right)} + \frac{e x^{3}}{3 c}"," ",0,"x**2*(-b*e/(2*c**2) + d/(2*c)) + x*(-a*e/c**2 + b**2*e/c**3 - b*d/c**2) + (-sqrt(-4*a*c + b**2)*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e - a*c**2*d - b**3*e + b**2*c*d)/(2*c**4))*log(x + (-3*a**2*b*c*e + 2*a**2*c**2*d + a*b**3*e - a*b**2*c*d + 4*a*c**4*(-sqrt(-4*a*c + b**2)*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e - a*c**2*d - b**3*e + b**2*c*d)/(2*c**4)) - b**2*c**3*(-sqrt(-4*a*c + b**2)*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e - a*c**2*d - b**3*e + b**2*c*d)/(2*c**4)))/(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)) + (sqrt(-4*a*c + b**2)*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e - a*c**2*d - b**3*e + b**2*c*d)/(2*c**4))*log(x + (-3*a**2*b*c*e + 2*a**2*c**2*d + a*b**3*e - a*b**2*c*d + 4*a*c**4*(sqrt(-4*a*c + b**2)*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e - a*c**2*d - b**3*e + b**2*c*d)/(2*c**4)) - b**2*c**3*(sqrt(-4*a*c + b**2)*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e - a*c**2*d - b**3*e + b**2*c*d)/(2*c**4)))/(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d)) + e*x**3/(3*c)","B",0
883,1,609,0,2.036223," ","integrate(x**2*(e*x+d)/(c*x**2+b*x+a),x)","x \left(- \frac{b e}{c^{2}} + \frac{d}{c}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e - b^{2} e + b c d}{2 c^{3}}\right) \log{\left(x + \frac{2 a^{2} c e - a b^{2} e + a b c d + 4 a c^{3} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e - b^{2} e + b c d}{2 c^{3}}\right) - b^{2} c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e - b^{2} e + b c d}{2 c^{3}}\right)}{3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e - b^{2} e + b c d}{2 c^{3}}\right) \log{\left(x + \frac{2 a^{2} c e - a b^{2} e + a b c d + 4 a c^{3} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e - b^{2} e + b c d}{2 c^{3}}\right) - b^{2} c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e - b^{2} e + b c d}{2 c^{3}}\right)}{3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d} \right)} + \frac{e x^{2}}{2 c}"," ",0,"x*(-b*e/c**2 + d/c) + (-sqrt(-4*a*c + b**2)*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)/(2*c**3*(4*a*c - b**2)) - (a*c*e - b**2*e + b*c*d)/(2*c**3))*log(x + (2*a**2*c*e - a*b**2*e + a*b*c*d + 4*a*c**3*(-sqrt(-4*a*c + b**2)*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)/(2*c**3*(4*a*c - b**2)) - (a*c*e - b**2*e + b*c*d)/(2*c**3)) - b**2*c**2*(-sqrt(-4*a*c + b**2)*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)/(2*c**3*(4*a*c - b**2)) - (a*c*e - b**2*e + b*c*d)/(2*c**3)))/(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)) + (sqrt(-4*a*c + b**2)*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)/(2*c**3*(4*a*c - b**2)) - (a*c*e - b**2*e + b*c*d)/(2*c**3))*log(x + (2*a**2*c*e - a*b**2*e + a*b*c*d + 4*a*c**3*(sqrt(-4*a*c + b**2)*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)/(2*c**3*(4*a*c - b**2)) - (a*c*e - b**2*e + b*c*d)/(2*c**3)) - b**2*c**2*(sqrt(-4*a*c + b**2)*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)/(2*c**3*(4*a*c - b**2)) - (a*c*e - b**2*e + b*c*d)/(2*c**3)))/(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d)) + e*x**2/(2*c)","B",0
884,1,423,0,1.345110," ","integrate(x*(e*x+d)/(c*x**2+b*x+a),x)","\left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e - b^{2} e + b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b e - c d}{2 c^{2}}\right) \log{\left(x + \frac{- a b e - 4 a c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e - b^{2} e + b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b e - c d}{2 c^{2}}\right) + 2 a c d + b^{2} c \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e - b^{2} e + b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b e - c d}{2 c^{2}}\right)}{2 a c e - b^{2} e + b c d} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e - b^{2} e + b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b e - c d}{2 c^{2}}\right) \log{\left(x + \frac{- a b e - 4 a c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e - b^{2} e + b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b e - c d}{2 c^{2}}\right) + 2 a c d + b^{2} c \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c e - b^{2} e + b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b e - c d}{2 c^{2}}\right)}{2 a c e - b^{2} e + b c d} \right)} + \frac{e x}{c}"," ",0,"(-sqrt(-4*a*c + b**2)*(2*a*c*e - b**2*e + b*c*d)/(2*c**2*(4*a*c - b**2)) - (b*e - c*d)/(2*c**2))*log(x + (-a*b*e - 4*a*c**2*(-sqrt(-4*a*c + b**2)*(2*a*c*e - b**2*e + b*c*d)/(2*c**2*(4*a*c - b**2)) - (b*e - c*d)/(2*c**2)) + 2*a*c*d + b**2*c*(-sqrt(-4*a*c + b**2)*(2*a*c*e - b**2*e + b*c*d)/(2*c**2*(4*a*c - b**2)) - (b*e - c*d)/(2*c**2)))/(2*a*c*e - b**2*e + b*c*d)) + (sqrt(-4*a*c + b**2)*(2*a*c*e - b**2*e + b*c*d)/(2*c**2*(4*a*c - b**2)) - (b*e - c*d)/(2*c**2))*log(x + (-a*b*e - 4*a*c**2*(sqrt(-4*a*c + b**2)*(2*a*c*e - b**2*e + b*c*d)/(2*c**2*(4*a*c - b**2)) - (b*e - c*d)/(2*c**2)) + 2*a*c*d + b**2*c*(sqrt(-4*a*c + b**2)*(2*a*c*e - b**2*e + b*c*d)/(2*c**2*(4*a*c - b**2)) - (b*e - c*d)/(2*c**2)))/(2*a*c*e - b**2*e + b*c*d)) + e*x/c","B",0
885,1,280,0,0.741172," ","integrate((e*x+d)/(c*x**2+b*x+a),x)","\left(\frac{e}{2 c} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 4 a c \left(\frac{e}{2 c} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) + 2 a e + b^{2} \left(\frac{e}{2 c} - \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) - b d}{b e - 2 c d} \right)} + \left(\frac{e}{2 c} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 4 a c \left(\frac{e}{2 c} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) + 2 a e + b^{2} \left(\frac{e}{2 c} + \frac{\sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c \left(4 a c - b^{2}\right)}\right) - b d}{b e - 2 c d} \right)}"," ",0,"(e/(2*c) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2)))*log(x + (-4*a*c*(e/(2*c) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) + 2*a*e + b**2*(e/(2*c) - sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) - b*d)/(b*e - 2*c*d)) + (e/(2*c) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2)))*log(x + (-4*a*c*(e/(2*c) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) + 2*a*e + b**2*(e/(2*c) + sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c*(4*a*c - b**2))) - b*d)/(b*e - 2*c*d))","B",0
886,-1,0,0,0.000000," ","integrate((e*x+d)/x/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate((e*x+d)/x**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate((e*x+d)/x**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((e*x+d)/x**4/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,1,1572,0,7.711043," ","integrate(x**4*(e*x+d)/(c*x**2+b*x+a)**2,x)","x \left(- \frac{2 b e}{c^{3}} + \frac{d}{c^{2}}\right) + \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right) \log{\left(x + \frac{16 a^{3} c^{2} e - 17 a^{2} b^{2} c e + 10 a^{2} b c^{2} d + 16 a^{2} c^{5} \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right) + 3 a b^{4} e - 2 a b^{3} c d - 8 a b^{2} c^{4} \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right) + b^{4} c^{3} \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right)}{30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d} \right)} + \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right) \log{\left(x + \frac{16 a^{3} c^{2} e - 17 a^{2} b^{2} c e + 10 a^{2} b c^{2} d + 16 a^{2} c^{5} \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right) + 3 a b^{4} e - 2 a b^{3} c d - 8 a b^{2} c^{4} \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right) + b^{4} c^{3} \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c e - 3 b^{2} e + 2 b c d}{2 c^{4}}\right)}{30 a^{2} b c^{2} e - 12 a^{2} c^{3} d - 20 a b^{3} c e + 12 a b^{2} c^{2} d + 3 b^{5} e - 2 b^{4} c d} \right)} + \frac{- 2 a^{3} c^{2} e + 4 a^{2} b^{2} c e - 3 a^{2} b c^{2} d - a b^{4} e + a b^{3} c d + x \left(- 5 a^{2} b c^{2} e + 2 a^{2} c^{3} d + 5 a b^{3} c e - 4 a b^{2} c^{2} d - b^{5} e + b^{4} c d\right)}{4 a^{2} c^{5} - a b^{2} c^{4} + x^{2} \left(4 a c^{6} - b^{2} c^{5}\right) + x \left(4 a b c^{5} - b^{3} c^{4}\right)} + \frac{e x^{2}}{2 c^{2}}"," ",0,"x*(-2*b*e/c**3 + d/c**2) + (-sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4))*log(x + (16*a**3*c**2*e - 17*a**2*b**2*c*e + 10*a**2*b*c**2*d + 16*a**2*c**5*(-sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4)) + 3*a*b**4*e - 2*a*b**3*c*d - 8*a*b**2*c**4*(-sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4)) + b**4*c**3*(-sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4)))/(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)) + (sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4))*log(x + (16*a**3*c**2*e - 17*a**2*b**2*c*e + 10*a**2*b*c**2*d + 16*a**2*c**5*(sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4)) + 3*a*b**4*e - 2*a*b**3*c*d - 8*a*b**2*c**4*(sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4)) + b**4*c**3*(sqrt(-(4*a*c - b**2)**3)*(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c*e - 3*b**2*e + 2*b*c*d)/(2*c**4)))/(30*a**2*b*c**2*e - 12*a**2*c**3*d - 20*a*b**3*c*e + 12*a*b**2*c**2*d + 3*b**5*e - 2*b**4*c*d)) + (-2*a**3*c**2*e + 4*a**2*b**2*c*e - 3*a**2*b*c**2*d - a*b**4*e + a*b**3*c*d + x*(-5*a**2*b*c**2*e + 2*a**2*c**3*d + 5*a*b**3*c*e - 4*a*b**2*c**2*d - b**5*e + b**4*c*d))/(4*a**2*c**5 - a*b**2*c**4 + x**2*(4*a*c**6 - b**2*c**5) + x*(4*a*b*c**5 - b**3*c**4)) + e*x**2/(2*c**2)","B",0
891,1,1248,0,5.403820," ","integrate(x**3*(e*x+d)/(c*x**2+b*x+a)**2,x)","\left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right) \log{\left(x + \frac{- 10 a^{2} b c e - 16 a^{2} c^{4} \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right) + 8 a^{2} c^{2} d + 2 a b^{3} e + 8 a b^{2} c^{3} \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right) - a b^{2} c d - b^{4} c^{2} \left(- \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right)}{12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d} \right)} + \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right) \log{\left(x + \frac{- 10 a^{2} b c e - 16 a^{2} c^{4} \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right) + 8 a^{2} c^{2} d + 2 a b^{3} e + 8 a b^{2} c^{3} \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right) - a b^{2} c d - b^{4} c^{2} \left(\frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d\right)}{2 c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 b e - c d}{2 c^{3}}\right)}{12 a^{2} c^{2} e - 12 a b^{2} c e + 6 a b c^{2} d + 2 b^{4} e - b^{3} c d} \right)} + \frac{- 3 a^{2} b c e + 2 a^{2} c^{2} d + a b^{3} e - a b^{2} c d + x \left(2 a^{2} c^{2} e - 4 a b^{2} c e + 3 a b c^{2} d + b^{4} e - b^{3} c d\right)}{4 a^{2} c^{4} - a b^{2} c^{3} + x^{2} \left(4 a c^{5} - b^{2} c^{4}\right) + x \left(4 a b c^{4} - b^{3} c^{3}\right)} + \frac{e x}{c^{2}}"," ",0,"(-sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3))*log(x + (-10*a**2*b*c*e - 16*a**2*c**4*(-sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3)) + 8*a**2*c**2*d + 2*a*b**3*e + 8*a*b**2*c**3*(-sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3)) - a*b**2*c*d - b**4*c**2*(-sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3)))/(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)) + (sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3))*log(x + (-10*a**2*b*c*e - 16*a**2*c**4*(sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3)) + 8*a**2*c**2*d + 2*a*b**3*e + 8*a*b**2*c**3*(sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3)) - a*b**2*c*d - b**4*c**2*(sqrt(-(4*a*c - b**2)**3)*(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)/(2*c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*b*e - c*d)/(2*c**3)))/(12*a**2*c**2*e - 12*a*b**2*c*e + 6*a*b*c**2*d + 2*b**4*e - b**3*c*d)) + (-3*a**2*b*c*e + 2*a**2*c**2*d + a*b**3*e - a*b**2*c*d + x*(2*a**2*c**2*e - 4*a*b**2*c*e + 3*a*b*c**2*d + b**4*e - b**3*c*d))/(4*a**2*c**4 - a*b**2*c**3 + x**2*(4*a*c**5 - b**2*c**4) + x*(4*a*b*c**4 - b**3*c**3)) + e*x/c**2","B",0
892,1,901,0,2.837444," ","integrate(x**2*(e*x+d)/(c*x**2+b*x+a)**2,x)","\left(\frac{e}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 8 a^{2} c e + 8 a b^{2} c^{2} \left(\frac{e}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - a b^{2} e - 2 a b c d - b^{4} c \left(\frac{e}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right)}{6 a b c e - 4 a c^{2} d - b^{3} e} \right)} + \left(\frac{e}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 8 a^{2} c e + 8 a b^{2} c^{2} \left(\frac{e}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - a b^{2} e - 2 a b c d - b^{4} c \left(\frac{e}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e - 4 a c^{2} d - b^{3} e\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right)}{6 a b c e - 4 a c^{2} d - b^{3} e} \right)} + \frac{2 a^{2} c e - a b^{2} e + a b c d + x \left(3 a b c e - 2 a c^{2} d - b^{3} e + b^{2} c d\right)}{4 a^{2} c^{3} - a b^{2} c^{2} + x^{2} \left(4 a c^{4} - b^{2} c^{3}\right) + x \left(4 a b c^{3} - b^{3} c^{2}\right)}"," ",0,"(e/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 8*a**2*c*e + 8*a*b**2*c**2*(e/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - a*b**2*e - 2*a*b*c*d - b**4*c*(e/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))))/(6*a*b*c*e - 4*a*c**2*d - b**3*e)) + (e/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 8*a**2*c*e + 8*a*b**2*c**2*(e/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - a*b**2*e - 2*a*b*c*d - b**4*c*(e/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e - 4*a*c**2*d - b**3*e)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))))/(6*a*b*c*e - 4*a*c**2*d - b**3*e)) + (2*a**2*c*e - a*b**2*e + a*b*c*d + x*(3*a*b*c*e - 2*a*c**2*d - b**3*e + b**2*c*d))/(4*a**2*c**3 - a*b**2*c**2 + x**2*(4*a*c**4 - b**2*c**3) + x*(4*a*b*c**3 - b**3*c**2))","B",0
893,1,379,0,1.048297," ","integrate(x*(e*x+d)/(c*x**2+b*x+a)**2,x)","- \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) \log{\left(x + \frac{- 16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) + 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) + 2 a b e - b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) - b^{2} d}{4 a c e - 2 b c d} \right)} + \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) \log{\left(x + \frac{16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) - 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) + 2 a b e + b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a e - b d\right) - b^{2} d}{4 a c e - 2 b c d} \right)} + \frac{a b e - 2 a c d + x \left(- 2 a c e + b^{2} e - b c d\right)}{4 a^{2} c^{2} - a b^{2} c + x^{2} \left(4 a c^{3} - b^{2} c^{2}\right) + x \left(4 a b c^{2} - b^{3} c\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d)*log(x + (-16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d) + 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d) + 2*a*b*e - b**4*sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d) - b**2*d)/(4*a*c*e - 2*b*c*d)) + sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d)*log(x + (16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d) - 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d) + 2*a*b*e + b**4*sqrt(-1/(4*a*c - b**2)**3)*(2*a*e - b*d) - b**2*d)/(4*a*c*e - 2*b*c*d)) + (a*b*e - 2*a*c*d + x*(-2*a*c*e + b**2*e - b*c*d))/(4*a**2*c**2 - a*b**2*c + x**2*(4*a*c**3 - b**2*c**2) + x*(4*a*b*c**2 - b**3*c))","B",0
894,1,359,0,0.950666," ","integrate((e*x+d)/(c*x**2+b*x+a)**2,x)","\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) \log{\left(x + \frac{- 16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) - b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{2} e - 2 b c d}{2 b c e - 4 c^{2} d} \right)} - \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) \log{\left(x + \frac{16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) - 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{2} e - 2 b c d}{2 b c e - 4 c^{2} d} \right)} + \frac{- 2 a e + b d + x \left(- b e + 2 c d\right)}{4 a^{2} c - a b^{2} + x^{2} \left(4 a c^{2} - b^{2} c\right) + x \left(4 a b c - b^{3}\right)}"," ",0,"sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d)*log(x + (-16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) - b**4*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**2*e - 2*b*c*d)/(2*b*c*e - 4*c**2*d)) - sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d)*log(x + (16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) - 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**4*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**2*e - 2*b*c*d)/(2*b*c*e - 4*c**2*d)) + (-2*a*e + b*d + x*(-b*e + 2*c*d))/(4*a**2*c - a*b**2 + x**2*(4*a*c**2 - b**2*c) + x*(4*a*b*c - b**3))","B",0
895,-1,0,0,0.000000," ","integrate((e*x+d)/x/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate((e*x+d)/x**2/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate((e*x+d)/x**3/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,1,8,0,0.096558," ","integrate((5+2*x)/(x**2+5*x+4),x)","\log{\left(x^{2} + 5 x + 4 \right)}"," ",0,"log(x**2 + 5*x + 4)","A",0
899,1,14,0,0.109151," ","integrate((7+3*x)/(x**2+6*x+8),x)","\frac{\log{\left(x + 2 \right)}}{2} + \frac{5 \log{\left(x + 4 \right)}}{2}"," ",0,"log(x + 2)/2 + 5*log(x + 4)/2","A",0
900,1,14,0,0.116286," ","integrate((5+2*x)/(x**2+4*x+5),x)","\log{\left(x^{2} + 4 x + 5 \right)} + \operatorname{atan}{\left(x + 2 \right)}"," ",0,"log(x**2 + 4*x + 5) + atan(x + 2)","A",0
901,1,39,0,0.151662," ","integrate((-2+7*x)/(2*x**2-16*x+42),x)","\frac{7 \log{\left(x^{2} - 8 x + 21 \right)}}{4} + \frac{13 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} - \frac{4 \sqrt{5}}{5} \right)}}{5}"," ",0,"7*log(x**2 - 8*x + 21)/4 + 13*sqrt(5)*atan(sqrt(5)*x/5 - 4*sqrt(5)/5)/5","A",0
902,1,49,0,0.123591," ","integrate((3+x)/(x**2+3*x+1),x)","\left(\frac{1}{2} + \frac{3 \sqrt{5}}{10}\right) \log{\left(x - \frac{\sqrt{5}}{2} + \frac{3}{2} \right)} + \left(\frac{1}{2} - \frac{3 \sqrt{5}}{10}\right) \log{\left(x + \frac{\sqrt{5}}{2} + \frac{3}{2} \right)}"," ",0,"(1/2 + 3*sqrt(5)/10)*log(x - sqrt(5)/2 + 3/2) + (1/2 - 3*sqrt(5)/10)*log(x + sqrt(5)/2 + 3/2)","A",0
903,1,42,0,0.123060," ","integrate((-1+2*x)/(4*x**2+8*x+1),x)","\left(\frac{1}{4} - \frac{\sqrt{3}}{4}\right) \log{\left(x - \frac{\sqrt{3}}{2} + 1 \right)} + \left(\frac{1}{4} + \frac{\sqrt{3}}{4}\right) \log{\left(x + \frac{\sqrt{3}}{2} + 1 \right)}"," ",0,"(1/4 - sqrt(3)/4)*log(x - sqrt(3)/2 + 1) + (1/4 + sqrt(3)/4)*log(x + sqrt(3)/2 + 1)","A",0
904,1,12,0,0.106936," ","integrate((3+2*x)/(4*x**2+12*x+13)**2,x)","- \frac{1}{16 x^{2} + 48 x + 52}"," ",0,"-1/(16*x**2 + 48*x + 52)","A",0
905,1,19,0,0.121322," ","integrate((4+x)/(x**2+4*x+5)**2,x)","\frac{2 x + 3}{2 x^{2} + 8 x + 10} + \operatorname{atan}{\left(x + 2 \right)}"," ",0,"(2*x + 3)/(2*x**2 + 8*x + 10) + atan(x + 2)","A",0
906,1,42,0,0.138791," ","integrate((-1+3*x)/(x**2+x+1)**2,x)","\frac{- 5 x - 7}{3 x^{2} + 3 x + 3} - \frac{10 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(-5*x - 7)/(3*x**2 + 3*x + 3) - 10*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/9","A",0
907,1,61,0,0.159544," ","integrate((1+x)/(x**2-x+1)**3,x)","\frac{2 x^{3} - 3 x^{2} + 4 x - 2}{2 x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"(2*x**3 - 3*x**2 + 4*x - 2)/(2*x**4 - 4*x**3 + 6*x**2 - 4*x + 2) + 2*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
908,1,7,0,0.071728," ","integrate(1/(B*x+A),x)","\frac{\log{\left(A + B x \right)}}{B}"," ",0,"log(A + B*x)/B","A",0
909,1,7,0,0.074260," ","integrate((B*x+A)/(B**2*x**2+2*A*B*x+A**2),x)","\frac{\log{\left(A + B x \right)}}{B}"," ",0,"log(A + B*x)/B","A",0
910,0,0,0,0.000000," ","integrate(x**4*(B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int x^{4} \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(x**4*(A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
911,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int x^{3} \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(x**3*(A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
912,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int x^{2} \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(x**2*(A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
913,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int x \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(x*(A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
914,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
915,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x, x)","F",0
916,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**2,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{2}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**2, x)","F",0
917,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**3,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{3}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**3, x)","F",0
918,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**4,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{4}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**4, x)","F",0
919,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**5,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{5}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**5, x)","F",0
920,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**6,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{6}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**6, x)","F",0
921,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**7,x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{7}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**7, x)","F",0
922,0,0,0,0.000000," ","integrate(x**4*(B*x+A)*(c*x**2+b*x+a)**(3/2),x)","\int x^{4} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*(A + B*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
923,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x+a)**(3/2),x)","\int x^{3} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(A + B*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
924,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**(3/2),x)","\int x^{2} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(A + B*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
925,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x+a)**(3/2),x)","\int x \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(A + B*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
926,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2),x)","\int \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
927,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x, x)","F",0
928,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**2,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**2, x)","F",0
929,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**3,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**3, x)","F",0
930,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**4,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**4, x)","F",0
931,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**5,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**5, x)","F",0
932,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**6,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**6, x)","F",0
933,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**7,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**7, x)","F",0
934,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(3/2)/x**8,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(3/2)/x**8, x)","F",0
935,0,0,0,0.000000," ","integrate(x**4*(B*x+A)*(c*x**2+b*x+a)**(5/2),x)","\int x^{4} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**4*(A + B*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
936,0,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x+a)**(5/2),x)","\int x^{3} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**3*(A + B*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
937,0,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**(5/2),x)","\int x^{2} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*(A + B*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
938,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x+a)**(5/2),x)","\int x \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*(A + B*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
939,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2),x)","\int \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
940,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x, x)","F",0
941,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**2,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**2, x)","F",0
942,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**3,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**3, x)","F",0
943,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**4,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**4, x)","F",0
944,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**5,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**5, x)","F",0
945,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**6,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**6, x)","F",0
946,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**7,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**7, x)","F",0
947,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**8,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{8}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**8, x)","F",0
948,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**9,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{9}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**9, x)","F",0
949,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(5/2)/x**10,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{x^{10}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**(5/2)/x**10, x)","F",0
950,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x**4*(A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
951,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x**3*(A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
952,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x**2*(A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
953,0,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x \left(A + B x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x*(A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
954,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
955,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{x \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*sqrt(a + b*x + c*x**2)), x)","F",0
956,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{x^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**2*sqrt(a + b*x + c*x**2)), x)","F",0
957,0,0,0,0.000000," ","integrate((B*x+A)/x**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{x^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**3*sqrt(a + b*x + c*x**2)), x)","F",0
958,0,0,0,0.000000," ","integrate((B*x+A)/x**4/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{x^{4} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**4*sqrt(a + b*x + c*x**2)), x)","F",0
959,0,0,0,0.000000," ","integrate((B*x+A)/x**5/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{x^{5} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**5*sqrt(a + b*x + c*x**2)), x)","F",0
960,0,0,0,0.000000," ","integrate((B*x+A)/x**6/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{x^{6} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**6*sqrt(a + b*x + c*x**2)), x)","F",0
961,0,0,0,0.000000," ","integrate(x**4*(B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{x^{4} \left(A + B x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*(A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
962,0,0,0,0.000000," ","integrate(x**3*(B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{x^{3} \left(A + B x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
963,0,0,0,0.000000," ","integrate(x**2*(B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{x^{2} \left(A + B x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
964,0,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{x \left(A + B x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
965,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + B x}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
966,0,0,0,0.000000," ","integrate((B*x+A)/x/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + B x}{x \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(a + b*x + c*x**2)**(3/2)), x)","F",0
967,0,0,0,0.000000," ","integrate((B*x+A)/x**2/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + B x}{x^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**2*(a + b*x + c*x**2)**(3/2)), x)","F",0
968,0,0,0,0.000000," ","integrate((B*x+A)/x**3/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + B x}{x^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x**3*(a + b*x + c*x**2)**(3/2)), x)","F",0
969,-1,0,0,0.000000," ","integrate((B*x+A)/x**4/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
970,-1,0,0,0.000000," ","integrate(x**4*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
971,-1,0,0,0.000000," ","integrate(x**3*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
972,-1,0,0,0.000000," ","integrate(x**2*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
973,-1,0,0,0.000000," ","integrate(x*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
974,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
975,-1,0,0,0.000000," ","integrate((B*x+A)/x/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
976,-1,0,0,0.000000," ","integrate((B*x+A)/x**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
977,-1,0,0,0.000000," ","integrate((B*x+A)/x**3/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
978,-1,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
979,-1,0,0,0.000000," ","integrate((e*x+d)/(c*x**2+b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
980,0,0,0,0.000000," ","integrate((1-x)/x/(x**2+3*x+1)**(1/2),x)","- \int \left(- \frac{1}{x \sqrt{x^{2} + 3 x + 1}}\right)\, dx - \int \frac{1}{\sqrt{x^{2} + 3 x + 1}}\, dx"," ",0,"-Integral(-1/(x*sqrt(x**2 + 3*x + 1)), x) - Integral(1/sqrt(x**2 + 3*x + 1), x)","F",0
981,1,70,0,8.079105," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x+a),x)","\frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{11}{2}}}{11} + \frac{2 A c x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{11}{2}}}{11} + \frac{2 B b x^{\frac{13}{2}}}{13} + \frac{2 B c x^{\frac{15}{2}}}{15}"," ",0,"2*A*a*x**(9/2)/9 + 2*A*b*x**(11/2)/11 + 2*A*c*x**(13/2)/13 + 2*B*a*x**(11/2)/11 + 2*B*b*x**(13/2)/13 + 2*B*c*x**(15/2)/15","A",0
982,1,70,0,3.971928," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x+a),x)","\frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 A c x^{\frac{11}{2}}}{11} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{11}{2}}}{11} + \frac{2 B c x^{\frac{13}{2}}}{13}"," ",0,"2*A*a*x**(7/2)/7 + 2*A*b*x**(9/2)/9 + 2*A*c*x**(11/2)/11 + 2*B*a*x**(9/2)/9 + 2*B*b*x**(11/2)/11 + 2*B*c*x**(13/2)/13","A",0
983,1,70,0,1.751145," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x+a),x)","\frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 A b x^{\frac{7}{2}}}{7} + \frac{2 A c x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{7}{2}}}{7} + \frac{2 B b x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{11}{2}}}{11}"," ",0,"2*A*a*x**(5/2)/5 + 2*A*b*x**(7/2)/7 + 2*A*c*x**(9/2)/9 + 2*B*a*x**(7/2)/7 + 2*B*b*x**(9/2)/9 + 2*B*c*x**(11/2)/11","A",0
984,1,53,0,2.791688," ","integrate((B*x+A)*(c*x**2+b*x+a)*x**(1/2),x)","\frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B c x^{\frac{9}{2}}}{9} + \frac{2 x^{\frac{7}{2}} \left(A c + B b\right)}{7} + \frac{2 x^{\frac{5}{2}} \left(A b + B a\right)}{5}"," ",0,"2*A*a*x**(3/2)/3 + 2*B*c*x**(9/2)/9 + 2*x**(7/2)*(A*c + B*b)/7 + 2*x**(5/2)*(A*b + B*a)/5","A",0
985,1,68,0,0.469277," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**(1/2),x)","2 A a \sqrt{x} + \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 A c x^{\frac{5}{2}}}{5} + \frac{2 B a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{7}{2}}}{7}"," ",0,"2*A*a*sqrt(x) + 2*A*b*x**(3/2)/3 + 2*A*c*x**(5/2)/5 + 2*B*a*x**(3/2)/3 + 2*B*b*x**(5/2)/5 + 2*B*c*x**(7/2)/7","A",0
986,1,65,0,0.638270," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**(3/2),x)","- \frac{2 A a}{\sqrt{x}} + 2 A b \sqrt{x} + \frac{2 A c x^{\frac{3}{2}}}{3} + 2 B a \sqrt{x} + \frac{2 B b x^{\frac{3}{2}}}{3} + \frac{2 B c x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a/sqrt(x) + 2*A*b*sqrt(x) + 2*A*c*x**(3/2)/3 + 2*B*a*sqrt(x) + 2*B*b*x**(3/2)/3 + 2*B*c*x**(5/2)/5","A",0
987,1,63,0,0.809130," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**(5/2),x)","- \frac{2 A a}{3 x^{\frac{3}{2}}} - \frac{2 A b}{\sqrt{x}} + 2 A c \sqrt{x} - \frac{2 B a}{\sqrt{x}} + 2 B b \sqrt{x} + \frac{2 B c x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a/(3*x**(3/2)) - 2*A*b/sqrt(x) + 2*A*c*sqrt(x) - 2*B*a/sqrt(x) + 2*B*b*sqrt(x) + 2*B*c*x**(3/2)/3","A",0
988,1,65,0,1.427947," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**(7/2),x)","- \frac{2 A a}{5 x^{\frac{5}{2}}} - \frac{2 A b}{3 x^{\frac{3}{2}}} - \frac{2 A c}{\sqrt{x}} - \frac{2 B a}{3 x^{\frac{3}{2}}} - \frac{2 B b}{\sqrt{x}} + 2 B c \sqrt{x}"," ",0,"-2*A*a/(5*x**(5/2)) - 2*A*b/(3*x**(3/2)) - 2*A*c/sqrt(x) - 2*B*a/(3*x**(3/2)) - 2*B*b/sqrt(x) + 2*B*c*sqrt(x)","A",0
989,1,70,0,3.089316," ","integrate((B*x+A)*(c*x**2+b*x+a)/x**(9/2),x)","- \frac{2 A a}{7 x^{\frac{7}{2}}} - \frac{2 A b}{5 x^{\frac{5}{2}}} - \frac{2 A c}{3 x^{\frac{3}{2}}} - \frac{2 B a}{5 x^{\frac{5}{2}}} - \frac{2 B b}{3 x^{\frac{3}{2}}} - \frac{2 B c}{\sqrt{x}}"," ",0,"-2*A*a/(7*x**(7/2)) - 2*A*b/(5*x**(5/2)) - 2*A*c/(3*x**(3/2)) - 2*B*a/(5*x**(5/2)) - 2*B*b/(3*x**(3/2)) - 2*B*c/sqrt(x)","A",0
990,1,162,0,16.111611," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x+a)**2,x)","\frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a b x^{\frac{11}{2}}}{11} + \frac{4 A a c x^{\frac{13}{2}}}{13} + \frac{2 A b^{2} x^{\frac{13}{2}}}{13} + \frac{4 A b c x^{\frac{15}{2}}}{15} + \frac{2 A c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a b x^{\frac{13}{2}}}{13} + \frac{4 B a c x^{\frac{15}{2}}}{15} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} + \frac{4 B b c x^{\frac{17}{2}}}{17} + \frac{2 B c^{2} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**2*x**(9/2)/9 + 4*A*a*b*x**(11/2)/11 + 4*A*a*c*x**(13/2)/13 + 2*A*b**2*x**(13/2)/13 + 4*A*b*c*x**(15/2)/15 + 2*A*c**2*x**(17/2)/17 + 2*B*a**2*x**(11/2)/11 + 4*B*a*b*x**(13/2)/13 + 4*B*a*c*x**(15/2)/15 + 2*B*b**2*x**(15/2)/15 + 4*B*b*c*x**(17/2)/17 + 2*B*c**2*x**(19/2)/19","A",0
991,1,162,0,9.003663," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x+a)**2,x)","\frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{4 A a b x^{\frac{9}{2}}}{9} + \frac{4 A a c x^{\frac{11}{2}}}{11} + \frac{2 A b^{2} x^{\frac{11}{2}}}{11} + \frac{4 A b c x^{\frac{13}{2}}}{13} + \frac{2 A c^{2} x^{\frac{15}{2}}}{15} + \frac{2 B a^{2} x^{\frac{9}{2}}}{9} + \frac{4 B a b x^{\frac{11}{2}}}{11} + \frac{4 B a c x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13} + \frac{4 B b c x^{\frac{15}{2}}}{15} + \frac{2 B c^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*A*a**2*x**(7/2)/7 + 4*A*a*b*x**(9/2)/9 + 4*A*a*c*x**(11/2)/11 + 2*A*b**2*x**(11/2)/11 + 4*A*b*c*x**(13/2)/13 + 2*A*c**2*x**(15/2)/15 + 2*B*a**2*x**(9/2)/9 + 4*B*a*b*x**(11/2)/11 + 4*B*a*c*x**(13/2)/13 + 2*B*b**2*x**(13/2)/13 + 4*B*b*c*x**(15/2)/15 + 2*B*c**2*x**(17/2)/17","A",0
992,1,162,0,5.769872," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x+a)**2,x)","\frac{2 A a^{2} x^{\frac{5}{2}}}{5} + \frac{4 A a b x^{\frac{7}{2}}}{7} + \frac{4 A a c x^{\frac{9}{2}}}{9} + \frac{2 A b^{2} x^{\frac{9}{2}}}{9} + \frac{4 A b c x^{\frac{11}{2}}}{11} + \frac{2 A c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} x^{\frac{7}{2}}}{7} + \frac{4 B a b x^{\frac{9}{2}}}{9} + \frac{4 B a c x^{\frac{11}{2}}}{11} + \frac{2 B b^{2} x^{\frac{11}{2}}}{11} + \frac{4 B b c x^{\frac{13}{2}}}{13} + \frac{2 B c^{2} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**2*x**(5/2)/5 + 4*A*a*b*x**(7/2)/7 + 4*A*a*c*x**(9/2)/9 + 2*A*b**2*x**(9/2)/9 + 4*A*b*c*x**(11/2)/11 + 2*A*c**2*x**(13/2)/13 + 2*B*a**2*x**(7/2)/7 + 4*B*a*b*x**(9/2)/9 + 4*B*a*c*x**(11/2)/11 + 2*B*b**2*x**(11/2)/11 + 4*B*b*c*x**(13/2)/13 + 2*B*c**2*x**(15/2)/15","A",0
993,1,121,0,5.598446," ","integrate((B*x+A)*(c*x**2+b*x+a)**2*x**(1/2),x)","\frac{2 A a^{2} x^{\frac{3}{2}}}{3} + \frac{2 B c^{2} x^{\frac{13}{2}}}{13} + \frac{2 x^{\frac{11}{2}} \left(A c^{2} + 2 B b c\right)}{11} + \frac{2 x^{\frac{9}{2}} \left(2 A b c + 2 B a c + B b^{2}\right)}{9} + \frac{2 x^{\frac{7}{2}} \left(2 A a c + A b^{2} + 2 B a b\right)}{7} + \frac{2 x^{\frac{5}{2}} \left(2 A a b + B a^{2}\right)}{5}"," ",0,"2*A*a**2*x**(3/2)/3 + 2*B*c**2*x**(13/2)/13 + 2*x**(11/2)*(A*c**2 + 2*B*b*c)/11 + 2*x**(9/2)*(2*A*b*c + 2*B*a*c + B*b**2)/9 + 2*x**(7/2)*(2*A*a*c + A*b**2 + 2*B*a*b)/7 + 2*x**(5/2)*(2*A*a*b + B*a**2)/5","A",0
994,1,160,0,2.050001," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**(1/2),x)","2 A a^{2} \sqrt{x} + \frac{4 A a b x^{\frac{3}{2}}}{3} + \frac{4 A a c x^{\frac{5}{2}}}{5} + \frac{2 A b^{2} x^{\frac{5}{2}}}{5} + \frac{4 A b c x^{\frac{7}{2}}}{7} + \frac{2 A c^{2} x^{\frac{9}{2}}}{9} + \frac{2 B a^{2} x^{\frac{3}{2}}}{3} + \frac{4 B a b x^{\frac{5}{2}}}{5} + \frac{4 B a c x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} x^{\frac{7}{2}}}{7} + \frac{4 B b c x^{\frac{9}{2}}}{9} + \frac{2 B c^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*A*a**2*sqrt(x) + 4*A*a*b*x**(3/2)/3 + 4*A*a*c*x**(5/2)/5 + 2*A*b**2*x**(5/2)/5 + 4*A*b*c*x**(7/2)/7 + 2*A*c**2*x**(9/2)/9 + 2*B*a**2*x**(3/2)/3 + 4*B*a*b*x**(5/2)/5 + 4*B*a*c*x**(7/2)/7 + 2*B*b**2*x**(7/2)/7 + 4*B*b*c*x**(9/2)/9 + 2*B*c**2*x**(11/2)/11","A",0
995,1,156,0,2.295222," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**(3/2),x)","- \frac{2 A a^{2}}{\sqrt{x}} + 4 A a b \sqrt{x} + \frac{4 A a c x^{\frac{3}{2}}}{3} + \frac{2 A b^{2} x^{\frac{3}{2}}}{3} + \frac{4 A b c x^{\frac{5}{2}}}{5} + \frac{2 A c^{2} x^{\frac{7}{2}}}{7} + 2 B a^{2} \sqrt{x} + \frac{4 B a b x^{\frac{3}{2}}}{3} + \frac{4 B a c x^{\frac{5}{2}}}{5} + \frac{2 B b^{2} x^{\frac{5}{2}}}{5} + \frac{4 B b c x^{\frac{7}{2}}}{7} + \frac{2 B c^{2} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**2/sqrt(x) + 4*A*a*b*sqrt(x) + 4*A*a*c*x**(3/2)/3 + 2*A*b**2*x**(3/2)/3 + 4*A*b*c*x**(5/2)/5 + 2*A*c**2*x**(7/2)/7 + 2*B*a**2*sqrt(x) + 4*B*a*b*x**(3/2)/3 + 4*B*a*c*x**(5/2)/5 + 2*B*b**2*x**(5/2)/5 + 4*B*b*c*x**(7/2)/7 + 2*B*c**2*x**(9/2)/9","A",0
996,1,153,0,2.885896," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**(5/2),x)","- \frac{2 A a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 A a b}{\sqrt{x}} + 4 A a c \sqrt{x} + 2 A b^{2} \sqrt{x} + \frac{4 A b c x^{\frac{3}{2}}}{3} + \frac{2 A c^{2} x^{\frac{5}{2}}}{5} - \frac{2 B a^{2}}{\sqrt{x}} + 4 B a b \sqrt{x} + \frac{4 B a c x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{3}{2}}}{3} + \frac{4 B b c x^{\frac{5}{2}}}{5} + \frac{2 B c^{2} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**2/(3*x**(3/2)) - 4*A*a*b/sqrt(x) + 4*A*a*c*sqrt(x) + 2*A*b**2*sqrt(x) + 4*A*b*c*x**(3/2)/3 + 2*A*c**2*x**(5/2)/5 - 2*B*a**2/sqrt(x) + 4*B*a*b*sqrt(x) + 4*B*a*c*x**(3/2)/3 + 2*B*b**2*x**(3/2)/3 + 4*B*b*c*x**(5/2)/5 + 2*B*c**2*x**(7/2)/7","A",0
997,1,151,0,3.939586," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**(7/2),x)","- \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a b}{3 x^{\frac{3}{2}}} - \frac{4 A a c}{\sqrt{x}} - \frac{2 A b^{2}}{\sqrt{x}} + 4 A b c \sqrt{x} + \frac{2 A c^{2} x^{\frac{3}{2}}}{3} - \frac{2 B a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 B a b}{\sqrt{x}} + 4 B a c \sqrt{x} + 2 B b^{2} \sqrt{x} + \frac{4 B b c x^{\frac{3}{2}}}{3} + \frac{2 B c^{2} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**2/(5*x**(5/2)) - 4*A*a*b/(3*x**(3/2)) - 4*A*a*c/sqrt(x) - 2*A*b**2/sqrt(x) + 4*A*b*c*sqrt(x) + 2*A*c**2*x**(3/2)/3 - 2*B*a**2/(3*x**(3/2)) - 4*B*a*b/sqrt(x) + 4*B*a*c*sqrt(x) + 2*B*b**2*sqrt(x) + 4*B*b*c*x**(3/2)/3 + 2*B*c**2*x**(5/2)/5","A",0
998,1,153,0,5.880710," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/x**(9/2),x)","- \frac{2 A a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 A a b}{5 x^{\frac{5}{2}}} - \frac{4 A a c}{3 x^{\frac{3}{2}}} - \frac{2 A b^{2}}{3 x^{\frac{3}{2}}} - \frac{4 A b c}{\sqrt{x}} + 2 A c^{2} \sqrt{x} - \frac{2 B a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 B a b}{3 x^{\frac{3}{2}}} - \frac{4 B a c}{\sqrt{x}} - \frac{2 B b^{2}}{\sqrt{x}} + 4 B b c \sqrt{x} + \frac{2 B c^{2} x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a**2/(7*x**(7/2)) - 4*A*a*b/(5*x**(5/2)) - 4*A*a*c/(3*x**(3/2)) - 2*A*b**2/(3*x**(3/2)) - 4*A*b*c/sqrt(x) + 2*A*c**2*sqrt(x) - 2*B*a**2/(5*x**(5/2)) - 4*B*a*b/(3*x**(3/2)) - 4*B*a*c/sqrt(x) - 2*B*b**2/sqrt(x) + 4*B*b*c*sqrt(x) + 2*B*c**2*x**(3/2)/3","A",0
999,1,294,0,36.590962," ","integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x+a)**3,x)","\frac{2 A a^{3} x^{\frac{9}{2}}}{9} + \frac{6 A a^{2} b x^{\frac{11}{2}}}{11} + \frac{6 A a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 A a b^{2} x^{\frac{13}{2}}}{13} + \frac{4 A a b c x^{\frac{15}{2}}}{5} + \frac{6 A a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A b^{3} x^{\frac{15}{2}}}{15} + \frac{6 A b^{2} c x^{\frac{17}{2}}}{17} + \frac{6 A b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 A c^{3} x^{\frac{21}{2}}}{21} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{6 B a^{2} b x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} c x^{\frac{15}{2}}}{5} + \frac{2 B a b^{2} x^{\frac{15}{2}}}{5} + \frac{12 B a b c x^{\frac{17}{2}}}{17} + \frac{6 B a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B b^{3} x^{\frac{17}{2}}}{17} + \frac{6 B b^{2} c x^{\frac{19}{2}}}{19} + \frac{2 B b c^{2} x^{\frac{21}{2}}}{7} + \frac{2 B c^{3} x^{\frac{23}{2}}}{23}"," ",0,"2*A*a**3*x**(9/2)/9 + 6*A*a**2*b*x**(11/2)/11 + 6*A*a**2*c*x**(13/2)/13 + 6*A*a*b**2*x**(13/2)/13 + 4*A*a*b*c*x**(15/2)/5 + 6*A*a*c**2*x**(17/2)/17 + 2*A*b**3*x**(15/2)/15 + 6*A*b**2*c*x**(17/2)/17 + 6*A*b*c**2*x**(19/2)/19 + 2*A*c**3*x**(21/2)/21 + 2*B*a**3*x**(11/2)/11 + 6*B*a**2*b*x**(13/2)/13 + 2*B*a**2*c*x**(15/2)/5 + 2*B*a*b**2*x**(15/2)/5 + 12*B*a*b*c*x**(17/2)/17 + 6*B*a*c**2*x**(19/2)/19 + 2*B*b**3*x**(17/2)/17 + 6*B*b**2*c*x**(19/2)/19 + 2*B*b*c**2*x**(21/2)/7 + 2*B*c**3*x**(23/2)/23","A",0
1000,1,294,0,17.201093," ","integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x+a)**3,x)","\frac{2 A a^{3} x^{\frac{7}{2}}}{7} + \frac{2 A a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 A a^{2} c x^{\frac{11}{2}}}{11} + \frac{6 A a b^{2} x^{\frac{11}{2}}}{11} + \frac{12 A a b c x^{\frac{13}{2}}}{13} + \frac{2 A a c^{2} x^{\frac{15}{2}}}{5} + \frac{2 A b^{3} x^{\frac{13}{2}}}{13} + \frac{2 A b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 A b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A c^{3} x^{\frac{19}{2}}}{19} + \frac{2 B a^{3} x^{\frac{9}{2}}}{9} + \frac{6 B a^{2} b x^{\frac{11}{2}}}{11} + \frac{6 B a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 B a b^{2} x^{\frac{13}{2}}}{13} + \frac{4 B a b c x^{\frac{15}{2}}}{5} + \frac{6 B a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B b^{3} x^{\frac{15}{2}}}{15} + \frac{6 B b^{2} c x^{\frac{17}{2}}}{17} + \frac{6 B b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B c^{3} x^{\frac{21}{2}}}{21}"," ",0,"2*A*a**3*x**(7/2)/7 + 2*A*a**2*b*x**(9/2)/3 + 6*A*a**2*c*x**(11/2)/11 + 6*A*a*b**2*x**(11/2)/11 + 12*A*a*b*c*x**(13/2)/13 + 2*A*a*c**2*x**(15/2)/5 + 2*A*b**3*x**(13/2)/13 + 2*A*b**2*c*x**(15/2)/5 + 6*A*b*c**2*x**(17/2)/17 + 2*A*c**3*x**(19/2)/19 + 2*B*a**3*x**(9/2)/9 + 6*B*a**2*b*x**(11/2)/11 + 6*B*a**2*c*x**(13/2)/13 + 6*B*a*b**2*x**(13/2)/13 + 4*B*a*b*c*x**(15/2)/5 + 6*B*a*c**2*x**(17/2)/17 + 2*B*b**3*x**(15/2)/15 + 6*B*b**2*c*x**(17/2)/17 + 6*B*b*c**2*x**(19/2)/19 + 2*B*c**3*x**(21/2)/21","A",0
1001,1,294,0,9.585827," ","integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x+a)**3,x)","\frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{6 A a^{2} b x^{\frac{7}{2}}}{7} + \frac{2 A a^{2} c x^{\frac{9}{2}}}{3} + \frac{2 A a b^{2} x^{\frac{9}{2}}}{3} + \frac{12 A a b c x^{\frac{11}{2}}}{11} + \frac{6 A a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 A b^{3} x^{\frac{11}{2}}}{11} + \frac{6 A b^{2} c x^{\frac{13}{2}}}{13} + \frac{2 A b c^{2} x^{\frac{15}{2}}}{5} + \frac{2 A c^{3} x^{\frac{17}{2}}}{17} + \frac{2 B a^{3} x^{\frac{7}{2}}}{7} + \frac{2 B a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 B a^{2} c x^{\frac{11}{2}}}{11} + \frac{6 B a b^{2} x^{\frac{11}{2}}}{11} + \frac{12 B a b c x^{\frac{13}{2}}}{13} + \frac{2 B a c^{2} x^{\frac{15}{2}}}{5} + \frac{2 B b^{3} x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 B b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B c^{3} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**3*x**(5/2)/5 + 6*A*a**2*b*x**(7/2)/7 + 2*A*a**2*c*x**(9/2)/3 + 2*A*a*b**2*x**(9/2)/3 + 12*A*a*b*c*x**(11/2)/11 + 6*A*a*c**2*x**(13/2)/13 + 2*A*b**3*x**(11/2)/11 + 6*A*b**2*c*x**(13/2)/13 + 2*A*b*c**2*x**(15/2)/5 + 2*A*c**3*x**(17/2)/17 + 2*B*a**3*x**(7/2)/7 + 2*B*a**2*b*x**(9/2)/3 + 6*B*a**2*c*x**(11/2)/11 + 6*B*a*b**2*x**(11/2)/11 + 12*B*a*b*c*x**(13/2)/13 + 2*B*a*c**2*x**(15/2)/5 + 2*B*b**3*x**(13/2)/13 + 2*B*b**2*c*x**(15/2)/5 + 6*B*b*c**2*x**(17/2)/17 + 2*B*c**3*x**(19/2)/19","A",0
1002,1,216,0,9.167872," ","integrate((B*x+A)*(c*x**2+b*x+a)**3*x**(1/2),x)","\frac{2 A a^{3} x^{\frac{3}{2}}}{3} + \frac{2 B c^{3} x^{\frac{17}{2}}}{17} + \frac{2 x^{\frac{15}{2}} \left(A c^{3} + 3 B b c^{2}\right)}{15} + \frac{2 x^{\frac{13}{2}} \left(3 A b c^{2} + 3 B a c^{2} + 3 B b^{2} c\right)}{13} + \frac{2 x^{\frac{11}{2}} \left(3 A a c^{2} + 3 A b^{2} c + 6 B a b c + B b^{3}\right)}{11} + \frac{2 x^{\frac{9}{2}} \left(6 A a b c + A b^{3} + 3 B a^{2} c + 3 B a b^{2}\right)}{9} + \frac{2 x^{\frac{7}{2}} \left(3 A a^{2} c + 3 A a b^{2} + 3 B a^{2} b\right)}{7} + \frac{2 x^{\frac{5}{2}} \left(3 A a^{2} b + B a^{3}\right)}{5}"," ",0,"2*A*a**3*x**(3/2)/3 + 2*B*c**3*x**(17/2)/17 + 2*x**(15/2)*(A*c**3 + 3*B*b*c**2)/15 + 2*x**(13/2)*(3*A*b*c**2 + 3*B*a*c**2 + 3*B*b**2*c)/13 + 2*x**(11/2)*(3*A*a*c**2 + 3*A*b**2*c + 6*B*a*b*c + B*b**3)/11 + 2*x**(9/2)*(6*A*a*b*c + A*b**3 + 3*B*a**2*c + 3*B*a*b**2)/9 + 2*x**(7/2)*(3*A*a**2*c + 3*A*a*b**2 + 3*B*a**2*b)/7 + 2*x**(5/2)*(3*A*a**2*b + B*a**3)/5","A",0
1003,1,291,0,5.896161," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**(1/2),x)","2 A a^{3} \sqrt{x} + 2 A a^{2} b x^{\frac{3}{2}} + \frac{6 A a^{2} c x^{\frac{5}{2}}}{5} + \frac{6 A a b^{2} x^{\frac{5}{2}}}{5} + \frac{12 A a b c x^{\frac{7}{2}}}{7} + \frac{2 A a c^{2} x^{\frac{9}{2}}}{3} + \frac{2 A b^{3} x^{\frac{7}{2}}}{7} + \frac{2 A b^{2} c x^{\frac{9}{2}}}{3} + \frac{6 A b c^{2} x^{\frac{11}{2}}}{11} + \frac{2 A c^{3} x^{\frac{13}{2}}}{13} + \frac{2 B a^{3} x^{\frac{3}{2}}}{3} + \frac{6 B a^{2} b x^{\frac{5}{2}}}{5} + \frac{6 B a^{2} c x^{\frac{7}{2}}}{7} + \frac{6 B a b^{2} x^{\frac{7}{2}}}{7} + \frac{4 B a b c x^{\frac{9}{2}}}{3} + \frac{6 B a c^{2} x^{\frac{11}{2}}}{11} + \frac{2 B b^{3} x^{\frac{9}{2}}}{9} + \frac{6 B b^{2} c x^{\frac{11}{2}}}{11} + \frac{6 B b c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B c^{3} x^{\frac{15}{2}}}{15}"," ",0,"2*A*a**3*sqrt(x) + 2*A*a**2*b*x**(3/2) + 6*A*a**2*c*x**(5/2)/5 + 6*A*a*b**2*x**(5/2)/5 + 12*A*a*b*c*x**(7/2)/7 + 2*A*a*c**2*x**(9/2)/3 + 2*A*b**3*x**(7/2)/7 + 2*A*b**2*c*x**(9/2)/3 + 6*A*b*c**2*x**(11/2)/11 + 2*A*c**3*x**(13/2)/13 + 2*B*a**3*x**(3/2)/3 + 6*B*a**2*b*x**(5/2)/5 + 6*B*a**2*c*x**(7/2)/7 + 6*B*a*b**2*x**(7/2)/7 + 4*B*a*b*c*x**(9/2)/3 + 6*B*a*c**2*x**(11/2)/11 + 2*B*b**3*x**(9/2)/9 + 6*B*b**2*c*x**(11/2)/11 + 6*B*b*c**2*x**(13/2)/13 + 2*B*c**3*x**(15/2)/15","A",0
1004,1,284,0,5.810962," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**(3/2),x)","- \frac{2 A a^{3}}{\sqrt{x}} + 6 A a^{2} b \sqrt{x} + 2 A a^{2} c x^{\frac{3}{2}} + 2 A a b^{2} x^{\frac{3}{2}} + \frac{12 A a b c x^{\frac{5}{2}}}{5} + \frac{6 A a c^{2} x^{\frac{7}{2}}}{7} + \frac{2 A b^{3} x^{\frac{5}{2}}}{5} + \frac{6 A b^{2} c x^{\frac{7}{2}}}{7} + \frac{2 A b c^{2} x^{\frac{9}{2}}}{3} + \frac{2 A c^{3} x^{\frac{11}{2}}}{11} + 2 B a^{3} \sqrt{x} + 2 B a^{2} b x^{\frac{3}{2}} + \frac{6 B a^{2} c x^{\frac{5}{2}}}{5} + \frac{6 B a b^{2} x^{\frac{5}{2}}}{5} + \frac{12 B a b c x^{\frac{7}{2}}}{7} + \frac{2 B a c^{2} x^{\frac{9}{2}}}{3} + \frac{2 B b^{3} x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} c x^{\frac{9}{2}}}{3} + \frac{6 B b c^{2} x^{\frac{11}{2}}}{11} + \frac{2 B c^{3} x^{\frac{13}{2}}}{13}"," ",0,"-2*A*a**3/sqrt(x) + 6*A*a**2*b*sqrt(x) + 2*A*a**2*c*x**(3/2) + 2*A*a*b**2*x**(3/2) + 12*A*a*b*c*x**(5/2)/5 + 6*A*a*c**2*x**(7/2)/7 + 2*A*b**3*x**(5/2)/5 + 6*A*b**2*c*x**(7/2)/7 + 2*A*b*c**2*x**(9/2)/3 + 2*A*c**3*x**(11/2)/11 + 2*B*a**3*sqrt(x) + 2*B*a**2*b*x**(3/2) + 6*B*a**2*c*x**(5/2)/5 + 6*B*a*b**2*x**(5/2)/5 + 12*B*a*b*c*x**(7/2)/7 + 2*B*a*c**2*x**(9/2)/3 + 2*B*b**3*x**(7/2)/7 + 2*B*b**2*c*x**(9/2)/3 + 6*B*b*c**2*x**(11/2)/11 + 2*B*c**3*x**(13/2)/13","A",0
1005,1,280,0,7.051292," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**(5/2),x)","- \frac{2 A a^{3}}{3 x^{\frac{3}{2}}} - \frac{6 A a^{2} b}{\sqrt{x}} + 6 A a^{2} c \sqrt{x} + 6 A a b^{2} \sqrt{x} + 4 A a b c x^{\frac{3}{2}} + \frac{6 A a c^{2} x^{\frac{5}{2}}}{5} + \frac{2 A b^{3} x^{\frac{3}{2}}}{3} + \frac{6 A b^{2} c x^{\frac{5}{2}}}{5} + \frac{6 A b c^{2} x^{\frac{7}{2}}}{7} + \frac{2 A c^{3} x^{\frac{9}{2}}}{9} - \frac{2 B a^{3}}{\sqrt{x}} + 6 B a^{2} b \sqrt{x} + 2 B a^{2} c x^{\frac{3}{2}} + 2 B a b^{2} x^{\frac{3}{2}} + \frac{12 B a b c x^{\frac{5}{2}}}{5} + \frac{6 B a c^{2} x^{\frac{7}{2}}}{7} + \frac{2 B b^{3} x^{\frac{5}{2}}}{5} + \frac{6 B b^{2} c x^{\frac{7}{2}}}{7} + \frac{2 B b c^{2} x^{\frac{9}{2}}}{3} + \frac{2 B c^{3} x^{\frac{11}{2}}}{11}"," ",0,"-2*A*a**3/(3*x**(3/2)) - 6*A*a**2*b/sqrt(x) + 6*A*a**2*c*sqrt(x) + 6*A*a*b**2*sqrt(x) + 4*A*a*b*c*x**(3/2) + 6*A*a*c**2*x**(5/2)/5 + 2*A*b**3*x**(3/2)/3 + 6*A*b**2*c*x**(5/2)/5 + 6*A*b*c**2*x**(7/2)/7 + 2*A*c**3*x**(9/2)/9 - 2*B*a**3/sqrt(x) + 6*B*a**2*b*sqrt(x) + 2*B*a**2*c*x**(3/2) + 2*B*a*b**2*x**(3/2) + 12*B*a*b*c*x**(5/2)/5 + 6*B*a*c**2*x**(7/2)/7 + 2*B*b**3*x**(5/2)/5 + 6*B*b**2*c*x**(7/2)/7 + 2*B*b*c**2*x**(9/2)/3 + 2*B*c**3*x**(11/2)/11","A",0
1006,1,275,0,10.669794," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**(7/2),x)","- \frac{2 A a^{3}}{5 x^{\frac{5}{2}}} - \frac{2 A a^{2} b}{x^{\frac{3}{2}}} - \frac{6 A a^{2} c}{\sqrt{x}} - \frac{6 A a b^{2}}{\sqrt{x}} + 12 A a b c \sqrt{x} + 2 A a c^{2} x^{\frac{3}{2}} + 2 A b^{3} \sqrt{x} + 2 A b^{2} c x^{\frac{3}{2}} + \frac{6 A b c^{2} x^{\frac{5}{2}}}{5} + \frac{2 A c^{3} x^{\frac{7}{2}}}{7} - \frac{2 B a^{3}}{3 x^{\frac{3}{2}}} - \frac{6 B a^{2} b}{\sqrt{x}} + 6 B a^{2} c \sqrt{x} + 6 B a b^{2} \sqrt{x} + 4 B a b c x^{\frac{3}{2}} + \frac{6 B a c^{2} x^{\frac{5}{2}}}{5} + \frac{2 B b^{3} x^{\frac{3}{2}}}{3} + \frac{6 B b^{2} c x^{\frac{5}{2}}}{5} + \frac{6 B b c^{2} x^{\frac{7}{2}}}{7} + \frac{2 B c^{3} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**3/(5*x**(5/2)) - 2*A*a**2*b/x**(3/2) - 6*A*a**2*c/sqrt(x) - 6*A*a*b**2/sqrt(x) + 12*A*a*b*c*sqrt(x) + 2*A*a*c**2*x**(3/2) + 2*A*b**3*sqrt(x) + 2*A*b**2*c*x**(3/2) + 6*A*b*c**2*x**(5/2)/5 + 2*A*c**3*x**(7/2)/7 - 2*B*a**3/(3*x**(3/2)) - 6*B*a**2*b/sqrt(x) + 6*B*a**2*c*sqrt(x) + 6*B*a*b**2*sqrt(x) + 4*B*a*b*c*x**(3/2) + 6*B*a*c**2*x**(5/2)/5 + 2*B*b**3*x**(3/2)/3 + 6*B*b**2*c*x**(5/2)/5 + 6*B*b*c**2*x**(7/2)/7 + 2*B*c**3*x**(9/2)/9","A",0
1007,1,270,0,12.898745," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**(9/2),x)","- \frac{2 A a^{3}}{7 x^{\frac{7}{2}}} - \frac{6 A a^{2} b}{5 x^{\frac{5}{2}}} - \frac{2 A a^{2} c}{x^{\frac{3}{2}}} - \frac{2 A a b^{2}}{x^{\frac{3}{2}}} - \frac{12 A a b c}{\sqrt{x}} + 6 A a c^{2} \sqrt{x} - \frac{2 A b^{3}}{\sqrt{x}} + 6 A b^{2} c \sqrt{x} + 2 A b c^{2} x^{\frac{3}{2}} + \frac{2 A c^{3} x^{\frac{5}{2}}}{5} - \frac{2 B a^{3}}{5 x^{\frac{5}{2}}} - \frac{2 B a^{2} b}{x^{\frac{3}{2}}} - \frac{6 B a^{2} c}{\sqrt{x}} - \frac{6 B a b^{2}}{\sqrt{x}} + 12 B a b c \sqrt{x} + 2 B a c^{2} x^{\frac{3}{2}} + 2 B b^{3} \sqrt{x} + 2 B b^{2} c x^{\frac{3}{2}} + \frac{6 B b c^{2} x^{\frac{5}{2}}}{5} + \frac{2 B c^{3} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**3/(7*x**(7/2)) - 6*A*a**2*b/(5*x**(5/2)) - 2*A*a**2*c/x**(3/2) - 2*A*a*b**2/x**(3/2) - 12*A*a*b*c/sqrt(x) + 6*A*a*c**2*sqrt(x) - 2*A*b**3/sqrt(x) + 6*A*b**2*c*sqrt(x) + 2*A*b*c**2*x**(3/2) + 2*A*c**3*x**(5/2)/5 - 2*B*a**3/(5*x**(5/2)) - 2*B*a**2*b/x**(3/2) - 6*B*a**2*c/sqrt(x) - 6*B*a*b**2/sqrt(x) + 12*B*a*b*c*sqrt(x) + 2*B*a*c**2*x**(3/2) + 2*B*b**3*sqrt(x) + 2*B*b**2*c*x**(3/2) + 6*B*b*c**2*x**(5/2)/5 + 2*B*c**3*x**(7/2)/7","A",0
1008,1,275,0,15.376231," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/x**(11/2),x)","- \frac{2 A a^{3}}{9 x^{\frac{9}{2}}} - \frac{6 A a^{2} b}{7 x^{\frac{7}{2}}} - \frac{6 A a^{2} c}{5 x^{\frac{5}{2}}} - \frac{6 A a b^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a b c}{x^{\frac{3}{2}}} - \frac{6 A a c^{2}}{\sqrt{x}} - \frac{2 A b^{3}}{3 x^{\frac{3}{2}}} - \frac{6 A b^{2} c}{\sqrt{x}} + 6 A b c^{2} \sqrt{x} + \frac{2 A c^{3} x^{\frac{3}{2}}}{3} - \frac{2 B a^{3}}{7 x^{\frac{7}{2}}} - \frac{6 B a^{2} b}{5 x^{\frac{5}{2}}} - \frac{2 B a^{2} c}{x^{\frac{3}{2}}} - \frac{2 B a b^{2}}{x^{\frac{3}{2}}} - \frac{12 B a b c}{\sqrt{x}} + 6 B a c^{2} \sqrt{x} - \frac{2 B b^{3}}{\sqrt{x}} + 6 B b^{2} c \sqrt{x} + 2 B b c^{2} x^{\frac{3}{2}} + \frac{2 B c^{3} x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a**3/(9*x**(9/2)) - 6*A*a**2*b/(7*x**(7/2)) - 6*A*a**2*c/(5*x**(5/2)) - 6*A*a*b**2/(5*x**(5/2)) - 4*A*a*b*c/x**(3/2) - 6*A*a*c**2/sqrt(x) - 2*A*b**3/(3*x**(3/2)) - 6*A*b**2*c/sqrt(x) + 6*A*b*c**2*sqrt(x) + 2*A*c**3*x**(3/2)/3 - 2*B*a**3/(7*x**(7/2)) - 6*B*a**2*b/(5*x**(5/2)) - 2*B*a**2*c/x**(3/2) - 2*B*a*b**2/x**(3/2) - 12*B*a*b*c/sqrt(x) + 6*B*a*c**2*sqrt(x) - 2*B*b**3/sqrt(x) + 6*B*b**2*c*sqrt(x) + 2*B*b*c**2*x**(3/2) + 2*B*c**3*x**(5/2)/5","A",0
1009,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1010,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1011,1,14158,0,22.133506," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x+a),x)","\begin{cases} - \frac{i A \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} + \frac{i A \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} + \frac{i B \sqrt{b} \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{2} \sqrt{\frac{1}{c}}} - \frac{i B \sqrt{b} \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{c^{2} \sqrt{\frac{1}{c}}} + \frac{2 B \sqrt{x}}{c} & \text{for}\: a = 0 \\- \frac{8 i A \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{1}{c}}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} + \frac{2 \sqrt{2} A b c \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} - \frac{2 \sqrt{2} A b c \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} + \frac{4 \sqrt{2} A c^{2} x \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} - \frac{4 \sqrt{2} A c^{2} x \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} + \frac{12 i B b^{\frac{3}{2}} c \sqrt{x} \sqrt{\frac{1}{c}}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} + \frac{16 i B \sqrt{b} c^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{c}}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} - \frac{3 \sqrt{2} B b^{2} \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} + \frac{3 \sqrt{2} B b^{2} \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} - \frac{6 \sqrt{2} B b c x \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} + \frac{6 \sqrt{2} B b c x \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{4 i b^{\frac{3}{2}} c^{2} \sqrt{\frac{1}{c}} + 8 i \sqrt{b} c^{3} x \sqrt{\frac{1}{c}}} & \text{for}\: a = \frac{b^{2}}{4 c} \\\frac{i A \sqrt{a} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} - \frac{i A \sqrt{a} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} + \frac{2 A \sqrt{x}}{b} - \frac{i B a^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{3} \sqrt{\frac{1}{b}}} + \frac{i B a^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{3} \sqrt{\frac{1}{b}}} - \frac{2 B a \sqrt{x}}{b^{2}} + \frac{2 B x^{\frac{3}{2}}}{3 b} & \text{for}\: c = 0 \\\frac{2 \sqrt{2} A a^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{2 \sqrt{2} A a^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{2 \sqrt{2} A a^{2} c^{3} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{2 \sqrt{2} A a^{2} c^{3} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A a b^{2} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A a b^{2} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{4 \sqrt{2} A a b^{2} c^{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{4 \sqrt{2} A a b^{2} c^{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A a b c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A a b c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{2 \sqrt{2} A a b c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{2 \sqrt{2} A a b c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A b^{4} c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A b^{4} c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A b^{3} c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A b^{3} c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B a^{2} b c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B a^{2} b c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{5 \sqrt{2} B a^{2} b c^{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{5 \sqrt{2} B a^{2} b c^{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{8 B a^{2} c^{3} \sqrt{x} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B a^{2} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B a^{2} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B a^{2} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B a^{2} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{5 \sqrt{2} B a b^{3} c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{5 \sqrt{2} B a b^{3} c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{10 B a b^{2} c^{2} \sqrt{x} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{3 \sqrt{2} B a b^{2} c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{3 \sqrt{2} B a b^{2} c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{6 B a b c^{2} \sqrt{x} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B b^{5} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B b^{5} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{2 B b^{4} c \sqrt{x} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B b^{4} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B b^{4} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{2 B b^{3} c \sqrt{x} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{4 a^{2} c^{4} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 5 a b^{2} c^{3} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - 3 a b c^{3} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{4} c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} + b^{3} c^{2} \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*A*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)) + I*A*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)) + I*B*sqrt(b)*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**2*sqrt(1/c)) - I*B*sqrt(b)*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(c**2*sqrt(1/c)) + 2*B*sqrt(x)/c, Eq(a, 0)), (-8*I*A*sqrt(b)*c**2*sqrt(x)*sqrt(1/c)/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) + 2*sqrt(2)*A*b*c*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) - 2*sqrt(2)*A*b*c*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) + 4*sqrt(2)*A*c**2*x*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) - 4*sqrt(2)*A*c**2*x*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) + 12*I*B*b**(3/2)*c*sqrt(x)*sqrt(1/c)/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) + 16*I*B*sqrt(b)*c**2*x**(3/2)*sqrt(1/c)/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) - 3*sqrt(2)*B*b**2*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) + 3*sqrt(2)*B*b**2*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) - 6*sqrt(2)*B*b*c*x*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)) + 6*sqrt(2)*B*b*c*x*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(4*I*b**(3/2)*c**2*sqrt(1/c) + 8*I*sqrt(b)*c**3*x*sqrt(1/c)), Eq(a, b**2/(4*c))), (I*A*sqrt(a)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) - I*A*sqrt(a)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) + 2*A*sqrt(x)/b - I*B*a**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**3*sqrt(1/b)) + I*B*a**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**3*sqrt(1/b)) - 2*B*a*sqrt(x)/b**2 + 2*B*x**(3/2)/(3*b), Eq(c, 0)), (2*sqrt(2)*A*a**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 2*sqrt(2)*A*a**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 2*sqrt(2)*A*a**2*c**3*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 2*sqrt(2)*A*a**2*c**3*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*a*b**2*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*a*b**2*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 4*sqrt(2)*A*a*b**2*c**2*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 4*sqrt(2)*A*a*b**2*c**2*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*a*b*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*a*b*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 2*sqrt(2)*A*a*b*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 2*sqrt(2)*A*a*b*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*b**4*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*b**4*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*b**3*c*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*b**3*c*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*a**2*b*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*a**2*b*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 5*sqrt(2)*B*a**2*b*c**2*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 5*sqrt(2)*B*a**2*b*c**2*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 8*B*a**2*c**3*sqrt(x)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*a**2*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*a**2*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*a**2*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*a**2*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 5*sqrt(2)*B*a*b**3*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 5*sqrt(2)*B*a*b**3*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 10*B*a*b**2*c**2*sqrt(x)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 3*sqrt(2)*B*a*b**2*c*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 3*sqrt(2)*B*a*b**2*c*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 6*B*a*b*c**2*sqrt(x)*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*b**5*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*b**5*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 2*B*b**4*c*sqrt(x)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*b**4*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*b**4*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 2*B*b**3*c*sqrt(x)*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/(4*a**2*c**4*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 5*a*b**2*c**3*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - 3*a*b*c**3*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**4*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) + b**3*c**2*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)), True))","B",0
1012,1,4663,0,24.863690," ","integrate((B*x+A)/(c*x**2+b*x+a)/x**(1/2),x)","\begin{cases} - \frac{2 A}{b \sqrt{x}} + \frac{i A \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{i A \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{b^{\frac{3}{2}} \sqrt{\frac{1}{c}}} - \frac{i B \log{\left(- i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} + \frac{i B \log{\left(i \sqrt{b} \sqrt{\frac{1}{c}} + \sqrt{x} \right)}}{\sqrt{b} c \sqrt{\frac{1}{c}}} & \text{for}\: a = 0 \\\frac{8 i A \sqrt{b} c^{2} \sqrt{x} \sqrt{\frac{1}{c}}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} + \frac{2 \sqrt{2} A b c \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} - \frac{2 \sqrt{2} A b c \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} + \frac{4 \sqrt{2} A c^{2} x \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} - \frac{4 \sqrt{2} A c^{2} x \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} - \frac{4 i B b^{\frac{3}{2}} c \sqrt{x} \sqrt{\frac{1}{c}}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} + \frac{\sqrt{2} B b^{2} \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} - \frac{\sqrt{2} B b^{2} \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} + \frac{2 \sqrt{2} B b c x \log{\left(- \frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} - \frac{2 \sqrt{2} B b c x \log{\left(\frac{\sqrt{2} i \sqrt{b} \sqrt{\frac{1}{c}}}{2} + \sqrt{x} \right)}}{2 i b^{\frac{5}{2}} c \sqrt{\frac{1}{c}} + 4 i b^{\frac{3}{2}} c^{2} x \sqrt{\frac{1}{c}}} & \text{for}\: a = \frac{b^{2}}{4 c} \\- \frac{i A \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{\sqrt{a} b \sqrt{\frac{1}{b}}} + \frac{i A \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{\sqrt{a} b \sqrt{\frac{1}{b}}} + \frac{i B \sqrt{a} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} - \frac{i B \sqrt{a} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} + \frac{2 B \sqrt{x}}{b} & \text{for}\: c = 0 \\- \frac{\sqrt{2} A b c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A b c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A b c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A b c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} A c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} A c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{2 \sqrt{2} B a c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{2 \sqrt{2} B a c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{2 \sqrt{2} B a c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{2 \sqrt{2} B a c \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B b^{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B b^{2} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} - \frac{\sqrt{2} B b \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} - \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} + \frac{\sqrt{2} B b \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} \log{\left(\sqrt{x} + \frac{\sqrt{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}}}{2} \right)}}{4 a c^{2} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b^{2} c \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}} - b c \sqrt{- 4 a c + b^{2}} \sqrt{- \frac{b}{c} - \frac{\sqrt{- 4 a c + b^{2}}}{c}} \sqrt{- \frac{b}{c} + \frac{\sqrt{- 4 a c + b^{2}}}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A/(b*sqrt(x)) + I*A*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(3/2)*sqrt(1/c)) - I*A*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(b**(3/2)*sqrt(1/c)) - I*B*log(-I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)) + I*B*log(I*sqrt(b)*sqrt(1/c) + sqrt(x))/(sqrt(b)*c*sqrt(1/c)), Eq(a, 0)), (8*I*A*sqrt(b)*c**2*sqrt(x)*sqrt(1/c)/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) + 2*sqrt(2)*A*b*c*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) - 2*sqrt(2)*A*b*c*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) + 4*sqrt(2)*A*c**2*x*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) - 4*sqrt(2)*A*c**2*x*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) - 4*I*B*b**(3/2)*c*sqrt(x)*sqrt(1/c)/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) + sqrt(2)*B*b**2*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) - sqrt(2)*B*b**2*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) + 2*sqrt(2)*B*b*c*x*log(-sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)) - 2*sqrt(2)*B*b*c*x*log(sqrt(2)*I*sqrt(b)*sqrt(1/c)/2 + sqrt(x))/(2*I*b**(5/2)*c*sqrt(1/c) + 4*I*b**(3/2)*c**2*x*sqrt(1/c)), Eq(a, b**2/(4*c))), (-I*A*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(sqrt(a)*b*sqrt(1/b)) + I*A*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(sqrt(a)*b*sqrt(1/b)) + I*B*sqrt(a)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) - I*B*sqrt(a)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) + 2*B*sqrt(x)/b, Eq(c, 0)), (-sqrt(2)*A*b*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*b*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*b*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*b*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*A*c*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*A*c*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 2*sqrt(2)*B*a*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 2*sqrt(2)*B*a*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + 2*sqrt(2)*B*a*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - 2*sqrt(2)*B*a*c*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*b**2*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*b**2*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) - sqrt(2)*B*b*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) - sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)) + sqrt(2)*B*b*sqrt(-4*a*c + b**2)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)*log(sqrt(x) + sqrt(2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)/2)/(4*a*c**2*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b**2*c*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c) - b*c*sqrt(-4*a*c + b**2)*sqrt(-b/c - sqrt(-4*a*c + b**2)/c)*sqrt(-b/c + sqrt(-4*a*c + b**2)/c)), True))","B",0
1013,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1014,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1015,-1,0,0,0.000000," ","integrate((B*x+A)/x**(7/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1016,-1,0,0,0.000000," ","integrate((B*x+A)/x**(9/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1017,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1018,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1019,-1,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1020,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**2/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1022,-1,0,0,0.000000," ","integrate((B*x+A)/x**(5/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1023,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x+A)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1024,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x+A)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x+A)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,-1,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1027,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate((B*x+A)/x**(3/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,0,0,0,0.000000," ","integrate((B*x+A)*x**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \sqrt{x} \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(x)*(A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
1030,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{\sqrt{x}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/sqrt(x), x)","F",0
1031,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**(3/2), x)","F",0
1032,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**(5/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**(5/2), x)","F",0
1033,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**(1/2)/x**(7/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + b x + c x^{2}}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + b*x + c*x**2)/x**(7/2), x)","F",0
1034,0,0,0,0.000000," ","integrate((2-5*x)*x**(7/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 2 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 5 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-2*x**(7/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(9/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1035,0,0,0,0.000000," ","integrate((2-5*x)*x**(5/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 2 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 5 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-2*x**(5/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(7/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1036,0,0,0,0.000000," ","integrate((2-5*x)*x**(3/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 2 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 5 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-2*x**(3/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(5/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1037,0,0,0,0.000000," ","integrate((2-5*x)*x**(1/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 2 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 5 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-2*sqrt(x)*sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(3/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1038,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(1/2)/x**(1/2),x)","- \int \left(- \frac{2 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{x}}\right)\, dx - \int 5 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-2*sqrt(3*x**2 + 5*x + 2)/sqrt(x), x) - Integral(5*sqrt(x)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1039,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(1/2)/x**(3/2),x)","- \int \left(- \frac{2 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{3}{2}}}\right)\, dx - \int \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{x}}\, dx"," ",0,"-Integral(-2*sqrt(3*x**2 + 5*x + 2)/x**(3/2), x) - Integral(5*sqrt(3*x**2 + 5*x + 2)/sqrt(x), x)","F",0
1040,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(1/2)/x**(5/2),x)","- \int \left(- \frac{2 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{5}{2}}}\right)\, dx - \int \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{3}{2}}}\, dx"," ",0,"-Integral(-2*sqrt(3*x**2 + 5*x + 2)/x**(5/2), x) - Integral(5*sqrt(3*x**2 + 5*x + 2)/x**(3/2), x)","F",0
1041,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(1/2)/x**(7/2),x)","- \int \left(- \frac{2 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{7}{2}}}\right)\, dx - \int \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{5}{2}}}\, dx"," ",0,"-Integral(-2*sqrt(3*x**2 + 5*x + 2)/x**(7/2), x) - Integral(5*sqrt(3*x**2 + 5*x + 2)/x**(5/2), x)","F",0
1042,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(1/2)/x**(9/2),x)","- \int \left(- \frac{2 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{9}{2}}}\right)\, dx - \int \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{7}{2}}}\, dx"," ",0,"-Integral(-2*sqrt(3*x**2 + 5*x + 2)/x**(9/2), x) - Integral(5*sqrt(3*x**2 + 5*x + 2)/x**(7/2), x)","F",0
1043,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(1/2)/x**(11/2),x)","- \int \left(- \frac{2 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{11}{2}}}\right)\, dx - \int \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{9}{2}}}\, dx"," ",0,"-Integral(-2*sqrt(3*x**2 + 5*x + 2)/x**(11/2), x) - Integral(5*sqrt(3*x**2 + 5*x + 2)/x**(9/2), x)","F",0
1044,0,0,0,0.000000," ","integrate((2-5*x)*x**(5/2)*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 4 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 19 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 15 x^{\frac{11}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-4*x**(5/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(19*x**(9/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(15*x**(11/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1045,0,0,0,0.000000," ","integrate((2-5*x)*x**(3/2)*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 4 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 19 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 15 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-4*x**(3/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(19*x**(7/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(15*x**(9/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1046,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)*x**(1/2),x)","- \int \left(- 4 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 19 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 15 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-4*sqrt(x)*sqrt(3*x**2 + 5*x + 2), x) - Integral(19*x**(5/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(15*x**(7/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1047,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(1/2),x)","- \int \left(- \frac{4 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{x}}\right)\, dx - \int 19 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 15 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-4*sqrt(3*x**2 + 5*x + 2)/sqrt(x), x) - Integral(19*x**(3/2)*sqrt(3*x**2 + 5*x + 2), x) - Integral(15*x**(5/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1048,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(3/2),x)","- \int \left(- \frac{4 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{3}{2}}}\right)\, dx - \int 19 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 15 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-4*sqrt(3*x**2 + 5*x + 2)/x**(3/2), x) - Integral(19*sqrt(x)*sqrt(3*x**2 + 5*x + 2), x) - Integral(15*x**(3/2)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1049,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(5/2),x)","- \int \left(- \frac{4 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{5}{2}}}\right)\, dx - \int \frac{19 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{x}}\, dx - \int 15 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-4*sqrt(3*x**2 + 5*x + 2)/x**(5/2), x) - Integral(19*sqrt(3*x**2 + 5*x + 2)/sqrt(x), x) - Integral(15*sqrt(x)*sqrt(3*x**2 + 5*x + 2), x)","F",0
1050,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(7/2),x)","- \int \left(- \frac{4 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{7}{2}}}\right)\, dx - \int \frac{19 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{3}{2}}}\, dx - \int \frac{15 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{x}}\, dx"," ",0,"-Integral(-4*sqrt(3*x**2 + 5*x + 2)/x**(7/2), x) - Integral(19*sqrt(3*x**2 + 5*x + 2)/x**(3/2), x) - Integral(15*sqrt(3*x**2 + 5*x + 2)/sqrt(x), x)","F",0
1051,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(9/2),x)","- \int \left(- \frac{4 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{9}{2}}}\right)\, dx - \int \frac{19 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{5}{2}}}\, dx - \int \frac{15 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{3}{2}}}\, dx"," ",0,"-Integral(-4*sqrt(3*x**2 + 5*x + 2)/x**(9/2), x) - Integral(19*sqrt(3*x**2 + 5*x + 2)/x**(5/2), x) - Integral(15*sqrt(3*x**2 + 5*x + 2)/x**(3/2), x)","F",0
1052,0,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(11/2),x)","- \int \left(- \frac{4 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{11}{2}}}\right)\, dx - \int \frac{19 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{7}{2}}}\, dx - \int \frac{15 \sqrt{3 x^{2} + 5 x + 2}}{x^{\frac{5}{2}}}\, dx"," ",0,"-Integral(-4*sqrt(3*x**2 + 5*x + 2)/x**(11/2), x) - Integral(19*sqrt(3*x**2 + 5*x + 2)/x**(7/2), x) - Integral(15*sqrt(3*x**2 + 5*x + 2)/x**(5/2), x)","F",0
1053,-1,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1054,-1,0,0,0.000000," ","integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1055,0,0,0,0.000000," ","integrate((B*x+A)/(e*x)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\sqrt{e x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
1056,0,0,0,0.000000," ","integrate((2-5*x)*x**(7/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2 x^{\frac{7}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{9}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*x**(7/2)/sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(9/2)/sqrt(3*x**2 + 5*x + 2), x)","F",0
1057,0,0,0,0.000000," ","integrate((2-5*x)*x**(5/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2 x^{\frac{5}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{7}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*x**(5/2)/sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(7/2)/sqrt(3*x**2 + 5*x + 2), x)","F",0
1058,0,0,0,0.000000," ","integrate((2-5*x)*x**(3/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2 x^{\frac{3}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{5}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*x**(3/2)/sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(5/2)/sqrt(3*x**2 + 5*x + 2), x)","F",0
1059,0,0,0,0.000000," ","integrate((2-5*x)*x**(1/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2 \sqrt{x}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{3}{2}}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*sqrt(x)/sqrt(3*x**2 + 5*x + 2), x) - Integral(5*x**(3/2)/sqrt(3*x**2 + 5*x + 2), x)","F",0
1060,0,0,0,0.000000," ","integrate((2-5*x)/x**(1/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2}{\sqrt{x} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 \sqrt{x}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2/(sqrt(x)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5*sqrt(x)/sqrt(3*x**2 + 5*x + 2), x)","F",0
1061,0,0,0,0.000000," ","integrate((2-5*x)/x**(3/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2}{x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5}{\sqrt{x} \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2/(x**(3/2)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5/(sqrt(x)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1062,0,0,0,0.000000," ","integrate((2-5*x)/x**(5/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2}{x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5}{x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2/(x**(5/2)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5/(x**(3/2)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1063,0,0,0,0.000000," ","integrate((2-5*x)/x**(7/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{2}{x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5}{x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2/(x**(7/2)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5/(x**(5/2)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1064,-1,0,0,0.000000," ","integrate((2-5*x)*x**(7/2)/(3*x**2+5*x+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,0,0,0,0.000000," ","integrate((2-5*x)*x**(5/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{2 x^{\frac{5}{2}}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{7}{2}}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*x**(5/2)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5*x**(7/2)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1066,0,0,0,0.000000," ","integrate((2-5*x)*x**(3/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{2 x^{\frac{3}{2}}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{5}{2}}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*x**(3/2)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5*x**(5/2)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1067,0,0,0,0.000000," ","integrate((2-5*x)*x**(1/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{2 \sqrt{x}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{3}{2}}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*sqrt(x)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5*x**(3/2)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1068,0,0,0,0.000000," ","integrate((2-5*x)/(3*x**2+5*x+2)**(3/2)/x**(1/2),x)","- \int \frac{5 \sqrt{x}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{2}{3 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(5*sqrt(x)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-2/(3*x**(5/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(3/2)*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(x)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1069,0,0,0,0.000000," ","integrate((2-5*x)/x**(3/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{5}{3 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{2}{3 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(5/(3*x**(5/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(3/2)*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(x)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-2/(3*x**(7/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(5/2)*sqrt(3*x**2 + 5*x + 2) + 2*x**(3/2)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1070,0,0,0,0.000000," ","integrate((2-5*x)/x**(5/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{5}{3 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{2}{3 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(5/(3*x**(7/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(5/2)*sqrt(3*x**2 + 5*x + 2) + 2*x**(3/2)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-2/(3*x**(9/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(7/2)*sqrt(3*x**2 + 5*x + 2) + 2*x**(5/2)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1071,0,0,0,0.000000," ","integrate((2-5*x)/x**(7/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{5}{3 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{2}{3 x^{\frac{11}{2}} \sqrt{3 x^{2} + 5 x + 2} + 5 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2} + 2 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(5/(3*x**(9/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(7/2)*sqrt(3*x**2 + 5*x + 2) + 2*x**(5/2)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-2/(3*x**(11/2)*sqrt(3*x**2 + 5*x + 2) + 5*x**(9/2)*sqrt(3*x**2 + 5*x + 2) + 2*x**(7/2)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1072,-1,0,0,0.000000," ","integrate((2-5*x)*x**(13/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1073,-1,0,0,0.000000," ","integrate((2-5*x)*x**(11/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1074,-1,0,0,0.000000," ","integrate((2-5*x)*x**(9/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1075,-1,0,0,0.000000," ","integrate((2-5*x)*x**(7/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1076,-1,0,0,0.000000," ","integrate((2-5*x)*x**(5/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1077,-1,0,0,0.000000," ","integrate((2-5*x)*x**(3/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1078,0,0,0,0.000000," ","integrate((2-5*x)*x**(1/2)/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{2 \sqrt{x}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{5 x^{\frac{3}{2}}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-2*sqrt(x)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(5*x**(3/2)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1079,0,0,0,0.000000," ","integrate((2-5*x)/(3*x**2+5*x+2)**(5/2)/x**(1/2),x)","- \int \frac{5 \sqrt{x}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{2}{9 x^{\frac{9}{2}} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{\frac{7}{2}} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{\frac{5}{2}} \sqrt{3 x^{2} + 5 x + 2} + 20 x^{\frac{3}{2}} \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{x} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(5*sqrt(x)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-2/(9*x**(9/2)*sqrt(3*x**2 + 5*x + 2) + 30*x**(7/2)*sqrt(3*x**2 + 5*x + 2) + 37*x**(5/2)*sqrt(3*x**2 + 5*x + 2) + 20*x**(3/2)*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(x)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
1080,-1,0,0,0.000000," ","integrate((2-5*x)/x**(3/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1081,-1,0,0,0.000000," ","integrate((2-5*x)/x**(5/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1082,-1,0,0,0.000000," ","integrate((2-5*x)/x**(7/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1083,1,11388,0,5.523623," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a)**3,x)","\begin{cases} \frac{- \frac{A a^{3}}{7 x^{7}} - \frac{A a^{2} b}{2 x^{6}} - \frac{3 A a^{2} c}{5 x^{5}} - \frac{3 A a b^{2}}{5 x^{5}} - \frac{3 A a b c}{2 x^{4}} - \frac{A a c^{2}}{x^{3}} - \frac{A b^{3}}{4 x^{4}} - \frac{A b^{2} c}{x^{3}} - \frac{3 A b c^{2}}{2 x^{2}} - \frac{A c^{3}}{x} - \frac{B a^{3}}{6 x^{6}} - \frac{3 B a^{2} b}{5 x^{5}} - \frac{3 B a^{2} c}{4 x^{4}} - \frac{3 B a b^{2}}{4 x^{4}} - \frac{2 B a b c}{x^{3}} - \frac{3 B a c^{2}}{2 x^{2}} - \frac{B b^{3}}{3 x^{3}} - \frac{3 B b^{2} c}{2 x^{2}} - \frac{3 B b c^{2}}{x} + B c^{3} \log{\left(x \right)}}{e^{8}} & \text{for}\: m = -8 \\\frac{- \frac{A a^{3}}{6 x^{6}} - \frac{3 A a^{2} b}{5 x^{5}} - \frac{3 A a^{2} c}{4 x^{4}} - \frac{3 A a b^{2}}{4 x^{4}} - \frac{2 A a b c}{x^{3}} - \frac{3 A a c^{2}}{2 x^{2}} - \frac{A b^{3}}{3 x^{3}} - \frac{3 A b^{2} c}{2 x^{2}} - \frac{3 A b c^{2}}{x} + A c^{3} \log{\left(x \right)} - \frac{B a^{3}}{5 x^{5}} - \frac{3 B a^{2} b}{4 x^{4}} - \frac{B a^{2} c}{x^{3}} - \frac{B a b^{2}}{x^{3}} - \frac{3 B a b c}{x^{2}} - \frac{3 B a c^{2}}{x} - \frac{B b^{3}}{2 x^{2}} - \frac{3 B b^{2} c}{x} + 3 B b c^{2} \log{\left(x \right)} + B c^{3} x}{e^{7}} & \text{for}\: m = -7 \\\frac{- \frac{A a^{3}}{5 x^{5}} - \frac{3 A a^{2} b}{4 x^{4}} - \frac{A a^{2} c}{x^{3}} - \frac{A a b^{2}}{x^{3}} - \frac{3 A a b c}{x^{2}} - \frac{3 A a c^{2}}{x} - \frac{A b^{3}}{2 x^{2}} - \frac{3 A b^{2} c}{x} + 3 A b c^{2} \log{\left(x \right)} + A c^{3} x - \frac{B a^{3}}{4 x^{4}} - \frac{B a^{2} b}{x^{3}} - \frac{3 B a^{2} c}{2 x^{2}} - \frac{3 B a b^{2}}{2 x^{2}} - \frac{6 B a b c}{x} + 3 B a c^{2} \log{\left(x \right)} - \frac{B b^{3}}{x} + 3 B b^{2} c \log{\left(x \right)} + 3 B b c^{2} x + \frac{B c^{3} x^{2}}{2}}{e^{6}} & \text{for}\: m = -6 \\\frac{- \frac{A a^{3}}{4 x^{4}} - \frac{A a^{2} b}{x^{3}} - \frac{3 A a^{2} c}{2 x^{2}} - \frac{3 A a b^{2}}{2 x^{2}} - \frac{6 A a b c}{x} + 3 A a c^{2} \log{\left(x \right)} - \frac{A b^{3}}{x} + 3 A b^{2} c \log{\left(x \right)} + 3 A b c^{2} x + \frac{A c^{3} x^{2}}{2} - \frac{B a^{3}}{3 x^{3}} - \frac{3 B a^{2} b}{2 x^{2}} - \frac{3 B a^{2} c}{x} - \frac{3 B a b^{2}}{x} + 6 B a b c \log{\left(x \right)} + 3 B a c^{2} x + B b^{3} \log{\left(x \right)} + 3 B b^{2} c x + \frac{3 B b c^{2} x^{2}}{2} + \frac{B c^{3} x^{3}}{3}}{e^{5}} & \text{for}\: m = -5 \\\frac{- \frac{A a^{3}}{3 x^{3}} - \frac{3 A a^{2} b}{2 x^{2}} - \frac{3 A a^{2} c}{x} - \frac{3 A a b^{2}}{x} + 6 A a b c \log{\left(x \right)} + 3 A a c^{2} x + A b^{3} \log{\left(x \right)} + 3 A b^{2} c x + \frac{3 A b c^{2} x^{2}}{2} + \frac{A c^{3} x^{3}}{3} - \frac{B a^{3}}{2 x^{2}} - \frac{3 B a^{2} b}{x} + 3 B a^{2} c \log{\left(x \right)} + 3 B a b^{2} \log{\left(x \right)} + 6 B a b c x + \frac{3 B a c^{2} x^{2}}{2} + B b^{3} x + \frac{3 B b^{2} c x^{2}}{2} + B b c^{2} x^{3} + \frac{B c^{3} x^{4}}{4}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a^{3}}{2 x^{2}} - \frac{3 A a^{2} b}{x} + 3 A a^{2} c \log{\left(x \right)} + 3 A a b^{2} \log{\left(x \right)} + 6 A a b c x + \frac{3 A a c^{2} x^{2}}{2} + A b^{3} x + \frac{3 A b^{2} c x^{2}}{2} + A b c^{2} x^{3} + \frac{A c^{3} x^{4}}{4} - \frac{B a^{3}}{x} + 3 B a^{2} b \log{\left(x \right)} + 3 B a^{2} c x + 3 B a b^{2} x + 3 B a b c x^{2} + B a c^{2} x^{3} + \frac{B b^{3} x^{2}}{2} + B b^{2} c x^{3} + \frac{3 B b c^{2} x^{4}}{4} + \frac{B c^{3} x^{5}}{5}}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a^{3}}{x} + 3 A a^{2} b \log{\left(x \right)} + 3 A a^{2} c x + 3 A a b^{2} x + 3 A a b c x^{2} + A a c^{2} x^{3} + \frac{A b^{3} x^{2}}{2} + A b^{2} c x^{3} + \frac{3 A b c^{2} x^{4}}{4} + \frac{A c^{3} x^{5}}{5} + B a^{3} \log{\left(x \right)} + 3 B a^{2} b x + \frac{3 B a^{2} c x^{2}}{2} + \frac{3 B a b^{2} x^{2}}{2} + 2 B a b c x^{3} + \frac{3 B a c^{2} x^{4}}{4} + \frac{B b^{3} x^{3}}{3} + \frac{3 B b^{2} c x^{4}}{4} + \frac{3 B b c^{2} x^{5}}{5} + \frac{B c^{3} x^{6}}{6}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a^{3} \log{\left(x \right)} + 3 A a^{2} b x + \frac{3 A a^{2} c x^{2}}{2} + \frac{3 A a b^{2} x^{2}}{2} + 2 A a b c x^{3} + \frac{3 A a c^{2} x^{4}}{4} + \frac{A b^{3} x^{3}}{3} + \frac{3 A b^{2} c x^{4}}{4} + \frac{3 A b c^{2} x^{5}}{5} + \frac{A c^{3} x^{6}}{6} + B a^{3} x + \frac{3 B a^{2} b x^{2}}{2} + B a^{2} c x^{3} + B a b^{2} x^{3} + \frac{3 B a b c x^{4}}{2} + \frac{3 B a c^{2} x^{5}}{5} + \frac{B b^{3} x^{4}}{4} + \frac{3 B b^{2} c x^{5}}{5} + \frac{B b c^{2} x^{6}}{2} + \frac{B c^{3} x^{7}}{7}}{e} & \text{for}\: m = -1 \\\frac{A a^{3} e^{m} m^{7} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35 A a^{3} e^{m} m^{6} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{511 A a^{3} e^{m} m^{5} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{4025 A a^{3} e^{m} m^{4} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{18424 A a^{3} e^{m} m^{3} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{48860 A a^{3} e^{m} m^{2} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69264 A a^{3} e^{m} m x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a^{3} e^{m} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A a^{2} b e^{m} m^{7} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{102 A a^{2} b e^{m} m^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1434 A a^{2} b e^{m} m^{5} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{10740 A a^{2} b e^{m} m^{4} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{45867 A a^{2} b e^{m} m^{3} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{110118 A a^{2} b e^{m} m^{2} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{134136 A a^{2} b e^{m} m x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{60480 A a^{2} b e^{m} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A a^{2} c e^{m} m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{99 A a^{2} c e^{m} m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1341 A a^{2} c e^{m} m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{9585 A a^{2} c e^{m} m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{38592 A a^{2} c e^{m} m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{86076 A a^{2} c e^{m} m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96144 A a^{2} c e^{m} m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a^{2} c e^{m} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A a b^{2} e^{m} m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{99 A a b^{2} e^{m} m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1341 A a b^{2} e^{m} m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{9585 A a b^{2} e^{m} m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{38592 A a b^{2} e^{m} m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{86076 A a b^{2} e^{m} m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96144 A a b^{2} e^{m} m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 A a b^{2} e^{m} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6 A a b c e^{m} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{192 A a b c e^{m} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2508 A a b c e^{m} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{17184 A a b c e^{m} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{65958 A a b c e^{m} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{139872 A a b c e^{m} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{149256 A a b c e^{m} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{60480 A a b c e^{m} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A a c^{2} e^{m} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{93 A a c^{2} e^{m} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1173 A a c^{2} e^{m} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7743 A a c^{2} e^{m} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28632 A a c^{2} e^{m} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{58692 A a c^{2} e^{m} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{60912 A a c^{2} e^{m} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{24192 A a c^{2} e^{m} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{A b^{3} e^{m} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{32 A b^{3} e^{m} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{418 A b^{3} e^{m} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2864 A b^{3} e^{m} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{10993 A b^{3} e^{m} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{23312 A b^{3} e^{m} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{24876 A b^{3} e^{m} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{10080 A b^{3} e^{m} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A b^{2} c e^{m} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{93 A b^{2} c e^{m} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1173 A b^{2} c e^{m} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7743 A b^{2} c e^{m} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28632 A b^{2} c e^{m} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{58692 A b^{2} c e^{m} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{60912 A b^{2} c e^{m} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{24192 A b^{2} c e^{m} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 A b c^{2} e^{m} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{90 A b c^{2} e^{m} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1098 A b c^{2} e^{m} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7020 A b c^{2} e^{m} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{25227 A b c^{2} e^{m} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{50490 A b c^{2} e^{m} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{51432 A b c^{2} e^{m} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 A b c^{2} e^{m} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{A c^{3} e^{m} m^{7} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{29 A c^{3} e^{m} m^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{343 A c^{3} e^{m} m^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2135 A c^{3} e^{m} m^{4} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7504 A c^{3} e^{m} m^{3} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14756 A c^{3} e^{m} m^{2} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14832 A c^{3} e^{m} m x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5760 A c^{3} e^{m} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B a^{3} e^{m} m^{7} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{34 B a^{3} e^{m} m^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{478 B a^{3} e^{m} m^{5} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3580 B a^{3} e^{m} m^{4} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15289 B a^{3} e^{m} m^{3} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{36706 B a^{3} e^{m} m^{2} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{44712 B a^{3} e^{m} m x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 B a^{3} e^{m} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B a^{2} b e^{m} m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{99 B a^{2} b e^{m} m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1341 B a^{2} b e^{m} m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{9585 B a^{2} b e^{m} m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{38592 B a^{2} b e^{m} m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{86076 B a^{2} b e^{m} m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96144 B a^{2} b e^{m} m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 B a^{2} b e^{m} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B a^{2} c e^{m} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96 B a^{2} c e^{m} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1254 B a^{2} c e^{m} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{8592 B a^{2} c e^{m} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{32979 B a^{2} c e^{m} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69936 B a^{2} c e^{m} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{74628 B a^{2} c e^{m} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{30240 B a^{2} c e^{m} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B a b^{2} e^{m} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{96 B a b^{2} e^{m} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1254 B a b^{2} e^{m} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{8592 B a b^{2} e^{m} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{32979 B a b^{2} e^{m} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69936 B a b^{2} e^{m} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{74628 B a b^{2} e^{m} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{30240 B a b^{2} e^{m} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6 B a b c e^{m} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{186 B a b c e^{m} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2346 B a b c e^{m} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{15486 B a b c e^{m} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{57264 B a b c e^{m} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{117384 B a b c e^{m} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{121824 B a b c e^{m} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{48384 B a b c e^{m} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B a c^{2} e^{m} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{90 B a c^{2} e^{m} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1098 B a c^{2} e^{m} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7020 B a c^{2} e^{m} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{25227 B a c^{2} e^{m} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{50490 B a c^{2} e^{m} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{51432 B a c^{2} e^{m} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 B a c^{2} e^{m} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B b^{3} e^{m} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{31 B b^{3} e^{m} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{391 B b^{3} e^{m} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2581 B b^{3} e^{m} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{9544 B b^{3} e^{m} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{19564 B b^{3} e^{m} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20304 B b^{3} e^{m} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{8064 B b^{3} e^{m} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B b^{2} c e^{m} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{90 B b^{2} c e^{m} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1098 B b^{2} c e^{m} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7020 B b^{2} c e^{m} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{25227 B b^{2} c e^{m} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{50490 B b^{2} c e^{m} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{51432 B b^{2} c e^{m} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{20160 B b^{2} c e^{m} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3 B b c^{2} e^{m} m^{7} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{87 B b c^{2} e^{m} m^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1029 B b c^{2} e^{m} m^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6405 B b c^{2} e^{m} m^{4} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{22512 B b c^{2} e^{m} m^{3} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{44268 B b c^{2} e^{m} m^{2} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{44496 B b c^{2} e^{m} m x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{17280 B b c^{2} e^{m} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{B c^{3} e^{m} m^{7} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28 B c^{3} e^{m} m^{6} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{322 B c^{3} e^{m} m^{5} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1960 B c^{3} e^{m} m^{4} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6769 B c^{3} e^{m} m^{3} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13132 B c^{3} e^{m} m^{2} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13068 B c^{3} e^{m} m x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5040 B c^{3} e^{m} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a**3/(7*x**7) - A*a**2*b/(2*x**6) - 3*A*a**2*c/(5*x**5) - 3*A*a*b**2/(5*x**5) - 3*A*a*b*c/(2*x**4) - A*a*c**2/x**3 - A*b**3/(4*x**4) - A*b**2*c/x**3 - 3*A*b*c**2/(2*x**2) - A*c**3/x - B*a**3/(6*x**6) - 3*B*a**2*b/(5*x**5) - 3*B*a**2*c/(4*x**4) - 3*B*a*b**2/(4*x**4) - 2*B*a*b*c/x**3 - 3*B*a*c**2/(2*x**2) - B*b**3/(3*x**3) - 3*B*b**2*c/(2*x**2) - 3*B*b*c**2/x + B*c**3*log(x))/e**8, Eq(m, -8)), ((-A*a**3/(6*x**6) - 3*A*a**2*b/(5*x**5) - 3*A*a**2*c/(4*x**4) - 3*A*a*b**2/(4*x**4) - 2*A*a*b*c/x**3 - 3*A*a*c**2/(2*x**2) - A*b**3/(3*x**3) - 3*A*b**2*c/(2*x**2) - 3*A*b*c**2/x + A*c**3*log(x) - B*a**3/(5*x**5) - 3*B*a**2*b/(4*x**4) - B*a**2*c/x**3 - B*a*b**2/x**3 - 3*B*a*b*c/x**2 - 3*B*a*c**2/x - B*b**3/(2*x**2) - 3*B*b**2*c/x + 3*B*b*c**2*log(x) + B*c**3*x)/e**7, Eq(m, -7)), ((-A*a**3/(5*x**5) - 3*A*a**2*b/(4*x**4) - A*a**2*c/x**3 - A*a*b**2/x**3 - 3*A*a*b*c/x**2 - 3*A*a*c**2/x - A*b**3/(2*x**2) - 3*A*b**2*c/x + 3*A*b*c**2*log(x) + A*c**3*x - B*a**3/(4*x**4) - B*a**2*b/x**3 - 3*B*a**2*c/(2*x**2) - 3*B*a*b**2/(2*x**2) - 6*B*a*b*c/x + 3*B*a*c**2*log(x) - B*b**3/x + 3*B*b**2*c*log(x) + 3*B*b*c**2*x + B*c**3*x**2/2)/e**6, Eq(m, -6)), ((-A*a**3/(4*x**4) - A*a**2*b/x**3 - 3*A*a**2*c/(2*x**2) - 3*A*a*b**2/(2*x**2) - 6*A*a*b*c/x + 3*A*a*c**2*log(x) - A*b**3/x + 3*A*b**2*c*log(x) + 3*A*b*c**2*x + A*c**3*x**2/2 - B*a**3/(3*x**3) - 3*B*a**2*b/(2*x**2) - 3*B*a**2*c/x - 3*B*a*b**2/x + 6*B*a*b*c*log(x) + 3*B*a*c**2*x + B*b**3*log(x) + 3*B*b**2*c*x + 3*B*b*c**2*x**2/2 + B*c**3*x**3/3)/e**5, Eq(m, -5)), ((-A*a**3/(3*x**3) - 3*A*a**2*b/(2*x**2) - 3*A*a**2*c/x - 3*A*a*b**2/x + 6*A*a*b*c*log(x) + 3*A*a*c**2*x + A*b**3*log(x) + 3*A*b**2*c*x + 3*A*b*c**2*x**2/2 + A*c**3*x**3/3 - B*a**3/(2*x**2) - 3*B*a**2*b/x + 3*B*a**2*c*log(x) + 3*B*a*b**2*log(x) + 6*B*a*b*c*x + 3*B*a*c**2*x**2/2 + B*b**3*x + 3*B*b**2*c*x**2/2 + B*b*c**2*x**3 + B*c**3*x**4/4)/e**4, Eq(m, -4)), ((-A*a**3/(2*x**2) - 3*A*a**2*b/x + 3*A*a**2*c*log(x) + 3*A*a*b**2*log(x) + 6*A*a*b*c*x + 3*A*a*c**2*x**2/2 + A*b**3*x + 3*A*b**2*c*x**2/2 + A*b*c**2*x**3 + A*c**3*x**4/4 - B*a**3/x + 3*B*a**2*b*log(x) + 3*B*a**2*c*x + 3*B*a*b**2*x + 3*B*a*b*c*x**2 + B*a*c**2*x**3 + B*b**3*x**2/2 + B*b**2*c*x**3 + 3*B*b*c**2*x**4/4 + B*c**3*x**5/5)/e**3, Eq(m, -3)), ((-A*a**3/x + 3*A*a**2*b*log(x) + 3*A*a**2*c*x + 3*A*a*b**2*x + 3*A*a*b*c*x**2 + A*a*c**2*x**3 + A*b**3*x**2/2 + A*b**2*c*x**3 + 3*A*b*c**2*x**4/4 + A*c**3*x**5/5 + B*a**3*log(x) + 3*B*a**2*b*x + 3*B*a**2*c*x**2/2 + 3*B*a*b**2*x**2/2 + 2*B*a*b*c*x**3 + 3*B*a*c**2*x**4/4 + B*b**3*x**3/3 + 3*B*b**2*c*x**4/4 + 3*B*b*c**2*x**5/5 + B*c**3*x**6/6)/e**2, Eq(m, -2)), ((A*a**3*log(x) + 3*A*a**2*b*x + 3*A*a**2*c*x**2/2 + 3*A*a*b**2*x**2/2 + 2*A*a*b*c*x**3 + 3*A*a*c**2*x**4/4 + A*b**3*x**3/3 + 3*A*b**2*c*x**4/4 + 3*A*b*c**2*x**5/5 + A*c**3*x**6/6 + B*a**3*x + 3*B*a**2*b*x**2/2 + B*a**2*c*x**3 + B*a*b**2*x**3 + 3*B*a*b*c*x**4/2 + 3*B*a*c**2*x**5/5 + B*b**3*x**4/4 + 3*B*b**2*c*x**5/5 + B*b*c**2*x**6/2 + B*c**3*x**7/7)/e, Eq(m, -1)), (A*a**3*e**m*m**7*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35*A*a**3*e**m*m**6*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 511*A*a**3*e**m*m**5*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 4025*A*a**3*e**m*m**4*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 18424*A*a**3*e**m*m**3*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 48860*A*a**3*e**m*m**2*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69264*A*a**3*e**m*m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a**3*e**m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*a**2*b*e**m*m**7*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 102*A*a**2*b*e**m*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1434*A*a**2*b*e**m*m**5*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 10740*A*a**2*b*e**m*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 45867*A*a**2*b*e**m*m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 110118*A*a**2*b*e**m*m**2*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 134136*A*a**2*b*e**m*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 60480*A*a**2*b*e**m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*a**2*c*e**m*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 99*A*a**2*c*e**m*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1341*A*a**2*c*e**m*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 9585*A*a**2*c*e**m*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 38592*A*a**2*c*e**m*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 86076*A*a**2*c*e**m*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96144*A*a**2*c*e**m*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a**2*c*e**m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*a*b**2*e**m*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 99*A*a*b**2*e**m*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1341*A*a*b**2*e**m*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 9585*A*a*b**2*e**m*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 38592*A*a*b**2*e**m*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 86076*A*a*b**2*e**m*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96144*A*a*b**2*e**m*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*A*a*b**2*e**m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6*A*a*b*c*e**m*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 192*A*a*b*c*e**m*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2508*A*a*b*c*e**m*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 17184*A*a*b*c*e**m*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 65958*A*a*b*c*e**m*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 139872*A*a*b*c*e**m*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 149256*A*a*b*c*e**m*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 60480*A*a*b*c*e**m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*a*c**2*e**m*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 93*A*a*c**2*e**m*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1173*A*a*c**2*e**m*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7743*A*a*c**2*e**m*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28632*A*a*c**2*e**m*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 58692*A*a*c**2*e**m*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 60912*A*a*c**2*e**m*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 24192*A*a*c**2*e**m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + A*b**3*e**m*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 32*A*b**3*e**m*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 418*A*b**3*e**m*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2864*A*b**3*e**m*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 10993*A*b**3*e**m*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 23312*A*b**3*e**m*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 24876*A*b**3*e**m*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 10080*A*b**3*e**m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*b**2*c*e**m*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 93*A*b**2*c*e**m*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1173*A*b**2*c*e**m*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7743*A*b**2*c*e**m*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28632*A*b**2*c*e**m*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 58692*A*b**2*c*e**m*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 60912*A*b**2*c*e**m*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 24192*A*b**2*c*e**m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*A*b*c**2*e**m*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 90*A*b*c**2*e**m*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1098*A*b*c**2*e**m*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7020*A*b*c**2*e**m*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 25227*A*b*c**2*e**m*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 50490*A*b*c**2*e**m*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 51432*A*b*c**2*e**m*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*A*b*c**2*e**m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + A*c**3*e**m*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 29*A*c**3*e**m*m**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 343*A*c**3*e**m*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2135*A*c**3*e**m*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7504*A*c**3*e**m*m**3*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14756*A*c**3*e**m*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14832*A*c**3*e**m*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5760*A*c**3*e**m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*a**3*e**m*m**7*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 34*B*a**3*e**m*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 478*B*a**3*e**m*m**5*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3580*B*a**3*e**m*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15289*B*a**3*e**m*m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 36706*B*a**3*e**m*m**2*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 44712*B*a**3*e**m*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*B*a**3*e**m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*a**2*b*e**m*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 99*B*a**2*b*e**m*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1341*B*a**2*b*e**m*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 9585*B*a**2*b*e**m*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 38592*B*a**2*b*e**m*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 86076*B*a**2*b*e**m*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96144*B*a**2*b*e**m*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*B*a**2*b*e**m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*a**2*c*e**m*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96*B*a**2*c*e**m*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1254*B*a**2*c*e**m*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 8592*B*a**2*c*e**m*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 32979*B*a**2*c*e**m*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69936*B*a**2*c*e**m*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 74628*B*a**2*c*e**m*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 30240*B*a**2*c*e**m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*a*b**2*e**m*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 96*B*a*b**2*e**m*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1254*B*a*b**2*e**m*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 8592*B*a*b**2*e**m*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 32979*B*a*b**2*e**m*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69936*B*a*b**2*e**m*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 74628*B*a*b**2*e**m*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 30240*B*a*b**2*e**m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6*B*a*b*c*e**m*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 186*B*a*b*c*e**m*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2346*B*a*b*c*e**m*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 15486*B*a*b*c*e**m*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 57264*B*a*b*c*e**m*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 117384*B*a*b*c*e**m*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 121824*B*a*b*c*e**m*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 48384*B*a*b*c*e**m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*a*c**2*e**m*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 90*B*a*c**2*e**m*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1098*B*a*c**2*e**m*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7020*B*a*c**2*e**m*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 25227*B*a*c**2*e**m*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 50490*B*a*c**2*e**m*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 51432*B*a*c**2*e**m*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*B*a*c**2*e**m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*b**3*e**m*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 31*B*b**3*e**m*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 391*B*b**3*e**m*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2581*B*b**3*e**m*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 9544*B*b**3*e**m*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 19564*B*b**3*e**m*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20304*B*b**3*e**m*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 8064*B*b**3*e**m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*b**2*c*e**m*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 90*B*b**2*c*e**m*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1098*B*b**2*c*e**m*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7020*B*b**2*c*e**m*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 25227*B*b**2*c*e**m*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 50490*B*b**2*c*e**m*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 51432*B*b**2*c*e**m*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 20160*B*b**2*c*e**m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3*B*b*c**2*e**m*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 87*B*b*c**2*e**m*m**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1029*B*b*c**2*e**m*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6405*B*b*c**2*e**m*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 22512*B*b*c**2*e**m*m**3*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 44268*B*b*c**2*e**m*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 44496*B*b*c**2*e**m*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 17280*B*b*c**2*e**m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + B*c**3*e**m*m**7*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28*B*c**3*e**m*m**6*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 322*B*c**3*e**m*m**5*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1960*B*c**3*e**m*m**4*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6769*B*c**3*e**m*m**3*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13132*B*c**3*e**m*m**2*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13068*B*c**3*e**m*m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5040*B*c**3*e**m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320), True))","A",0
1084,1,4150,0,2.628989," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a)**2,x)","\begin{cases} \frac{- \frac{A a^{2}}{5 x^{5}} - \frac{A a b}{2 x^{4}} - \frac{2 A a c}{3 x^{3}} - \frac{A b^{2}}{3 x^{3}} - \frac{A b c}{x^{2}} - \frac{A c^{2}}{x} - \frac{B a^{2}}{4 x^{4}} - \frac{2 B a b}{3 x^{3}} - \frac{B a c}{x^{2}} - \frac{B b^{2}}{2 x^{2}} - \frac{2 B b c}{x} + B c^{2} \log{\left(x \right)}}{e^{6}} & \text{for}\: m = -6 \\\frac{- \frac{A a^{2}}{4 x^{4}} - \frac{2 A a b}{3 x^{3}} - \frac{A a c}{x^{2}} - \frac{A b^{2}}{2 x^{2}} - \frac{2 A b c}{x} + A c^{2} \log{\left(x \right)} - \frac{B a^{2}}{3 x^{3}} - \frac{B a b}{x^{2}} - \frac{2 B a c}{x} - \frac{B b^{2}}{x} + 2 B b c \log{\left(x \right)} + B c^{2} x}{e^{5}} & \text{for}\: m = -5 \\\frac{- \frac{A a^{2}}{3 x^{3}} - \frac{A a b}{x^{2}} - \frac{2 A a c}{x} - \frac{A b^{2}}{x} + 2 A b c \log{\left(x \right)} + A c^{2} x - \frac{B a^{2}}{2 x^{2}} - \frac{2 B a b}{x} + 2 B a c \log{\left(x \right)} + B b^{2} \log{\left(x \right)} + 2 B b c x + \frac{B c^{2} x^{2}}{2}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a^{2}}{2 x^{2}} - \frac{2 A a b}{x} + 2 A a c \log{\left(x \right)} + A b^{2} \log{\left(x \right)} + 2 A b c x + \frac{A c^{2} x^{2}}{2} - \frac{B a^{2}}{x} + 2 B a b \log{\left(x \right)} + 2 B a c x + B b^{2} x + B b c x^{2} + \frac{B c^{2} x^{3}}{3}}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a^{2}}{x} + 2 A a b \log{\left(x \right)} + 2 A a c x + A b^{2} x + A b c x^{2} + \frac{A c^{2} x^{3}}{3} + B a^{2} \log{\left(x \right)} + 2 B a b x + B a c x^{2} + \frac{B b^{2} x^{2}}{2} + \frac{2 B b c x^{3}}{3} + \frac{B c^{2} x^{4}}{4}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a^{2} \log{\left(x \right)} + 2 A a b x + A a c x^{2} + \frac{A b^{2} x^{2}}{2} + \frac{2 A b c x^{3}}{3} + \frac{A c^{2} x^{4}}{4} + B a^{2} x + B a b x^{2} + \frac{2 B a c x^{3}}{3} + \frac{B b^{2} x^{3}}{3} + \frac{B b c x^{4}}{2} + \frac{B c^{2} x^{5}}{5}}{e} & \text{for}\: m = -1 \\\frac{A a^{2} e^{m} m^{5} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{20 A a^{2} e^{m} m^{4} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{155 A a^{2} e^{m} m^{3} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{580 A a^{2} e^{m} m^{2} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1044 A a^{2} e^{m} m x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{720 A a^{2} e^{m} x x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 A a b e^{m} m^{5} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{38 A a b e^{m} m^{4} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{274 A a b e^{m} m^{3} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{922 A a b e^{m} m^{2} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1404 A a b e^{m} m x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{720 A a b e^{m} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 A a c e^{m} m^{5} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{36 A a c e^{m} m^{4} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{242 A a c e^{m} m^{3} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{744 A a c e^{m} m^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1016 A a c e^{m} m x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{480 A a c e^{m} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{A b^{2} e^{m} m^{5} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{18 A b^{2} e^{m} m^{4} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{121 A b^{2} e^{m} m^{3} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{372 A b^{2} e^{m} m^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{508 A b^{2} e^{m} m x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{240 A b^{2} e^{m} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 A b c e^{m} m^{5} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{34 A b c e^{m} m^{4} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{214 A b c e^{m} m^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{614 A b c e^{m} m^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{792 A b c e^{m} m x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{360 A b c e^{m} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{A c^{2} e^{m} m^{5} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{16 A c^{2} e^{m} m^{4} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{95 A c^{2} e^{m} m^{3} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{260 A c^{2} e^{m} m^{2} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{324 A c^{2} e^{m} m x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{144 A c^{2} e^{m} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B a^{2} e^{m} m^{5} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{19 B a^{2} e^{m} m^{4} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{137 B a^{2} e^{m} m^{3} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{461 B a^{2} e^{m} m^{2} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{702 B a^{2} e^{m} m x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{360 B a^{2} e^{m} x^{2} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 B a b e^{m} m^{5} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{36 B a b e^{m} m^{4} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{242 B a b e^{m} m^{3} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{744 B a b e^{m} m^{2} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{1016 B a b e^{m} m x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{480 B a b e^{m} x^{3} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 B a c e^{m} m^{5} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{34 B a c e^{m} m^{4} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{214 B a c e^{m} m^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{614 B a c e^{m} m^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{792 B a c e^{m} m x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{360 B a c e^{m} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B b^{2} e^{m} m^{5} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{17 B b^{2} e^{m} m^{4} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{107 B b^{2} e^{m} m^{3} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{307 B b^{2} e^{m} m^{2} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{396 B b^{2} e^{m} m x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{180 B b^{2} e^{m} x^{4} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{2 B b c e^{m} m^{5} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{32 B b c e^{m} m^{4} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{190 B b c e^{m} m^{3} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{520 B b c e^{m} m^{2} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{648 B b c e^{m} m x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{288 B b c e^{m} x^{5} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{B c^{2} e^{m} m^{5} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{15 B c^{2} e^{m} m^{4} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{85 B c^{2} e^{m} m^{3} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{225 B c^{2} e^{m} m^{2} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{274 B c^{2} e^{m} m x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} + \frac{120 B c^{2} e^{m} x^{6} x^{m}}{m^{6} + 21 m^{5} + 175 m^{4} + 735 m^{3} + 1624 m^{2} + 1764 m + 720} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a**2/(5*x**5) - A*a*b/(2*x**4) - 2*A*a*c/(3*x**3) - A*b**2/(3*x**3) - A*b*c/x**2 - A*c**2/x - B*a**2/(4*x**4) - 2*B*a*b/(3*x**3) - B*a*c/x**2 - B*b**2/(2*x**2) - 2*B*b*c/x + B*c**2*log(x))/e**6, Eq(m, -6)), ((-A*a**2/(4*x**4) - 2*A*a*b/(3*x**3) - A*a*c/x**2 - A*b**2/(2*x**2) - 2*A*b*c/x + A*c**2*log(x) - B*a**2/(3*x**3) - B*a*b/x**2 - 2*B*a*c/x - B*b**2/x + 2*B*b*c*log(x) + B*c**2*x)/e**5, Eq(m, -5)), ((-A*a**2/(3*x**3) - A*a*b/x**2 - 2*A*a*c/x - A*b**2/x + 2*A*b*c*log(x) + A*c**2*x - B*a**2/(2*x**2) - 2*B*a*b/x + 2*B*a*c*log(x) + B*b**2*log(x) + 2*B*b*c*x + B*c**2*x**2/2)/e**4, Eq(m, -4)), ((-A*a**2/(2*x**2) - 2*A*a*b/x + 2*A*a*c*log(x) + A*b**2*log(x) + 2*A*b*c*x + A*c**2*x**2/2 - B*a**2/x + 2*B*a*b*log(x) + 2*B*a*c*x + B*b**2*x + B*b*c*x**2 + B*c**2*x**3/3)/e**3, Eq(m, -3)), ((-A*a**2/x + 2*A*a*b*log(x) + 2*A*a*c*x + A*b**2*x + A*b*c*x**2 + A*c**2*x**3/3 + B*a**2*log(x) + 2*B*a*b*x + B*a*c*x**2 + B*b**2*x**2/2 + 2*B*b*c*x**3/3 + B*c**2*x**4/4)/e**2, Eq(m, -2)), ((A*a**2*log(x) + 2*A*a*b*x + A*a*c*x**2 + A*b**2*x**2/2 + 2*A*b*c*x**3/3 + A*c**2*x**4/4 + B*a**2*x + B*a*b*x**2 + 2*B*a*c*x**3/3 + B*b**2*x**3/3 + B*b*c*x**4/2 + B*c**2*x**5/5)/e, Eq(m, -1)), (A*a**2*e**m*m**5*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 20*A*a**2*e**m*m**4*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 155*A*a**2*e**m*m**3*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 580*A*a**2*e**m*m**2*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1044*A*a**2*e**m*m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 720*A*a**2*e**m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*A*a*b*e**m*m**5*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 38*A*a*b*e**m*m**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 274*A*a*b*e**m*m**3*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 922*A*a*b*e**m*m**2*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1404*A*a*b*e**m*m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 720*A*a*b*e**m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*A*a*c*e**m*m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 36*A*a*c*e**m*m**4*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 242*A*a*c*e**m*m**3*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 744*A*a*c*e**m*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1016*A*a*c*e**m*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 480*A*a*c*e**m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + A*b**2*e**m*m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 18*A*b**2*e**m*m**4*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 121*A*b**2*e**m*m**3*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 372*A*b**2*e**m*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 508*A*b**2*e**m*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 240*A*b**2*e**m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*A*b*c*e**m*m**5*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 34*A*b*c*e**m*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 214*A*b*c*e**m*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 614*A*b*c*e**m*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 792*A*b*c*e**m*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 360*A*b*c*e**m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + A*c**2*e**m*m**5*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 16*A*c**2*e**m*m**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 95*A*c**2*e**m*m**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 260*A*c**2*e**m*m**2*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 324*A*c**2*e**m*m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 144*A*c**2*e**m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*a**2*e**m*m**5*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 19*B*a**2*e**m*m**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 137*B*a**2*e**m*m**3*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 461*B*a**2*e**m*m**2*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 702*B*a**2*e**m*m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 360*B*a**2*e**m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*B*a*b*e**m*m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 36*B*a*b*e**m*m**4*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 242*B*a*b*e**m*m**3*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 744*B*a*b*e**m*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1016*B*a*b*e**m*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 480*B*a*b*e**m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*B*a*c*e**m*m**5*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 34*B*a*c*e**m*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 214*B*a*c*e**m*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 614*B*a*c*e**m*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 792*B*a*c*e**m*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 360*B*a*c*e**m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*b**2*e**m*m**5*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 17*B*b**2*e**m*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 107*B*b**2*e**m*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 307*B*b**2*e**m*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 396*B*b**2*e**m*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 180*B*b**2*e**m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2*B*b*c*e**m*m**5*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 32*B*b*c*e**m*m**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 190*B*b*c*e**m*m**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 520*B*b*c*e**m*m**2*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 648*B*b*c*e**m*m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 288*B*b*c*e**m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + B*c**2*e**m*m**5*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 15*B*c**2*e**m*m**4*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 85*B*c**2*e**m*m**3*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 225*B*c**2*e**m*m**2*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 274*B*c**2*e**m*m*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 120*B*c**2*e**m*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720), True))","A",0
1085,1,1022,0,1.017770," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a),x)","\begin{cases} \frac{- \frac{A a}{3 x^{3}} - \frac{A b}{2 x^{2}} - \frac{A c}{x} - \frac{B a}{2 x^{2}} - \frac{B b}{x} + B c \log{\left(x \right)}}{e^{4}} & \text{for}\: m = -4 \\\frac{- \frac{A a}{2 x^{2}} - \frac{A b}{x} + A c \log{\left(x \right)} - \frac{B a}{x} + B b \log{\left(x \right)} + B c x}{e^{3}} & \text{for}\: m = -3 \\\frac{- \frac{A a}{x} + A b \log{\left(x \right)} + A c x + B a \log{\left(x \right)} + B b x + \frac{B c x^{2}}{2}}{e^{2}} & \text{for}\: m = -2 \\\frac{A a \log{\left(x \right)} + A b x + \frac{A c x^{2}}{2} + B a x + \frac{B b x^{2}}{2} + \frac{B c x^{3}}{3}}{e} & \text{for}\: m = -1 \\\frac{A a e^{m} m^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{9 A a e^{m} m^{2} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{26 A a e^{m} m x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 A a e^{m} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{A b e^{m} m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 A b e^{m} m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{19 A b e^{m} m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{12 A b e^{m} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{A c e^{m} m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{7 A c e^{m} m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{14 A c e^{m} m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 A c e^{m} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B a e^{m} m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 B a e^{m} m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{19 B a e^{m} m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{12 B a e^{m} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B b e^{m} m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{7 B b e^{m} m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{14 B b e^{m} m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{8 B b e^{m} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{B c e^{m} m^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 B c e^{m} m^{2} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{11 B c e^{m} m x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 B c e^{m} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a/(3*x**3) - A*b/(2*x**2) - A*c/x - B*a/(2*x**2) - B*b/x + B*c*log(x))/e**4, Eq(m, -4)), ((-A*a/(2*x**2) - A*b/x + A*c*log(x) - B*a/x + B*b*log(x) + B*c*x)/e**3, Eq(m, -3)), ((-A*a/x + A*b*log(x) + A*c*x + B*a*log(x) + B*b*x + B*c*x**2/2)/e**2, Eq(m, -2)), ((A*a*log(x) + A*b*x + A*c*x**2/2 + B*a*x + B*b*x**2/2 + B*c*x**3/3)/e, Eq(m, -1)), (A*a*e**m*m**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 9*A*a*e**m*m**2*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 26*A*a*e**m*m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*A*a*e**m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + A*b*e**m*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*A*b*e**m*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 19*A*b*e**m*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 12*A*b*e**m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + A*c*e**m*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 7*A*c*e**m*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 14*A*c*e**m*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*A*c*e**m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*a*e**m*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*B*a*e**m*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 19*B*a*e**m*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 12*B*a*e**m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*b*e**m*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 7*B*b*e**m*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 14*B*b*e**m*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 8*B*b*e**m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + B*c*e**m*m**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*B*c*e**m*m**2*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 11*B*c*e**m*m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*B*c*e**m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24), True))","A",0
1086,0,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)/(c*x**2+b*x+a),x)","\int \frac{\left(e x\right)^{m} \left(A + B x\right)}{a + b x + c x^{2}}\, dx"," ",0,"Integral((e*x)**m*(A + B*x)/(a + b*x + c*x**2), x)","F",0
1087,-1,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,0,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a)**(5/2),x)","\int \left(e x\right)^{m} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((e*x)**m*(A + B*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
1089,0,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a)**(3/2),x)","\int \left(e x\right)^{m} \left(A + B x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((e*x)**m*(A + B*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
1090,0,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int \left(e x\right)^{m} \left(A + B x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((e*x)**m*(A + B*x)*sqrt(a + b*x + c*x**2), x)","F",0
1091,0,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(e x\right)^{m} \left(A + B x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((e*x)**m*(A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
1092,0,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(e x\right)^{m} \left(A + B x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((e*x)**m*(A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
1093,-1,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1094,-1,0,0,0.000000," ","integrate((e*x)**m*(B*x+A)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1095,-1,0,0,0.000000," ","integrate(x**3*(B*x+A)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1096,-1,0,0,0.000000," ","integrate(x**2*(B*x+A)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1097,0,0,0,0.000000," ","integrate(x*(B*x+A)*(c*x**2+b*x+a)**p,x)","\int x \left(A + B x\right) \left(a + b x + c x^{2}\right)^{p}\, dx"," ",0,"Integral(x*(A + B*x)*(a + b*x + c*x**2)**p, x)","F",0
1098,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**p,x)","\int \left(A + B x\right) \left(a + b x + c x^{2}\right)^{p}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**p, x)","F",0
1099,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**p/x,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{p}}{x}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**p/x, x)","F",0
1100,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**p/x**2,x)","\int \frac{\left(A + B x\right) \left(a + b x + c x^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((A + B*x)*(a + b*x + c*x**2)**p/x**2, x)","F",0
1101,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,1,4537,0,4.745873," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+b*x),x)","\begin{cases} d^{m} \left(\frac{A b x^{2}}{2} + \frac{A c x^{3}}{3} + \frac{B b x^{3}}{3} + \frac{B c x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{A b d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 A b e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 A c d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A c d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A c e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 B b d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 B b d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 B b e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 B c d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 B c d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B c e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{A b d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 A b e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 A c d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A c d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A c e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 B b d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 B b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 B b d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B b e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 B c d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B c d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B c e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\\frac{2 A b d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A b d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A b e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A c e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} - \frac{4 B b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 B b d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 B b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B b e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 B c d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{B c e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\- \frac{A b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{A b x}{e} + \frac{A c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{A c d x}{e^{2}} + \frac{A c x^{2}}{2 e} + \frac{B b d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{B b d x}{e^{2}} + \frac{B b x^{2}}{2 e} - \frac{B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{B c d^{2} x}{e^{3}} - \frac{B c d x^{2}}{2 e^{2}} + \frac{B c x^{3}}{3 e} & \text{for}\: m = -1 \\- \frac{A b d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 A b d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 A b d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A b d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 A b d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 A b d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A b e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A b e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 A b e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 A b e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 A c d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A c d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 A c d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 A c d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A c d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 A c d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 A c d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A c e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 A c e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 A c e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A c e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B b d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B b d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 B b d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 B b d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B b d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 B b d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 B b d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B b e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 B b e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 B b e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B b e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 B c d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B c d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B c d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B c d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 B c d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B c d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B c e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 B c e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(A*b*x**2/2 + A*c*x**3/3 + B*b*x**3/3 + B*c*x**4/4), Eq(e, 0)), (-A*b*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*A*b*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*A*c*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*c*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*c*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*B*b*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*B*b*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*B*b*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*c*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*B*c*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*B*c*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*c*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-A*b*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*A*b*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*c*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*A*c*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*c*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*c*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*c*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*b*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*B*b*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*B*b*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*B*b*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*b*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*c*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*B*c*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*c*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*c*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*c*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*c*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (2*A*b*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*A*b*d*e**2/(2*d*e**4 + 2*e**5*x) + 2*A*b*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*c*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*c*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*A*c*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*A*c*e**3*x**2/(2*d*e**4 + 2*e**5*x) - 4*B*b*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*B*b*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*B*b*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*B*b*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**3/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*B*c*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + B*c*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (-A*b*d*log(d/e + x)/e**2 + A*b*x/e + A*c*d**2*log(d/e + x)/e**3 - A*c*d*x/e**2 + A*c*x**2/(2*e) + B*b*d**2*log(d/e + x)/e**3 - B*b*d*x/e**2 + B*b*x**2/(2*e) - B*c*d**3*log(d/e + x)/e**4 + B*c*d**2*x/e**3 - B*c*d*x**2/(2*e**2) + B*c*x**3/(3*e), Eq(m, -1)), (-A*b*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*A*b*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*A*b*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*b*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*A*b*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*A*b*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*b*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*b*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*A*b*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*A*b*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*A*c*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*c*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*A*c*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*A*c*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*c*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*A*c*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*A*c*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*c*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*A*c*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*A*c*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*c*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*b*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*b*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*B*b*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*B*b*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*b*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*B*b*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*B*b*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*b*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*B*b*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*B*b*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*b*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*B*c*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*c*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*c*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*c*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*B*c*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*c*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*c*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*B*c*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
1103,1,230,0,0.104090," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+b*x),x)","\frac{A b d^{4} x^{2}}{2} + \frac{B c e^{4} x^{8}}{8} + x^{7} \left(\frac{A c e^{4}}{7} + \frac{B b e^{4}}{7} + \frac{4 B c d e^{3}}{7}\right) + x^{6} \left(\frac{A b e^{4}}{6} + \frac{2 A c d e^{3}}{3} + \frac{2 B b d e^{3}}{3} + B c d^{2} e^{2}\right) + x^{5} \left(\frac{4 A b d e^{3}}{5} + \frac{6 A c d^{2} e^{2}}{5} + \frac{6 B b d^{2} e^{2}}{5} + \frac{4 B c d^{3} e}{5}\right) + x^{4} \left(\frac{3 A b d^{2} e^{2}}{2} + A c d^{3} e + B b d^{3} e + \frac{B c d^{4}}{4}\right) + x^{3} \left(\frac{4 A b d^{3} e}{3} + \frac{A c d^{4}}{3} + \frac{B b d^{4}}{3}\right)"," ",0,"A*b*d**4*x**2/2 + B*c*e**4*x**8/8 + x**7*(A*c*e**4/7 + B*b*e**4/7 + 4*B*c*d*e**3/7) + x**6*(A*b*e**4/6 + 2*A*c*d*e**3/3 + 2*B*b*d*e**3/3 + B*c*d**2*e**2) + x**5*(4*A*b*d*e**3/5 + 6*A*c*d**2*e**2/5 + 6*B*b*d**2*e**2/5 + 4*B*c*d**3*e/5) + x**4*(3*A*b*d**2*e**2/2 + A*c*d**3*e + B*b*d**3*e + B*c*d**4/4) + x**3*(4*A*b*d**3*e/3 + A*c*d**4/3 + B*b*d**4/3)","B",0
1104,1,177,0,0.092779," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x),x)","\frac{A b d^{3} x^{2}}{2} + \frac{B c e^{3} x^{7}}{7} + x^{6} \left(\frac{A c e^{3}}{6} + \frac{B b e^{3}}{6} + \frac{B c d e^{2}}{2}\right) + x^{5} \left(\frac{A b e^{3}}{5} + \frac{3 A c d e^{2}}{5} + \frac{3 B b d e^{2}}{5} + \frac{3 B c d^{2} e}{5}\right) + x^{4} \left(\frac{3 A b d e^{2}}{4} + \frac{3 A c d^{2} e}{4} + \frac{3 B b d^{2} e}{4} + \frac{B c d^{3}}{4}\right) + x^{3} \left(A b d^{2} e + \frac{A c d^{3}}{3} + \frac{B b d^{3}}{3}\right)"," ",0,"A*b*d**3*x**2/2 + B*c*e**3*x**7/7 + x**6*(A*c*e**3/6 + B*b*e**3/6 + B*c*d*e**2/2) + x**5*(A*b*e**3/5 + 3*A*c*d*e**2/5 + 3*B*b*d*e**2/5 + 3*B*c*d**2*e/5) + x**4*(3*A*b*d*e**2/4 + 3*A*c*d**2*e/4 + 3*B*b*d**2*e/4 + B*c*d**3/4) + x**3*(A*b*d**2*e + A*c*d**3/3 + B*b*d**3/3)","A",0
1105,1,121,0,0.084085," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x),x)","\frac{A b d^{2} x^{2}}{2} + \frac{B c e^{2} x^{6}}{6} + x^{5} \left(\frac{A c e^{2}}{5} + \frac{B b e^{2}}{5} + \frac{2 B c d e}{5}\right) + x^{4} \left(\frac{A b e^{2}}{4} + \frac{A c d e}{2} + \frac{B b d e}{2} + \frac{B c d^{2}}{4}\right) + x^{3} \left(\frac{2 A b d e}{3} + \frac{A c d^{2}}{3} + \frac{B b d^{2}}{3}\right)"," ",0,"A*b*d**2*x**2/2 + B*c*e**2*x**6/6 + x**5*(A*c*e**2/5 + B*b*e**2/5 + 2*B*c*d*e/5) + x**4*(A*b*e**2/4 + A*c*d*e/2 + B*b*d*e/2 + B*c*d**2/4) + x**3*(2*A*b*d*e/3 + A*c*d**2/3 + B*b*d**2/3)","A",0
1106,1,66,0,0.073315," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x),x)","\frac{A b d x^{2}}{2} + \frac{B c e x^{5}}{5} + x^{4} \left(\frac{A c e}{4} + \frac{B b e}{4} + \frac{B c d}{4}\right) + x^{3} \left(\frac{A b e}{3} + \frac{A c d}{3} + \frac{B b d}{3}\right)"," ",0,"A*b*d*x**2/2 + B*c*e*x**5/5 + x**4*(A*c*e/4 + B*b*e/4 + B*c*d/4) + x**3*(A*b*e/3 + A*c*d/3 + B*b*d/3)","A",0
1107,1,29,0,0.065189," ","integrate((B*x+A)*(c*x**2+b*x),x)","\frac{A b x^{2}}{2} + \frac{B c x^{4}}{4} + x^{3} \left(\frac{A c}{3} + \frac{B b}{3}\right)"," ",0,"A*b*x**2/2 + B*c*x**4/4 + x**3*(A*c/3 + B*b/3)","A",0
1108,1,95,0,0.340537," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d),x)","\frac{B c x^{3}}{3 e} + \frac{d \left(- A e + B d\right) \left(b e - c d\right) \log{\left(d + e x \right)}}{e^{4}} + x^{2} \left(\frac{A c}{2 e} + \frac{B b}{2 e} - \frac{B c d}{2 e^{2}}\right) + x \left(\frac{A b}{e} - \frac{A c d}{e^{2}} - \frac{B b d}{e^{2}} + \frac{B c d^{2}}{e^{3}}\right)"," ",0,"B*c*x**3/(3*e) + d*(-A*e + B*d)*(b*e - c*d)*log(d + e*x)/e**4 + x**2*(A*c/(2*e) + B*b/(2*e) - B*c*d/(2*e**2)) + x*(A*b/e - A*c*d/e**2 - B*b*d/e**2 + B*c*d**2/e**3)","A",0
1109,1,121,0,0.658051," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**2,x)","\frac{B c x^{2}}{2 e^{2}} + x \left(\frac{A c}{e^{2}} + \frac{B b}{e^{2}} - \frac{2 B c d}{e^{3}}\right) + \frac{A b d e^{2} - A c d^{2} e - B b d^{2} e + B c d^{3}}{d e^{4} + e^{5} x} - \frac{\left(- A b e^{2} + 2 A c d e + 2 B b d e - 3 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x**2/(2*e**2) + x*(A*c/e**2 + B*b/e**2 - 2*B*c*d/e**3) + (A*b*d*e**2 - A*c*d**2*e - B*b*d**2*e + B*c*d**3)/(d*e**4 + e**5*x) - (-A*b*e**2 + 2*A*c*d*e + 2*B*b*d*e - 3*B*c*d**2)*log(d + e*x)/e**4","A",0
1110,1,138,0,1.491203," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**3,x)","\frac{B c x}{e^{3}} + \frac{- A b d e^{2} + 3 A c d^{2} e + 3 B b d^{2} e - 5 B c d^{3} + x \left(- 2 A b e^{3} + 4 A c d e^{2} + 4 B b d e^{2} - 6 B c d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{\left(A c e + B b e - 3 B c d\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x/e**3 + (-A*b*d*e**2 + 3*A*c*d**2*e + 3*B*b*d**2*e - 5*B*c*d**3 + x*(-2*A*b*e**3 + 4*A*c*d*e**2 + 4*B*b*d*e**2 - 6*B*c*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + (A*c*e + B*b*e - 3*B*c*d)*log(d + e*x)/e**4","A",0
1111,1,158,0,3.200277," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**4,x)","\frac{B c \log{\left(d + e x \right)}}{e^{4}} + \frac{- A b d e^{2} - 2 A c d^{2} e - 2 B b d^{2} e + 11 B c d^{3} + x^{2} \left(- 6 A c e^{3} - 6 B b e^{3} + 18 B c d e^{2}\right) + x \left(- 3 A b e^{3} - 6 A c d e^{2} - 6 B b d e^{2} + 27 B c d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"B*c*log(d + e*x)/e**4 + (-A*b*d*e**2 - 2*A*c*d**2*e - 2*B*b*d**2*e + 11*B*c*d**3 + x**2*(-6*A*c*e**3 - 6*B*b*e**3 + 18*B*c*d*e**2) + x*(-3*A*b*e**3 - 6*A*c*d*e**2 - 6*B*b*d*e**2 + 27*B*c*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
1112,1,168,0,6.108601," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**5,x)","\frac{- A b d e^{2} - A c d^{2} e - B b d^{2} e - 3 B c d^{3} - 12 B c e^{3} x^{3} + x^{2} \left(- 6 A c e^{3} - 6 B b e^{3} - 18 B c d e^{2}\right) + x \left(- 4 A b e^{3} - 4 A c d e^{2} - 4 B b d e^{2} - 12 B c d^{2} e\right)}{12 d^{4} e^{4} + 48 d^{3} e^{5} x + 72 d^{2} e^{6} x^{2} + 48 d e^{7} x^{3} + 12 e^{8} x^{4}}"," ",0,"(-A*b*d*e**2 - A*c*d**2*e - B*b*d**2*e - 3*B*c*d**3 - 12*B*c*e**3*x**3 + x**2*(-6*A*c*e**3 - 6*B*b*e**3 - 18*B*c*d*e**2) + x*(-4*A*b*e**3 - 4*A*c*d*e**2 - 4*B*b*d*e**2 - 12*B*c*d**2*e))/(12*d**4*e**4 + 48*d**3*e**5*x + 72*d**2*e**6*x**2 + 48*d*e**7*x**3 + 12*e**8*x**4)","A",0
1113,1,185,0,10.372858," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**6,x)","\frac{- 3 A b d e^{2} - 2 A c d^{2} e - 2 B b d^{2} e - 3 B c d^{3} - 30 B c e^{3} x^{3} + x^{2} \left(- 20 A c e^{3} - 20 B b e^{3} - 30 B c d e^{2}\right) + x \left(- 15 A b e^{3} - 10 A c d e^{2} - 10 B b d e^{2} - 15 B c d^{2} e\right)}{60 d^{5} e^{4} + 300 d^{4} e^{5} x + 600 d^{3} e^{6} x^{2} + 600 d^{2} e^{7} x^{3} + 300 d e^{8} x^{4} + 60 e^{9} x^{5}}"," ",0,"(-3*A*b*d*e**2 - 2*A*c*d**2*e - 2*B*b*d**2*e - 3*B*c*d**3 - 30*B*c*e**3*x**3 + x**2*(-20*A*c*e**3 - 20*B*b*e**3 - 30*B*c*d*e**2) + x*(-15*A*b*e**3 - 10*A*c*d*e**2 - 10*B*b*d*e**2 - 15*B*c*d**2*e))/(60*d**5*e**4 + 300*d**4*e**5*x + 600*d**3*e**6*x**2 + 600*d**2*e**7*x**3 + 300*d*e**8*x**4 + 60*e**9*x**5)","A",0
1114,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1115,1,301,0,0.113418," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x)**2,x)","\frac{A b^{2} d^{3} x^{3}}{3} + \frac{B c^{2} e^{3} x^{9}}{9} + x^{8} \left(\frac{A c^{2} e^{3}}{8} + \frac{B b c e^{3}}{4} + \frac{3 B c^{2} d e^{2}}{8}\right) + x^{7} \left(\frac{2 A b c e^{3}}{7} + \frac{3 A c^{2} d e^{2}}{7} + \frac{B b^{2} e^{3}}{7} + \frac{6 B b c d e^{2}}{7} + \frac{3 B c^{2} d^{2} e}{7}\right) + x^{6} \left(\frac{A b^{2} e^{3}}{6} + A b c d e^{2} + \frac{A c^{2} d^{2} e}{2} + \frac{B b^{2} d e^{2}}{2} + B b c d^{2} e + \frac{B c^{2} d^{3}}{6}\right) + x^{5} \left(\frac{3 A b^{2} d e^{2}}{5} + \frac{6 A b c d^{2} e}{5} + \frac{A c^{2} d^{3}}{5} + \frac{3 B b^{2} d^{2} e}{5} + \frac{2 B b c d^{3}}{5}\right) + x^{4} \left(\frac{3 A b^{2} d^{2} e}{4} + \frac{A b c d^{3}}{2} + \frac{B b^{2} d^{3}}{4}\right)"," ",0,"A*b**2*d**3*x**3/3 + B*c**2*e**3*x**9/9 + x**8*(A*c**2*e**3/8 + B*b*c*e**3/4 + 3*B*c**2*d*e**2/8) + x**7*(2*A*b*c*e**3/7 + 3*A*c**2*d*e**2/7 + B*b**2*e**3/7 + 6*B*b*c*d*e**2/7 + 3*B*c**2*d**2*e/7) + x**6*(A*b**2*e**3/6 + A*b*c*d*e**2 + A*c**2*d**2*e/2 + B*b**2*d*e**2/2 + B*b*c*d**2*e + B*c**2*d**3/6) + x**5*(3*A*b**2*d*e**2/5 + 6*A*b*c*d**2*e/5 + A*c**2*d**3/5 + 3*B*b**2*d**2*e/5 + 2*B*b*c*d**3/5) + x**4*(3*A*b**2*d**2*e/4 + A*b*c*d**3/2 + B*b**2*d**3/4)","A",0
1116,1,212,0,0.101074," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x)**2,x)","\frac{A b^{2} d^{2} x^{3}}{3} + \frac{B c^{2} e^{2} x^{8}}{8} + x^{7} \left(\frac{A c^{2} e^{2}}{7} + \frac{2 B b c e^{2}}{7} + \frac{2 B c^{2} d e}{7}\right) + x^{6} \left(\frac{A b c e^{2}}{3} + \frac{A c^{2} d e}{3} + \frac{B b^{2} e^{2}}{6} + \frac{2 B b c d e}{3} + \frac{B c^{2} d^{2}}{6}\right) + x^{5} \left(\frac{A b^{2} e^{2}}{5} + \frac{4 A b c d e}{5} + \frac{A c^{2} d^{2}}{5} + \frac{2 B b^{2} d e}{5} + \frac{2 B b c d^{2}}{5}\right) + x^{4} \left(\frac{A b^{2} d e}{2} + \frac{A b c d^{2}}{2} + \frac{B b^{2} d^{2}}{4}\right)"," ",0,"A*b**2*d**2*x**3/3 + B*c**2*e**2*x**8/8 + x**7*(A*c**2*e**2/7 + 2*B*b*c*e**2/7 + 2*B*c**2*d*e/7) + x**6*(A*b*c*e**2/3 + A*c**2*d*e/3 + B*b**2*e**2/6 + 2*B*b*c*d*e/3 + B*c**2*d**2/6) + x**5*(A*b**2*e**2/5 + 4*A*b*c*d*e/5 + A*c**2*d**2/5 + 2*B*b**2*d*e/5 + 2*B*b*c*d**2/5) + x**4*(A*b**2*d*e/2 + A*b*c*d**2/2 + B*b**2*d**2/4)","A",0
1117,1,121,0,0.085675," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x)**2,x)","\frac{A b^{2} d x^{3}}{3} + \frac{B c^{2} e x^{7}}{7} + x^{6} \left(\frac{A c^{2} e}{6} + \frac{B b c e}{3} + \frac{B c^{2} d}{6}\right) + x^{5} \left(\frac{2 A b c e}{5} + \frac{A c^{2} d}{5} + \frac{B b^{2} e}{5} + \frac{2 B b c d}{5}\right) + x^{4} \left(\frac{A b^{2} e}{4} + \frac{A b c d}{2} + \frac{B b^{2} d}{4}\right)"," ",0,"A*b**2*d*x**3/3 + B*c**2*e*x**7/7 + x**6*(A*c**2*e/6 + B*b*c*e/3 + B*c**2*d/6) + x**5*(2*A*b*c*e/5 + A*c**2*d/5 + B*b**2*e/5 + 2*B*b*c*d/5) + x**4*(A*b**2*e/4 + A*b*c*d/2 + B*b**2*d/4)","A",0
1118,1,54,0,0.076211," ","integrate((B*x+A)*(c*x**2+b*x)**2,x)","\frac{A b^{2} x^{3}}{3} + \frac{B c^{2} x^{6}}{6} + x^{5} \left(\frac{A c^{2}}{5} + \frac{2 B b c}{5}\right) + x^{4} \left(\frac{A b c}{2} + \frac{B b^{2}}{4}\right)"," ",0,"A*b**2*x**3/3 + B*c**2*x**6/6 + x**5*(A*c**2/5 + 2*B*b*c/5) + x**4*(A*b*c/2 + B*b**2/4)","A",0
1119,1,280,0,0.621075," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d),x)","\frac{B c^{2} x^{5}}{5 e} - \frac{d^{2} \left(- A e + B d\right) \left(b e - c d\right)^{2} \log{\left(d + e x \right)}}{e^{6}} + x^{4} \left(\frac{A c^{2}}{4 e} + \frac{B b c}{2 e} - \frac{B c^{2} d}{4 e^{2}}\right) + x^{3} \left(\frac{2 A b c}{3 e} - \frac{A c^{2} d}{3 e^{2}} + \frac{B b^{2}}{3 e} - \frac{2 B b c d}{3 e^{2}} + \frac{B c^{2} d^{2}}{3 e^{3}}\right) + x^{2} \left(\frac{A b^{2}}{2 e} - \frac{A b c d}{e^{2}} + \frac{A c^{2} d^{2}}{2 e^{3}} - \frac{B b^{2} d}{2 e^{2}} + \frac{B b c d^{2}}{e^{3}} - \frac{B c^{2} d^{3}}{2 e^{4}}\right) + x \left(- \frac{A b^{2} d}{e^{2}} + \frac{2 A b c d^{2}}{e^{3}} - \frac{A c^{2} d^{3}}{e^{4}} + \frac{B b^{2} d^{2}}{e^{3}} - \frac{2 B b c d^{3}}{e^{4}} + \frac{B c^{2} d^{4}}{e^{5}}\right)"," ",0,"B*c**2*x**5/(5*e) - d**2*(-A*e + B*d)*(b*e - c*d)**2*log(d + e*x)/e**6 + x**4*(A*c**2/(4*e) + B*b*c/(2*e) - B*c**2*d/(4*e**2)) + x**3*(2*A*b*c/(3*e) - A*c**2*d/(3*e**2) + B*b**2/(3*e) - 2*B*b*c*d/(3*e**2) + B*c**2*d**2/(3*e**3)) + x**2*(A*b**2/(2*e) - A*b*c*d/e**2 + A*c**2*d**2/(2*e**3) - B*b**2*d/(2*e**2) + B*b*c*d**2/e**3 - B*c**2*d**3/(2*e**4)) + x*(-A*b**2*d/e**2 + 2*A*b*c*d**2/e**3 - A*c**2*d**3/e**4 + B*b**2*d**2/e**3 - 2*B*b*c*d**3/e**4 + B*c**2*d**4/e**5)","A",0
1120,1,316,0,1.386375," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**2,x)","\frac{B c^{2} x^{4}}{4 e^{2}} + \frac{d \left(b e - c d\right) \left(- 2 A b e^{2} + 4 A c d e + 3 B b d e - 5 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{6}} + x^{3} \left(\frac{A c^{2}}{3 e^{2}} + \frac{2 B b c}{3 e^{2}} - \frac{2 B c^{2} d}{3 e^{3}}\right) + x^{2} \left(\frac{A b c}{e^{2}} - \frac{A c^{2} d}{e^{3}} + \frac{B b^{2}}{2 e^{2}} - \frac{2 B b c d}{e^{3}} + \frac{3 B c^{2} d^{2}}{2 e^{4}}\right) + x \left(\frac{A b^{2}}{e^{2}} - \frac{4 A b c d}{e^{3}} + \frac{3 A c^{2} d^{2}}{e^{4}} - \frac{2 B b^{2} d}{e^{3}} + \frac{6 B b c d^{2}}{e^{4}} - \frac{4 B c^{2} d^{3}}{e^{5}}\right) + \frac{- A b^{2} d^{2} e^{3} + 2 A b c d^{3} e^{2} - A c^{2} d^{4} e + B b^{2} d^{3} e^{2} - 2 B b c d^{4} e + B c^{2} d^{5}}{d e^{6} + e^{7} x}"," ",0,"B*c**2*x**4/(4*e**2) + d*(b*e - c*d)*(-2*A*b*e**2 + 4*A*c*d*e + 3*B*b*d*e - 5*B*c*d**2)*log(d + e*x)/e**6 + x**3*(A*c**2/(3*e**2) + 2*B*b*c/(3*e**2) - 2*B*c**2*d/(3*e**3)) + x**2*(A*b*c/e**2 - A*c**2*d/e**3 + B*b**2/(2*e**2) - 2*B*b*c*d/e**3 + 3*B*c**2*d**2/(2*e**4)) + x*(A*b**2/e**2 - 4*A*b*c*d/e**3 + 3*A*c**2*d**2/e**4 - 2*B*b**2*d/e**3 + 6*B*b*c*d**2/e**4 - 4*B*c**2*d**3/e**5) + (-A*b**2*d**2*e**3 + 2*A*b*c*d**3*e**2 - A*c**2*d**4*e + B*b**2*d**3*e**2 - 2*B*b*c*d**4*e + B*c**2*d**5)/(d*e**6 + e**7*x)","A",0
1121,1,362,0,4.072225," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**3,x)","\frac{B c^{2} x^{3}}{3 e^{3}} + x^{2} \left(\frac{A c^{2}}{2 e^{3}} + \frac{B b c}{e^{3}} - \frac{3 B c^{2} d}{2 e^{4}}\right) + x \left(\frac{2 A b c}{e^{3}} - \frac{3 A c^{2} d}{e^{4}} + \frac{B b^{2}}{e^{3}} - \frac{6 B b c d}{e^{4}} + \frac{6 B c^{2} d^{2}}{e^{5}}\right) + \frac{3 A b^{2} d^{2} e^{3} - 10 A b c d^{3} e^{2} + 7 A c^{2} d^{4} e - 5 B b^{2} d^{3} e^{2} + 14 B b c d^{4} e - 9 B c^{2} d^{5} + x \left(4 A b^{2} d e^{4} - 12 A b c d^{2} e^{3} + 8 A c^{2} d^{3} e^{2} - 6 B b^{2} d^{2} e^{3} + 16 B b c d^{3} e^{2} - 10 B c^{2} d^{4} e\right)}{2 d^{2} e^{6} + 4 d e^{7} x + 2 e^{8} x^{2}} - \frac{\left(- A b^{2} e^{3} + 6 A b c d e^{2} - 6 A c^{2} d^{2} e + 3 B b^{2} d e^{2} - 12 B b c d^{2} e + 10 B c^{2} d^{3}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**3/(3*e**3) + x**2*(A*c**2/(2*e**3) + B*b*c/e**3 - 3*B*c**2*d/(2*e**4)) + x*(2*A*b*c/e**3 - 3*A*c**2*d/e**4 + B*b**2/e**3 - 6*B*b*c*d/e**4 + 6*B*c**2*d**2/e**5) + (3*A*b**2*d**2*e**3 - 10*A*b*c*d**3*e**2 + 7*A*c**2*d**4*e - 5*B*b**2*d**3*e**2 + 14*B*b*c*d**4*e - 9*B*c**2*d**5 + x*(4*A*b**2*d*e**4 - 12*A*b*c*d**2*e**3 + 8*A*c**2*d**3*e**2 - 6*B*b**2*d**2*e**3 + 16*B*b*c*d**3*e**2 - 10*B*c**2*d**4*e))/(2*d**2*e**6 + 4*d*e**7*x + 2*e**8*x**2) - (-A*b**2*e**3 + 6*A*b*c*d*e**2 - 6*A*c**2*d**2*e + 3*B*b**2*d*e**2 - 12*B*b*c*d**2*e + 10*B*c**2*d**3)*log(d + e*x)/e**6","A",0
1122,1,374,0,11.733181," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**4,x)","\frac{B c^{2} x^{2}}{2 e^{4}} + x \left(\frac{A c^{2}}{e^{4}} + \frac{2 B b c}{e^{4}} - \frac{4 B c^{2} d}{e^{5}}\right) + \frac{- 2 A b^{2} d^{2} e^{3} + 22 A b c d^{3} e^{2} - 26 A c^{2} d^{4} e + 11 B b^{2} d^{3} e^{2} - 52 B b c d^{4} e + 47 B c^{2} d^{5} + x^{2} \left(- 6 A b^{2} e^{5} + 36 A b c d e^{4} - 36 A c^{2} d^{2} e^{3} + 18 B b^{2} d e^{4} - 72 B b c d^{2} e^{3} + 60 B c^{2} d^{3} e^{2}\right) + x \left(- 6 A b^{2} d e^{4} + 54 A b c d^{2} e^{3} - 60 A c^{2} d^{3} e^{2} + 27 B b^{2} d^{2} e^{3} - 120 B b c d^{3} e^{2} + 105 B c^{2} d^{4} e\right)}{6 d^{3} e^{6} + 18 d^{2} e^{7} x + 18 d e^{8} x^{2} + 6 e^{9} x^{3}} + \frac{\left(2 A b c e^{2} - 4 A c^{2} d e + B b^{2} e^{2} - 8 B b c d e + 10 B c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**2/(2*e**4) + x*(A*c**2/e**4 + 2*B*b*c/e**4 - 4*B*c**2*d/e**5) + (-2*A*b**2*d**2*e**3 + 22*A*b*c*d**3*e**2 - 26*A*c**2*d**4*e + 11*B*b**2*d**3*e**2 - 52*B*b*c*d**4*e + 47*B*c**2*d**5 + x**2*(-6*A*b**2*e**5 + 36*A*b*c*d*e**4 - 36*A*c**2*d**2*e**3 + 18*B*b**2*d*e**4 - 72*B*b*c*d**2*e**3 + 60*B*c**2*d**3*e**2) + x*(-6*A*b**2*d*e**4 + 54*A*b*c*d**2*e**3 - 60*A*c**2*d**3*e**2 + 27*B*b**2*d**2*e**3 - 120*B*b*c*d**3*e**2 + 105*B*c**2*d**4*e))/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + (2*A*b*c*e**2 - 4*A*c**2*d*e + B*b**2*e**2 - 8*B*b*c*d*e + 10*B*c**2*d**2)*log(d + e*x)/e**6","A",0
1123,1,381,0,32.260200," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**5,x)","\frac{B c^{2} x}{e^{5}} + \frac{c \left(A c e + 2 B b e - 5 B c d\right) \log{\left(d + e x \right)}}{e^{6}} + \frac{- A b^{2} d^{2} e^{3} - 6 A b c d^{3} e^{2} + 25 A c^{2} d^{4} e - 3 B b^{2} d^{3} e^{2} + 50 B b c d^{4} e - 77 B c^{2} d^{5} + x^{3} \left(- 24 A b c e^{5} + 48 A c^{2} d e^{4} - 12 B b^{2} e^{5} + 96 B b c d e^{4} - 120 B c^{2} d^{2} e^{3}\right) + x^{2} \left(- 6 A b^{2} e^{5} - 36 A b c d e^{4} + 108 A c^{2} d^{2} e^{3} - 18 B b^{2} d e^{4} + 216 B b c d^{2} e^{3} - 300 B c^{2} d^{3} e^{2}\right) + x \left(- 4 A b^{2} d e^{4} - 24 A b c d^{2} e^{3} + 88 A c^{2} d^{3} e^{2} - 12 B b^{2} d^{2} e^{3} + 176 B b c d^{3} e^{2} - 260 B c^{2} d^{4} e\right)}{12 d^{4} e^{6} + 48 d^{3} e^{7} x + 72 d^{2} e^{8} x^{2} + 48 d e^{9} x^{3} + 12 e^{10} x^{4}}"," ",0,"B*c**2*x/e**5 + c*(A*c*e + 2*B*b*e - 5*B*c*d)*log(d + e*x)/e**6 + (-A*b**2*d**2*e**3 - 6*A*b*c*d**3*e**2 + 25*A*c**2*d**4*e - 3*B*b**2*d**3*e**2 + 50*B*b*c*d**4*e - 77*B*c**2*d**5 + x**3*(-24*A*b*c*e**5 + 48*A*c**2*d*e**4 - 12*B*b**2*e**5 + 96*B*b*c*d*e**4 - 120*B*c**2*d**2*e**3) + x**2*(-6*A*b**2*e**5 - 36*A*b*c*d*e**4 + 108*A*c**2*d**2*e**3 - 18*B*b**2*d*e**4 + 216*B*b*c*d**2*e**3 - 300*B*c**2*d**3*e**2) + x*(-4*A*b**2*d*e**4 - 24*A*b*c*d**2*e**3 + 88*A*c**2*d**3*e**2 - 12*B*b**2*d**2*e**3 + 176*B*b*c*d**3*e**2 - 260*B*c**2*d**4*e))/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4)","A",0
1124,1,405,0,94.462493," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**6,x)","\frac{B c^{2} \log{\left(d + e x \right)}}{e^{6}} + \frac{- 2 A b^{2} d^{2} e^{3} - 6 A b c d^{3} e^{2} - 12 A c^{2} d^{4} e - 3 B b^{2} d^{3} e^{2} - 24 B b c d^{4} e + 137 B c^{2} d^{5} + x^{4} \left(- 60 A c^{2} e^{5} - 120 B b c e^{5} + 300 B c^{2} d e^{4}\right) + x^{3} \left(- 60 A b c e^{5} - 120 A c^{2} d e^{4} - 30 B b^{2} e^{5} - 240 B b c d e^{4} + 900 B c^{2} d^{2} e^{3}\right) + x^{2} \left(- 20 A b^{2} e^{5} - 60 A b c d e^{4} - 120 A c^{2} d^{2} e^{3} - 30 B b^{2} d e^{4} - 240 B b c d^{2} e^{3} + 1100 B c^{2} d^{3} e^{2}\right) + x \left(- 10 A b^{2} d e^{4} - 30 A b c d^{2} e^{3} - 60 A c^{2} d^{3} e^{2} - 15 B b^{2} d^{2} e^{3} - 120 B b c d^{3} e^{2} + 625 B c^{2} d^{4} e\right)}{60 d^{5} e^{6} + 300 d^{4} e^{7} x + 600 d^{3} e^{8} x^{2} + 600 d^{2} e^{9} x^{3} + 300 d e^{10} x^{4} + 60 e^{11} x^{5}}"," ",0,"B*c**2*log(d + e*x)/e**6 + (-2*A*b**2*d**2*e**3 - 6*A*b*c*d**3*e**2 - 12*A*c**2*d**4*e - 3*B*b**2*d**3*e**2 - 24*B*b*c*d**4*e + 137*B*c**2*d**5 + x**4*(-60*A*c**2*e**5 - 120*B*b*c*e**5 + 300*B*c**2*d*e**4) + x**3*(-60*A*b*c*e**5 - 120*A*c**2*d*e**4 - 30*B*b**2*e**5 - 240*B*b*c*d*e**4 + 900*B*c**2*d**2*e**3) + x**2*(-20*A*b**2*e**5 - 60*A*b*c*d*e**4 - 120*A*c**2*d**2*e**3 - 30*B*b**2*d*e**4 - 240*B*b*c*d**2*e**3 + 1100*B*c**2*d**3*e**2) + x*(-10*A*b**2*d*e**4 - 30*A*b*c*d**2*e**3 - 60*A*c**2*d**3*e**2 - 15*B*b**2*d**2*e**3 - 120*B*b*c*d**3*e**2 + 625*B*c**2*d**4*e))/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5)","A",0
1125,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1127,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1128,1,564,0,0.147378," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+b*x)**3,x)","\frac{A b^{3} d^{4} x^{4}}{4} + \frac{B c^{3} e^{4} x^{12}}{12} + x^{11} \left(\frac{A c^{3} e^{4}}{11} + \frac{3 B b c^{2} e^{4}}{11} + \frac{4 B c^{3} d e^{3}}{11}\right) + x^{10} \left(\frac{3 A b c^{2} e^{4}}{10} + \frac{2 A c^{3} d e^{3}}{5} + \frac{3 B b^{2} c e^{4}}{10} + \frac{6 B b c^{2} d e^{3}}{5} + \frac{3 B c^{3} d^{2} e^{2}}{5}\right) + x^{9} \left(\frac{A b^{2} c e^{4}}{3} + \frac{4 A b c^{2} d e^{3}}{3} + \frac{2 A c^{3} d^{2} e^{2}}{3} + \frac{B b^{3} e^{4}}{9} + \frac{4 B b^{2} c d e^{3}}{3} + 2 B b c^{2} d^{2} e^{2} + \frac{4 B c^{3} d^{3} e}{9}\right) + x^{8} \left(\frac{A b^{3} e^{4}}{8} + \frac{3 A b^{2} c d e^{3}}{2} + \frac{9 A b c^{2} d^{2} e^{2}}{4} + \frac{A c^{3} d^{3} e}{2} + \frac{B b^{3} d e^{3}}{2} + \frac{9 B b^{2} c d^{2} e^{2}}{4} + \frac{3 B b c^{2} d^{3} e}{2} + \frac{B c^{3} d^{4}}{8}\right) + x^{7} \left(\frac{4 A b^{3} d e^{3}}{7} + \frac{18 A b^{2} c d^{2} e^{2}}{7} + \frac{12 A b c^{2} d^{3} e}{7} + \frac{A c^{3} d^{4}}{7} + \frac{6 B b^{3} d^{2} e^{2}}{7} + \frac{12 B b^{2} c d^{3} e}{7} + \frac{3 B b c^{2} d^{4}}{7}\right) + x^{6} \left(A b^{3} d^{2} e^{2} + 2 A b^{2} c d^{3} e + \frac{A b c^{2} d^{4}}{2} + \frac{2 B b^{3} d^{3} e}{3} + \frac{B b^{2} c d^{4}}{2}\right) + x^{5} \left(\frac{4 A b^{3} d^{3} e}{5} + \frac{3 A b^{2} c d^{4}}{5} + \frac{B b^{3} d^{4}}{5}\right)"," ",0,"A*b**3*d**4*x**4/4 + B*c**3*e**4*x**12/12 + x**11*(A*c**3*e**4/11 + 3*B*b*c**2*e**4/11 + 4*B*c**3*d*e**3/11) + x**10*(3*A*b*c**2*e**4/10 + 2*A*c**3*d*e**3/5 + 3*B*b**2*c*e**4/10 + 6*B*b*c**2*d*e**3/5 + 3*B*c**3*d**2*e**2/5) + x**9*(A*b**2*c*e**4/3 + 4*A*b*c**2*d*e**3/3 + 2*A*c**3*d**2*e**2/3 + B*b**3*e**4/9 + 4*B*b**2*c*d*e**3/3 + 2*B*b*c**2*d**2*e**2 + 4*B*c**3*d**3*e/9) + x**8*(A*b**3*e**4/8 + 3*A*b**2*c*d*e**3/2 + 9*A*b*c**2*d**2*e**2/4 + A*c**3*d**3*e/2 + B*b**3*d*e**3/2 + 9*B*b**2*c*d**2*e**2/4 + 3*B*b*c**2*d**3*e/2 + B*c**3*d**4/8) + x**7*(4*A*b**3*d*e**3/7 + 18*A*b**2*c*d**2*e**2/7 + 12*A*b*c**2*d**3*e/7 + A*c**3*d**4/7 + 6*B*b**3*d**2*e**2/7 + 12*B*b**2*c*d**3*e/7 + 3*B*b*c**2*d**4/7) + x**6*(A*b**3*d**2*e**2 + 2*A*b**2*c*d**3*e + A*b*c**2*d**4/2 + 2*B*b**3*d**3*e/3 + B*b**2*c*d**4/2) + x**5*(4*A*b**3*d**3*e/5 + 3*A*b**2*c*d**4/5 + B*b**3*d**4/5)","A",0
1129,1,430,0,0.131250," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x)**3,x)","\frac{A b^{3} d^{3} x^{4}}{4} + \frac{B c^{3} e^{3} x^{11}}{11} + x^{10} \left(\frac{A c^{3} e^{3}}{10} + \frac{3 B b c^{2} e^{3}}{10} + \frac{3 B c^{3} d e^{2}}{10}\right) + x^{9} \left(\frac{A b c^{2} e^{3}}{3} + \frac{A c^{3} d e^{2}}{3} + \frac{B b^{2} c e^{3}}{3} + B b c^{2} d e^{2} + \frac{B c^{3} d^{2} e}{3}\right) + x^{8} \left(\frac{3 A b^{2} c e^{3}}{8} + \frac{9 A b c^{2} d e^{2}}{8} + \frac{3 A c^{3} d^{2} e}{8} + \frac{B b^{3} e^{3}}{8} + \frac{9 B b^{2} c d e^{2}}{8} + \frac{9 B b c^{2} d^{2} e}{8} + \frac{B c^{3} d^{3}}{8}\right) + x^{7} \left(\frac{A b^{3} e^{3}}{7} + \frac{9 A b^{2} c d e^{2}}{7} + \frac{9 A b c^{2} d^{2} e}{7} + \frac{A c^{3} d^{3}}{7} + \frac{3 B b^{3} d e^{2}}{7} + \frac{9 B b^{2} c d^{2} e}{7} + \frac{3 B b c^{2} d^{3}}{7}\right) + x^{6} \left(\frac{A b^{3} d e^{2}}{2} + \frac{3 A b^{2} c d^{2} e}{2} + \frac{A b c^{2} d^{3}}{2} + \frac{B b^{3} d^{2} e}{2} + \frac{B b^{2} c d^{3}}{2}\right) + x^{5} \left(\frac{3 A b^{3} d^{2} e}{5} + \frac{3 A b^{2} c d^{3}}{5} + \frac{B b^{3} d^{3}}{5}\right)"," ",0,"A*b**3*d**3*x**4/4 + B*c**3*e**3*x**11/11 + x**10*(A*c**3*e**3/10 + 3*B*b*c**2*e**3/10 + 3*B*c**3*d*e**2/10) + x**9*(A*b*c**2*e**3/3 + A*c**3*d*e**2/3 + B*b**2*c*e**3/3 + B*b*c**2*d*e**2 + B*c**3*d**2*e/3) + x**8*(3*A*b**2*c*e**3/8 + 9*A*b*c**2*d*e**2/8 + 3*A*c**3*d**2*e/8 + B*b**3*e**3/8 + 9*B*b**2*c*d*e**2/8 + 9*B*b*c**2*d**2*e/8 + B*c**3*d**3/8) + x**7*(A*b**3*e**3/7 + 9*A*b**2*c*d*e**2/7 + 9*A*b*c**2*d**2*e/7 + A*c**3*d**3/7 + 3*B*b**3*d*e**2/7 + 9*B*b**2*c*d**2*e/7 + 3*B*b*c**2*d**3/7) + x**6*(A*b**3*d*e**2/2 + 3*A*b**2*c*d**2*e/2 + A*b*c**2*d**3/2 + B*b**3*d**2*e/2 + B*b**2*c*d**3/2) + x**5*(3*A*b**3*d**2*e/5 + 3*A*b**2*c*d**3/5 + B*b**3*d**3/5)","A",0
1130,1,303,0,0.114692," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x)**3,x)","\frac{A b^{3} d^{2} x^{4}}{4} + \frac{B c^{3} e^{2} x^{10}}{10} + x^{9} \left(\frac{A c^{3} e^{2}}{9} + \frac{B b c^{2} e^{2}}{3} + \frac{2 B c^{3} d e}{9}\right) + x^{8} \left(\frac{3 A b c^{2} e^{2}}{8} + \frac{A c^{3} d e}{4} + \frac{3 B b^{2} c e^{2}}{8} + \frac{3 B b c^{2} d e}{4} + \frac{B c^{3} d^{2}}{8}\right) + x^{7} \left(\frac{3 A b^{2} c e^{2}}{7} + \frac{6 A b c^{2} d e}{7} + \frac{A c^{3} d^{2}}{7} + \frac{B b^{3} e^{2}}{7} + \frac{6 B b^{2} c d e}{7} + \frac{3 B b c^{2} d^{2}}{7}\right) + x^{6} \left(\frac{A b^{3} e^{2}}{6} + A b^{2} c d e + \frac{A b c^{2} d^{2}}{2} + \frac{B b^{3} d e}{3} + \frac{B b^{2} c d^{2}}{2}\right) + x^{5} \left(\frac{2 A b^{3} d e}{5} + \frac{3 A b^{2} c d^{2}}{5} + \frac{B b^{3} d^{2}}{5}\right)"," ",0,"A*b**3*d**2*x**4/4 + B*c**3*e**2*x**10/10 + x**9*(A*c**3*e**2/9 + B*b*c**2*e**2/3 + 2*B*c**3*d*e/9) + x**8*(3*A*b*c**2*e**2/8 + A*c**3*d*e/4 + 3*B*b**2*c*e**2/8 + 3*B*b*c**2*d*e/4 + B*c**3*d**2/8) + x**7*(3*A*b**2*c*e**2/7 + 6*A*b*c**2*d*e/7 + A*c**3*d**2/7 + B*b**3*e**2/7 + 6*B*b**2*c*d*e/7 + 3*B*b*c**2*d**2/7) + x**6*(A*b**3*e**2/6 + A*b**2*c*d*e + A*b*c**2*d**2/2 + B*b**3*d*e/3 + B*b**2*c*d**2/2) + x**5*(2*A*b**3*d*e/5 + 3*A*b**2*c*d**2/5 + B*b**3*d**2/5)","A",0
1131,1,177,0,0.094115," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x)**3,x)","\frac{A b^{3} d x^{4}}{4} + \frac{B c^{3} e x^{9}}{9} + x^{8} \left(\frac{A c^{3} e}{8} + \frac{3 B b c^{2} e}{8} + \frac{B c^{3} d}{8}\right) + x^{7} \left(\frac{3 A b c^{2} e}{7} + \frac{A c^{3} d}{7} + \frac{3 B b^{2} c e}{7} + \frac{3 B b c^{2} d}{7}\right) + x^{6} \left(\frac{A b^{2} c e}{2} + \frac{A b c^{2} d}{2} + \frac{B b^{3} e}{6} + \frac{B b^{2} c d}{2}\right) + x^{5} \left(\frac{A b^{3} e}{5} + \frac{3 A b^{2} c d}{5} + \frac{B b^{3} d}{5}\right)"," ",0,"A*b**3*d*x**4/4 + B*c**3*e*x**9/9 + x**8*(A*c**3*e/8 + 3*B*b*c**2*e/8 + B*c**3*d/8) + x**7*(3*A*b*c**2*e/7 + A*c**3*d/7 + 3*B*b**2*c*e/7 + 3*B*b*c**2*d/7) + x**6*(A*b**2*c*e/2 + A*b*c**2*d/2 + B*b**3*e/6 + B*b**2*c*d/2) + x**5*(A*b**3*e/5 + 3*A*b**2*c*d/5 + B*b**3*d/5)","A",0
1132,1,80,0,0.082593," ","integrate((B*x+A)*(c*x**2+b*x)**3,x)","\frac{A b^{3} x^{4}}{4} + \frac{B c^{3} x^{8}}{8} + x^{7} \left(\frac{A c^{3}}{7} + \frac{3 B b c^{2}}{7}\right) + x^{6} \left(\frac{A b c^{2}}{2} + \frac{B b^{2} c}{2}\right) + x^{5} \left(\frac{3 A b^{2} c}{5} + \frac{B b^{3}}{5}\right)"," ",0,"A*b**3*x**4/4 + B*c**3*x**8/8 + x**7*(A*c**3/7 + 3*B*b*c**2/7) + x**6*(A*b*c**2/2 + B*b**2*c/2) + x**5*(3*A*b**2*c/5 + B*b**3/5)","A",0
1133,1,578,0,1.007904," ","integrate((B*x+A)*(c*x**2+b*x)**3/(e*x+d),x)","\frac{B c^{3} x^{7}}{7 e} + \frac{d^{3} \left(- A e + B d\right) \left(b e - c d\right)^{3} \log{\left(d + e x \right)}}{e^{8}} + x^{6} \left(\frac{A c^{3}}{6 e} + \frac{B b c^{2}}{2 e} - \frac{B c^{3} d}{6 e^{2}}\right) + x^{5} \left(\frac{3 A b c^{2}}{5 e} - \frac{A c^{3} d}{5 e^{2}} + \frac{3 B b^{2} c}{5 e} - \frac{3 B b c^{2} d}{5 e^{2}} + \frac{B c^{3} d^{2}}{5 e^{3}}\right) + x^{4} \left(\frac{3 A b^{2} c}{4 e} - \frac{3 A b c^{2} d}{4 e^{2}} + \frac{A c^{3} d^{2}}{4 e^{3}} + \frac{B b^{3}}{4 e} - \frac{3 B b^{2} c d}{4 e^{2}} + \frac{3 B b c^{2} d^{2}}{4 e^{3}} - \frac{B c^{3} d^{3}}{4 e^{4}}\right) + x^{3} \left(\frac{A b^{3}}{3 e} - \frac{A b^{2} c d}{e^{2}} + \frac{A b c^{2} d^{2}}{e^{3}} - \frac{A c^{3} d^{3}}{3 e^{4}} - \frac{B b^{3} d}{3 e^{2}} + \frac{B b^{2} c d^{2}}{e^{3}} - \frac{B b c^{2} d^{3}}{e^{4}} + \frac{B c^{3} d^{4}}{3 e^{5}}\right) + x^{2} \left(- \frac{A b^{3} d}{2 e^{2}} + \frac{3 A b^{2} c d^{2}}{2 e^{3}} - \frac{3 A b c^{2} d^{3}}{2 e^{4}} + \frac{A c^{3} d^{4}}{2 e^{5}} + \frac{B b^{3} d^{2}}{2 e^{3}} - \frac{3 B b^{2} c d^{3}}{2 e^{4}} + \frac{3 B b c^{2} d^{4}}{2 e^{5}} - \frac{B c^{3} d^{5}}{2 e^{6}}\right) + x \left(\frac{A b^{3} d^{2}}{e^{3}} - \frac{3 A b^{2} c d^{3}}{e^{4}} + \frac{3 A b c^{2} d^{4}}{e^{5}} - \frac{A c^{3} d^{5}}{e^{6}} - \frac{B b^{3} d^{3}}{e^{4}} + \frac{3 B b^{2} c d^{4}}{e^{5}} - \frac{3 B b c^{2} d^{5}}{e^{6}} + \frac{B c^{3} d^{6}}{e^{7}}\right)"," ",0,"B*c**3*x**7/(7*e) + d**3*(-A*e + B*d)*(b*e - c*d)**3*log(d + e*x)/e**8 + x**6*(A*c**3/(6*e) + B*b*c**2/(2*e) - B*c**3*d/(6*e**2)) + x**5*(3*A*b*c**2/(5*e) - A*c**3*d/(5*e**2) + 3*B*b**2*c/(5*e) - 3*B*b*c**2*d/(5*e**2) + B*c**3*d**2/(5*e**3)) + x**4*(3*A*b**2*c/(4*e) - 3*A*b*c**2*d/(4*e**2) + A*c**3*d**2/(4*e**3) + B*b**3/(4*e) - 3*B*b**2*c*d/(4*e**2) + 3*B*b*c**2*d**2/(4*e**3) - B*c**3*d**3/(4*e**4)) + x**3*(A*b**3/(3*e) - A*b**2*c*d/e**2 + A*b*c**2*d**2/e**3 - A*c**3*d**3/(3*e**4) - B*b**3*d/(3*e**2) + B*b**2*c*d**2/e**3 - B*b*c**2*d**3/e**4 + B*c**3*d**4/(3*e**5)) + x**2*(-A*b**3*d/(2*e**2) + 3*A*b**2*c*d**2/(2*e**3) - 3*A*b*c**2*d**3/(2*e**4) + A*c**3*d**4/(2*e**5) + B*b**3*d**2/(2*e**3) - 3*B*b**2*c*d**3/(2*e**4) + 3*B*b*c**2*d**4/(2*e**5) - B*c**3*d**5/(2*e**6)) + x*(A*b**3*d**2/e**3 - 3*A*b**2*c*d**3/e**4 + 3*A*b*c**2*d**4/e**5 - A*c**3*d**5/e**6 - B*b**3*d**3/e**4 + 3*B*b**2*c*d**4/e**5 - 3*B*b*c**2*d**5/e**6 + B*c**3*d**6/e**7)","B",0
1134,1,619,0,2.288209," ","integrate((B*x+A)*(c*x**2+b*x)**3/(e*x+d)**2,x)","\frac{B c^{3} x^{6}}{6 e^{2}} - \frac{d^{2} \left(b e - c d\right)^{2} \left(- 3 A b e^{2} + 6 A c d e + 4 B b d e - 7 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{8}} + x^{5} \left(\frac{A c^{3}}{5 e^{2}} + \frac{3 B b c^{2}}{5 e^{2}} - \frac{2 B c^{3} d}{5 e^{3}}\right) + x^{4} \left(\frac{3 A b c^{2}}{4 e^{2}} - \frac{A c^{3} d}{2 e^{3}} + \frac{3 B b^{2} c}{4 e^{2}} - \frac{3 B b c^{2} d}{2 e^{3}} + \frac{3 B c^{3} d^{2}}{4 e^{4}}\right) + x^{3} \left(\frac{A b^{2} c}{e^{2}} - \frac{2 A b c^{2} d}{e^{3}} + \frac{A c^{3} d^{2}}{e^{4}} + \frac{B b^{3}}{3 e^{2}} - \frac{2 B b^{2} c d}{e^{3}} + \frac{3 B b c^{2} d^{2}}{e^{4}} - \frac{4 B c^{3} d^{3}}{3 e^{5}}\right) + x^{2} \left(\frac{A b^{3}}{2 e^{2}} - \frac{3 A b^{2} c d}{e^{3}} + \frac{9 A b c^{2} d^{2}}{2 e^{4}} - \frac{2 A c^{3} d^{3}}{e^{5}} - \frac{B b^{3} d}{e^{3}} + \frac{9 B b^{2} c d^{2}}{2 e^{4}} - \frac{6 B b c^{2} d^{3}}{e^{5}} + \frac{5 B c^{3} d^{4}}{2 e^{6}}\right) + x \left(- \frac{2 A b^{3} d}{e^{3}} + \frac{9 A b^{2} c d^{2}}{e^{4}} - \frac{12 A b c^{2} d^{3}}{e^{5}} + \frac{5 A c^{3} d^{4}}{e^{6}} + \frac{3 B b^{3} d^{2}}{e^{4}} - \frac{12 B b^{2} c d^{3}}{e^{5}} + \frac{15 B b c^{2} d^{4}}{e^{6}} - \frac{6 B c^{3} d^{5}}{e^{7}}\right) + \frac{A b^{3} d^{3} e^{4} - 3 A b^{2} c d^{4} e^{3} + 3 A b c^{2} d^{5} e^{2} - A c^{3} d^{6} e - B b^{3} d^{4} e^{3} + 3 B b^{2} c d^{5} e^{2} - 3 B b c^{2} d^{6} e + B c^{3} d^{7}}{d e^{8} + e^{9} x}"," ",0,"B*c**3*x**6/(6*e**2) - d**2*(b*e - c*d)**2*(-3*A*b*e**2 + 6*A*c*d*e + 4*B*b*d*e - 7*B*c*d**2)*log(d + e*x)/e**8 + x**5*(A*c**3/(5*e**2) + 3*B*b*c**2/(5*e**2) - 2*B*c**3*d/(5*e**3)) + x**4*(3*A*b*c**2/(4*e**2) - A*c**3*d/(2*e**3) + 3*B*b**2*c/(4*e**2) - 3*B*b*c**2*d/(2*e**3) + 3*B*c**3*d**2/(4*e**4)) + x**3*(A*b**2*c/e**2 - 2*A*b*c**2*d/e**3 + A*c**3*d**2/e**4 + B*b**3/(3*e**2) - 2*B*b**2*c*d/e**3 + 3*B*b*c**2*d**2/e**4 - 4*B*c**3*d**3/(3*e**5)) + x**2*(A*b**3/(2*e**2) - 3*A*b**2*c*d/e**3 + 9*A*b*c**2*d**2/(2*e**4) - 2*A*c**3*d**3/e**5 - B*b**3*d/e**3 + 9*B*b**2*c*d**2/(2*e**4) - 6*B*b*c**2*d**3/e**5 + 5*B*c**3*d**4/(2*e**6)) + x*(-2*A*b**3*d/e**3 + 9*A*b**2*c*d**2/e**4 - 12*A*b*c**2*d**3/e**5 + 5*A*c**3*d**4/e**6 + 3*B*b**3*d**2/e**4 - 12*B*b**2*c*d**3/e**5 + 15*B*b*c**2*d**4/e**6 - 6*B*c**3*d**5/e**7) + (A*b**3*d**3*e**4 - 3*A*b**2*c*d**4*e**3 + 3*A*b*c**2*d**5*e**2 - A*c**3*d**6*e - B*b**3*d**4*e**3 + 3*B*b**2*c*d**5*e**2 - 3*B*b*c**2*d**6*e + B*c**3*d**7)/(d*e**8 + e**9*x)","B",0
1135,1,660,0,7.265541," ","integrate((B*x+A)*(c*x**2+b*x)**3/(e*x+d)**3,x)","\frac{B c^{3} x^{5}}{5 e^{3}} + \frac{3 d \left(b e - c d\right) \left(- A b^{2} e^{3} + 5 A b c d e^{2} - 5 A c^{2} d^{2} e + 2 B b^{2} d e^{2} - 8 B b c d^{2} e + 7 B c^{2} d^{3}\right) \log{\left(d + e x \right)}}{e^{8}} + x^{4} \left(\frac{A c^{3}}{4 e^{3}} + \frac{3 B b c^{2}}{4 e^{3}} - \frac{3 B c^{3} d}{4 e^{4}}\right) + x^{3} \left(\frac{A b c^{2}}{e^{3}} - \frac{A c^{3} d}{e^{4}} + \frac{B b^{2} c}{e^{3}} - \frac{3 B b c^{2} d}{e^{4}} + \frac{2 B c^{3} d^{2}}{e^{5}}\right) + x^{2} \left(\frac{3 A b^{2} c}{2 e^{3}} - \frac{9 A b c^{2} d}{2 e^{4}} + \frac{3 A c^{3} d^{2}}{e^{5}} + \frac{B b^{3}}{2 e^{3}} - \frac{9 B b^{2} c d}{2 e^{4}} + \frac{9 B b c^{2} d^{2}}{e^{5}} - \frac{5 B c^{3} d^{3}}{e^{6}}\right) + x \left(\frac{A b^{3}}{e^{3}} - \frac{9 A b^{2} c d}{e^{4}} + \frac{18 A b c^{2} d^{2}}{e^{5}} - \frac{10 A c^{3} d^{3}}{e^{6}} - \frac{3 B b^{3} d}{e^{4}} + \frac{18 B b^{2} c d^{2}}{e^{5}} - \frac{30 B b c^{2} d^{3}}{e^{6}} + \frac{15 B c^{3} d^{4}}{e^{7}}\right) + \frac{- 5 A b^{3} d^{3} e^{4} + 21 A b^{2} c d^{4} e^{3} - 27 A b c^{2} d^{5} e^{2} + 11 A c^{3} d^{6} e + 7 B b^{3} d^{4} e^{3} - 27 B b^{2} c d^{5} e^{2} + 33 B b c^{2} d^{6} e - 13 B c^{3} d^{7} + x \left(- 6 A b^{3} d^{2} e^{5} + 24 A b^{2} c d^{3} e^{4} - 30 A b c^{2} d^{4} e^{3} + 12 A c^{3} d^{5} e^{2} + 8 B b^{3} d^{3} e^{4} - 30 B b^{2} c d^{4} e^{3} + 36 B b c^{2} d^{5} e^{2} - 14 B c^{3} d^{6} e\right)}{2 d^{2} e^{8} + 4 d e^{9} x + 2 e^{10} x^{2}}"," ",0,"B*c**3*x**5/(5*e**3) + 3*d*(b*e - c*d)*(-A*b**2*e**3 + 5*A*b*c*d*e**2 - 5*A*c**2*d**2*e + 2*B*b**2*d*e**2 - 8*B*b*c*d**2*e + 7*B*c**2*d**3)*log(d + e*x)/e**8 + x**4*(A*c**3/(4*e**3) + 3*B*b*c**2/(4*e**3) - 3*B*c**3*d/(4*e**4)) + x**3*(A*b*c**2/e**3 - A*c**3*d/e**4 + B*b**2*c/e**3 - 3*B*b*c**2*d/e**4 + 2*B*c**3*d**2/e**5) + x**2*(3*A*b**2*c/(2*e**3) - 9*A*b*c**2*d/(2*e**4) + 3*A*c**3*d**2/e**5 + B*b**3/(2*e**3) - 9*B*b**2*c*d/(2*e**4) + 9*B*b*c**2*d**2/e**5 - 5*B*c**3*d**3/e**6) + x*(A*b**3/e**3 - 9*A*b**2*c*d/e**4 + 18*A*b*c**2*d**2/e**5 - 10*A*c**3*d**3/e**6 - 3*B*b**3*d/e**4 + 18*B*b**2*c*d**2/e**5 - 30*B*b*c**2*d**3/e**6 + 15*B*c**3*d**4/e**7) + (-5*A*b**3*d**3*e**4 + 21*A*b**2*c*d**4*e**3 - 27*A*b*c**2*d**5*e**2 + 11*A*c**3*d**6*e + 7*B*b**3*d**4*e**3 - 27*B*b**2*c*d**5*e**2 + 33*B*b*c**2*d**6*e - 13*B*c**3*d**7 + x*(-6*A*b**3*d**2*e**5 + 24*A*b**2*c*d**3*e**4 - 30*A*b*c**2*d**4*e**3 + 12*A*c**3*d**5*e**2 + 8*B*b**3*d**3*e**4 - 30*B*b**2*c*d**4*e**3 + 36*B*b*c**2*d**5*e**2 - 14*B*c**3*d**6*e))/(2*d**2*e**8 + 4*d*e**9*x + 2*e**10*x**2)","A",0
1136,1,700,0,23.064990," ","integrate((B*x+A)*(c*x**2+b*x)**3/(e*x+d)**4,x)","\frac{B c^{3} x^{4}}{4 e^{4}} + x^{3} \left(\frac{A c^{3}}{3 e^{4}} + \frac{B b c^{2}}{e^{4}} - \frac{4 B c^{3} d}{3 e^{5}}\right) + x^{2} \left(\frac{3 A b c^{2}}{2 e^{4}} - \frac{2 A c^{3} d}{e^{5}} + \frac{3 B b^{2} c}{2 e^{4}} - \frac{6 B b c^{2} d}{e^{5}} + \frac{5 B c^{3} d^{2}}{e^{6}}\right) + x \left(\frac{3 A b^{2} c}{e^{4}} - \frac{12 A b c^{2} d}{e^{5}} + \frac{10 A c^{3} d^{2}}{e^{6}} + \frac{B b^{3}}{e^{4}} - \frac{12 B b^{2} c d}{e^{5}} + \frac{30 B b c^{2} d^{2}}{e^{6}} - \frac{20 B c^{3} d^{3}}{e^{7}}\right) + \frac{11 A b^{3} d^{3} e^{4} - 78 A b^{2} c d^{4} e^{3} + 141 A b c^{2} d^{5} e^{2} - 74 A c^{3} d^{6} e - 26 B b^{3} d^{4} e^{3} + 141 B b^{2} c d^{5} e^{2} - 222 B b c^{2} d^{6} e + 107 B c^{3} d^{7} + x^{2} \left(18 A b^{3} d e^{6} - 108 A b^{2} c d^{2} e^{5} + 180 A b c^{2} d^{3} e^{4} - 90 A c^{3} d^{4} e^{3} - 36 B b^{3} d^{2} e^{5} + 180 B b^{2} c d^{3} e^{4} - 270 B b c^{2} d^{4} e^{3} + 126 B c^{3} d^{5} e^{2}\right) + x \left(27 A b^{3} d^{2} e^{5} - 180 A b^{2} c d^{3} e^{4} + 315 A b c^{2} d^{4} e^{3} - 162 A c^{3} d^{5} e^{2} - 60 B b^{3} d^{3} e^{4} + 315 B b^{2} c d^{4} e^{3} - 486 B b c^{2} d^{5} e^{2} + 231 B c^{3} d^{6} e\right)}{6 d^{3} e^{8} + 18 d^{2} e^{9} x + 18 d e^{10} x^{2} + 6 e^{11} x^{3}} - \frac{\left(- A b^{3} e^{4} + 12 A b^{2} c d e^{3} - 30 A b c^{2} d^{2} e^{2} + 20 A c^{3} d^{3} e + 4 B b^{3} d e^{3} - 30 B b^{2} c d^{2} e^{2} + 60 B b c^{2} d^{3} e - 35 B c^{3} d^{4}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"B*c**3*x**4/(4*e**4) + x**3*(A*c**3/(3*e**4) + B*b*c**2/e**4 - 4*B*c**3*d/(3*e**5)) + x**2*(3*A*b*c**2/(2*e**4) - 2*A*c**3*d/e**5 + 3*B*b**2*c/(2*e**4) - 6*B*b*c**2*d/e**5 + 5*B*c**3*d**2/e**6) + x*(3*A*b**2*c/e**4 - 12*A*b*c**2*d/e**5 + 10*A*c**3*d**2/e**6 + B*b**3/e**4 - 12*B*b**2*c*d/e**5 + 30*B*b*c**2*d**2/e**6 - 20*B*c**3*d**3/e**7) + (11*A*b**3*d**3*e**4 - 78*A*b**2*c*d**4*e**3 + 141*A*b*c**2*d**5*e**2 - 74*A*c**3*d**6*e - 26*B*b**3*d**4*e**3 + 141*B*b**2*c*d**5*e**2 - 222*B*b*c**2*d**6*e + 107*B*c**3*d**7 + x**2*(18*A*b**3*d*e**6 - 108*A*b**2*c*d**2*e**5 + 180*A*b*c**2*d**3*e**4 - 90*A*c**3*d**4*e**3 - 36*B*b**3*d**2*e**5 + 180*B*b**2*c*d**3*e**4 - 270*B*b*c**2*d**4*e**3 + 126*B*c**3*d**5*e**2) + x*(27*A*b**3*d**2*e**5 - 180*A*b**2*c*d**3*e**4 + 315*A*b*c**2*d**4*e**3 - 162*A*c**3*d**5*e**2 - 60*B*b**3*d**3*e**4 + 315*B*b**2*c*d**4*e**3 - 486*B*b*c**2*d**5*e**2 + 231*B*c**3*d**6*e))/(6*d**3*e**8 + 18*d**2*e**9*x + 18*d*e**10*x**2 + 6*e**11*x**3) - (-A*b**3*e**4 + 12*A*b**2*c*d*e**3 - 30*A*b*c**2*d**2*e**2 + 20*A*c**3*d**3*e + 4*B*b**3*d*e**3 - 30*B*b**2*c*d**2*e**2 + 60*B*b*c**2*d**3*e - 35*B*c**3*d**4)*log(d + e*x)/e**8","A",0
1137,1,396,0,7.179658," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+b*x),x)","\frac{A d^{4} \log{\left(x \right)}}{b} + \frac{B e^{4} x^{4}}{4 c} + x^{3} \left(\frac{A e^{4}}{3 c} - \frac{B b e^{4}}{3 c^{2}} + \frac{4 B d e^{3}}{3 c}\right) + x^{2} \left(- \frac{A b e^{4}}{2 c^{2}} + \frac{2 A d e^{3}}{c} + \frac{B b^{2} e^{4}}{2 c^{3}} - \frac{2 B b d e^{3}}{c^{2}} + \frac{3 B d^{2} e^{2}}{c}\right) + x \left(\frac{A b^{2} e^{4}}{c^{3}} - \frac{4 A b d e^{3}}{c^{2}} + \frac{6 A d^{2} e^{2}}{c} - \frac{B b^{3} e^{4}}{c^{4}} + \frac{4 B b^{2} d e^{3}}{c^{3}} - \frac{6 B b d^{2} e^{2}}{c^{2}} + \frac{4 B d^{3} e}{c}\right) + \frac{\left(- A c + B b\right) \left(b e - c d\right)^{4} \log{\left(x + \frac{- A b c^{4} d^{4} + \frac{b \left(- A c + B b\right) \left(b e - c d\right)^{4}}{c}}{- A b^{4} c e^{4} + 4 A b^{3} c^{2} d e^{3} - 6 A b^{2} c^{3} d^{2} e^{2} + 4 A b c^{4} d^{3} e - 2 A c^{5} d^{4} + B b^{5} e^{4} - 4 B b^{4} c d e^{3} + 6 B b^{3} c^{2} d^{2} e^{2} - 4 B b^{2} c^{3} d^{3} e + B b c^{4} d^{4}} \right)}}{b c^{5}}"," ",0,"A*d**4*log(x)/b + B*e**4*x**4/(4*c) + x**3*(A*e**4/(3*c) - B*b*e**4/(3*c**2) + 4*B*d*e**3/(3*c)) + x**2*(-A*b*e**4/(2*c**2) + 2*A*d*e**3/c + B*b**2*e**4/(2*c**3) - 2*B*b*d*e**3/c**2 + 3*B*d**2*e**2/c) + x*(A*b**2*e**4/c**3 - 4*A*b*d*e**3/c**2 + 6*A*d**2*e**2/c - B*b**3*e**4/c**4 + 4*B*b**2*d*e**3/c**3 - 6*B*b*d**2*e**2/c**2 + 4*B*d**3*e/c) + (-A*c + B*b)*(b*e - c*d)**4*log(x + (-A*b*c**4*d**4 + b*(-A*c + B*b)*(b*e - c*d)**4/c)/(-A*b**4*c*e**4 + 4*A*b**3*c**2*d*e**3 - 6*A*b**2*c**3*d**2*e**2 + 4*A*b*c**4*d**3*e - 2*A*c**5*d**4 + B*b**5*e**4 - 4*B*b**4*c*d*e**3 + 6*B*b**3*c**2*d**2*e**2 - 4*B*b**2*c**3*d**3*e + B*b*c**4*d**4))/(b*c**5)","A",0
1138,1,264,0,4.587545," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x),x)","\frac{A d^{3} \log{\left(x \right)}}{b} + \frac{B e^{3} x^{3}}{3 c} + x^{2} \left(\frac{A e^{3}}{2 c} - \frac{B b e^{3}}{2 c^{2}} + \frac{3 B d e^{2}}{2 c}\right) + x \left(- \frac{A b e^{3}}{c^{2}} + \frac{3 A d e^{2}}{c} + \frac{B b^{2} e^{3}}{c^{3}} - \frac{3 B b d e^{2}}{c^{2}} + \frac{3 B d^{2} e}{c}\right) - \frac{\left(- A c + B b\right) \left(b e - c d\right)^{3} \log{\left(x + \frac{A b c^{3} d^{3} + \frac{b \left(- A c + B b\right) \left(b e - c d\right)^{3}}{c}}{- A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}} \right)}}{b c^{4}}"," ",0,"A*d**3*log(x)/b + B*e**3*x**3/(3*c) + x**2*(A*e**3/(2*c) - B*b*e**3/(2*c**2) + 3*B*d*e**2/(2*c)) + x*(-A*b*e**3/c**2 + 3*A*d*e**2/c + B*b**2*e**3/c**3 - 3*B*b*d*e**2/c**2 + 3*B*d**2*e/c) - (-A*c + B*b)*(b*e - c*d)**3*log(x + (A*b*c**3*d**3 + b*(-A*c + B*b)*(b*e - c*d)**3/c)/(-A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3))/(b*c**4)","B",0
1139,1,163,0,2.803012," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x),x)","\frac{A d^{2} \log{\left(x \right)}}{b} + \frac{B e^{2} x^{2}}{2 c} + x \left(\frac{A e^{2}}{c} - \frac{B b e^{2}}{c^{2}} + \frac{2 B d e}{c}\right) + \frac{\left(- A c + B b\right) \left(b e - c d\right)^{2} \log{\left(x + \frac{- A b c^{2} d^{2} + \frac{b \left(- A c + B b\right) \left(b e - c d\right)^{2}}{c}}{- A b^{2} c e^{2} + 2 A b c^{2} d e - 2 A c^{3} d^{2} + B b^{3} e^{2} - 2 B b^{2} c d e + B b c^{2} d^{2}} \right)}}{b c^{3}}"," ",0,"A*d**2*log(x)/b + B*e**2*x**2/(2*c) + x*(A*e**2/c - B*b*e**2/c**2 + 2*B*d*e/c) + (-A*c + B*b)*(b*e - c*d)**2*log(x + (-A*b*c**2*d**2 + b*(-A*c + B*b)*(b*e - c*d)**2/c)/(-A*b**2*c*e**2 + 2*A*b*c**2*d*e - 2*A*c**3*d**2 + B*b**3*e**2 - 2*B*b**2*c*d*e + B*b*c**2*d**2))/(b*c**3)","B",0
1140,1,88,0,1.363879," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x),x)","\frac{A d \log{\left(x \right)}}{b} + \frac{B e x}{c} - \frac{\left(- A c + B b\right) \left(b e - c d\right) \log{\left(x + \frac{A b c d + \frac{b \left(- A c + B b\right) \left(b e - c d\right)}{c}}{- A b c e + 2 A c^{2} d + B b^{2} e - B b c d} \right)}}{b c^{2}}"," ",0,"A*d*log(x)/b + B*e*x/c - (-A*c + B*b)*(b*e - c*d)*log(x + (A*b*c*d + b*(-A*c + B*b)*(b*e - c*d)/c)/(-A*b*c*e + 2*A*c**2*d + B*b**2*e - B*b*c*d))/(b*c**2)","B",0
1141,1,41,0,0.412029," ","integrate((B*x+A)/(c*x**2+b*x),x)","\frac{A \log{\left(x \right)}}{b} + \frac{\left(- A c + B b\right) \log{\left(x + \frac{- A b + \frac{b \left(- A c + B b\right)}{c}}{- 2 A c + B b} \right)}}{b c}"," ",0,"A*log(x)/b + (-A*c + B*b)*log(x + (-A*b + b*(-A*c + B*b)/c)/(-2*A*c + B*b))/(b*c)","A",0
1142,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1143,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1144,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1145,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**4/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1146,1,644,0,15.978013," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+b*x)**2,x)","\frac{B e^{4} x^{2}}{2 c^{2}} + x \left(\frac{A e^{4}}{c^{2}} - \frac{2 B b e^{4}}{c^{3}} + \frac{4 B d e^{3}}{c^{2}}\right) + \frac{- A b c^{4} d^{4} + x \left(- A b^{4} c e^{4} + 4 A b^{3} c^{2} d e^{3} - 6 A b^{2} c^{3} d^{2} e^{2} + 4 A b c^{4} d^{3} e - 2 A c^{5} d^{4} + B b^{5} e^{4} - 4 B b^{4} c d e^{3} + 6 B b^{3} c^{2} d^{2} e^{2} - 4 B b^{2} c^{3} d^{3} e + B b c^{4} d^{4}\right)}{b^{3} c^{4} x + b^{2} c^{5} x^{2}} + \frac{d^{3} \left(4 A b e - 2 A c d + B b d\right) \log{\left(x + \frac{- 4 A b^{2} c^{3} d^{3} e + 2 A b c^{4} d^{4} - B b^{2} c^{3} d^{4} + b c^{3} d^{3} \left(4 A b e - 2 A c d + B b d\right)}{- 2 A b^{4} c e^{4} + 4 A b^{3} c^{2} d e^{3} - 8 A b c^{4} d^{3} e + 4 A c^{5} d^{4} + 3 B b^{5} e^{4} - 8 B b^{4} c d e^{3} + 6 B b^{3} c^{2} d^{2} e^{2} - 2 B b c^{4} d^{4}} \right)}}{b^{3}} + \frac{\left(b e - c d\right)^{3} \left(- 2 A b c e - 2 A c^{2} d + 3 B b^{2} e + B b c d\right) \log{\left(x + \frac{- 4 A b^{2} c^{3} d^{3} e + 2 A b c^{4} d^{4} - B b^{2} c^{3} d^{4} + \frac{b \left(b e - c d\right)^{3} \left(- 2 A b c e - 2 A c^{2} d + 3 B b^{2} e + B b c d\right)}{c}}{- 2 A b^{4} c e^{4} + 4 A b^{3} c^{2} d e^{3} - 8 A b c^{4} d^{3} e + 4 A c^{5} d^{4} + 3 B b^{5} e^{4} - 8 B b^{4} c d e^{3} + 6 B b^{3} c^{2} d^{2} e^{2} - 2 B b c^{4} d^{4}} \right)}}{b^{3} c^{4}}"," ",0,"B*e**4*x**2/(2*c**2) + x*(A*e**4/c**2 - 2*B*b*e**4/c**3 + 4*B*d*e**3/c**2) + (-A*b*c**4*d**4 + x*(-A*b**4*c*e**4 + 4*A*b**3*c**2*d*e**3 - 6*A*b**2*c**3*d**2*e**2 + 4*A*b*c**4*d**3*e - 2*A*c**5*d**4 + B*b**5*e**4 - 4*B*b**4*c*d*e**3 + 6*B*b**3*c**2*d**2*e**2 - 4*B*b**2*c**3*d**3*e + B*b*c**4*d**4))/(b**3*c**4*x + b**2*c**5*x**2) + d**3*(4*A*b*e - 2*A*c*d + B*b*d)*log(x + (-4*A*b**2*c**3*d**3*e + 2*A*b*c**4*d**4 - B*b**2*c**3*d**4 + b*c**3*d**3*(4*A*b*e - 2*A*c*d + B*b*d))/(-2*A*b**4*c*e**4 + 4*A*b**3*c**2*d*e**3 - 8*A*b*c**4*d**3*e + 4*A*c**5*d**4 + 3*B*b**5*e**4 - 8*B*b**4*c*d*e**3 + 6*B*b**3*c**2*d**2*e**2 - 2*B*b*c**4*d**4))/b**3 + (b*e - c*d)**3*(-2*A*b*c*e - 2*A*c**2*d + 3*B*b**2*e + B*b*c*d)*log(x + (-4*A*b**2*c**3*d**3*e + 2*A*b*c**4*d**4 - B*b**2*c**3*d**4 + b*(b*e - c*d)**3*(-2*A*b*c*e - 2*A*c**2*d + 3*B*b**2*e + B*b*c*d)/c)/(-2*A*b**4*c*e**4 + 4*A*b**3*c**2*d*e**3 - 8*A*b*c**4*d**3*e + 4*A*c**5*d**4 + 3*B*b**5*e**4 - 8*B*b**4*c*d*e**3 + 6*B*b**3*c**2*d**2*e**2 - 2*B*b*c**4*d**4))/(b**3*c**4)","B",0
1147,1,502,0,9.383804," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x)**2,x)","\frac{B e^{3} x}{c^{2}} + \frac{- A b c^{3} d^{3} + x \left(A b^{3} c e^{3} - 3 A b^{2} c^{2} d e^{2} + 3 A b c^{3} d^{2} e - 2 A c^{4} d^{3} - B b^{4} e^{3} + 3 B b^{3} c d e^{2} - 3 B b^{2} c^{2} d^{2} e + B b c^{3} d^{3}\right)}{b^{3} c^{3} x + b^{2} c^{4} x^{2}} + \frac{d^{2} \left(3 A b e - 2 A c d + B b d\right) \log{\left(x + \frac{3 A b^{2} c^{2} d^{2} e - 2 A b c^{3} d^{3} + B b^{2} c^{2} d^{3} - b c^{2} d^{2} \left(3 A b e - 2 A c d + B b d\right)}{- A b^{3} c e^{3} + 6 A b c^{3} d^{2} e - 4 A c^{4} d^{3} + 2 B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 2 B b c^{3} d^{3}} \right)}}{b^{3}} - \frac{\left(b e - c d\right)^{2} \left(- A b c e - 2 A c^{2} d + 2 B b^{2} e + B b c d\right) \log{\left(x + \frac{3 A b^{2} c^{2} d^{2} e - 2 A b c^{3} d^{3} + B b^{2} c^{2} d^{3} + \frac{b \left(b e - c d\right)^{2} \left(- A b c e - 2 A c^{2} d + 2 B b^{2} e + B b c d\right)}{c}}{- A b^{3} c e^{3} + 6 A b c^{3} d^{2} e - 4 A c^{4} d^{3} + 2 B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 2 B b c^{3} d^{3}} \right)}}{b^{3} c^{3}}"," ",0,"B*e**3*x/c**2 + (-A*b*c**3*d**3 + x*(A*b**3*c*e**3 - 3*A*b**2*c**2*d*e**2 + 3*A*b*c**3*d**2*e - 2*A*c**4*d**3 - B*b**4*e**3 + 3*B*b**3*c*d*e**2 - 3*B*b**2*c**2*d**2*e + B*b*c**3*d**3))/(b**3*c**3*x + b**2*c**4*x**2) + d**2*(3*A*b*e - 2*A*c*d + B*b*d)*log(x + (3*A*b**2*c**2*d**2*e - 2*A*b*c**3*d**3 + B*b**2*c**2*d**3 - b*c**2*d**2*(3*A*b*e - 2*A*c*d + B*b*d))/(-A*b**3*c*e**3 + 6*A*b*c**3*d**2*e - 4*A*c**4*d**3 + 2*B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 2*B*b*c**3*d**3))/b**3 - (b*e - c*d)**2*(-A*b*c*e - 2*A*c**2*d + 2*B*b**2*e + B*b*c*d)*log(x + (3*A*b**2*c**2*d**2*e - 2*A*b*c**3*d**3 + B*b**2*c**2*d**3 + b*(b*e - c*d)**2*(-A*b*c*e - 2*A*c**2*d + 2*B*b**2*e + B*b*c*d)/c)/(-A*b**3*c*e**3 + 6*A*b*c**3*d**2*e - 4*A*c**4*d**3 + 2*B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 2*B*b*c**3*d**3))/(b**3*c**3)","B",0
1148,1,367,0,3.861499," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x)**2,x)","\frac{- A b c^{2} d^{2} + x \left(- A b^{2} c e^{2} + 2 A b c^{2} d e - 2 A c^{3} d^{2} + B b^{3} e^{2} - 2 B b^{2} c d e + B b c^{2} d^{2}\right)}{b^{3} c^{2} x + b^{2} c^{3} x^{2}} + \frac{d \left(2 A b e - 2 A c d + B b d\right) \log{\left(x + \frac{- 2 A b^{2} c d e + 2 A b c^{2} d^{2} - B b^{2} c d^{2} + b c d \left(2 A b e - 2 A c d + B b d\right)}{- 4 A b c^{2} d e + 4 A c^{3} d^{2} + B b^{3} e^{2} - 2 B b c^{2} d^{2}} \right)}}{b^{3}} + \frac{\left(b e - c d\right) \left(- 2 A c^{2} d + B b^{2} e + B b c d\right) \log{\left(x + \frac{- 2 A b^{2} c d e + 2 A b c^{2} d^{2} - B b^{2} c d^{2} + \frac{b \left(b e - c d\right) \left(- 2 A c^{2} d + B b^{2} e + B b c d\right)}{c}}{- 4 A b c^{2} d e + 4 A c^{3} d^{2} + B b^{3} e^{2} - 2 B b c^{2} d^{2}} \right)}}{b^{3} c^{2}}"," ",0,"(-A*b*c**2*d**2 + x*(-A*b**2*c*e**2 + 2*A*b*c**2*d*e - 2*A*c**3*d**2 + B*b**3*e**2 - 2*B*b**2*c*d*e + B*b*c**2*d**2))/(b**3*c**2*x + b**2*c**3*x**2) + d*(2*A*b*e - 2*A*c*d + B*b*d)*log(x + (-2*A*b**2*c*d*e + 2*A*b*c**2*d**2 - B*b**2*c*d**2 + b*c*d*(2*A*b*e - 2*A*c*d + B*b*d))/(-4*A*b*c**2*d*e + 4*A*c**3*d**2 + B*b**3*e**2 - 2*B*b*c**2*d**2))/b**3 + (b*e - c*d)*(-2*A*c**2*d + B*b**2*e + B*b*c*d)*log(x + (-2*A*b**2*c*d*e + 2*A*b*c**2*d**2 - B*b**2*c*d**2 + b*(b*e - c*d)*(-2*A*c**2*d + B*b**2*e + B*b*c*d)/c)/(-4*A*b*c**2*d*e + 4*A*c**3*d**2 + B*b**3*e**2 - 2*B*b*c**2*d**2))/(b**3*c**2)","B",0
1149,1,233,0,1.220926," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x)**2,x)","\frac{- A b c d + x \left(A b c e - 2 A c^{2} d - B b^{2} e + B b c d\right)}{b^{3} c x + b^{2} c^{2} x^{2}} + \frac{\left(A b e - 2 A c d + B b d\right) \log{\left(x + \frac{A b^{2} e - 2 A b c d + B b^{2} d - b \left(A b e - 2 A c d + B b d\right)}{2 A b c e - 4 A c^{2} d + 2 B b c d} \right)}}{b^{3}} - \frac{\left(A b e - 2 A c d + B b d\right) \log{\left(x + \frac{A b^{2} e - 2 A b c d + B b^{2} d + b \left(A b e - 2 A c d + B b d\right)}{2 A b c e - 4 A c^{2} d + 2 B b c d} \right)}}{b^{3}}"," ",0,"(-A*b*c*d + x*(A*b*c*e - 2*A*c**2*d - B*b**2*e + B*b*c*d))/(b**3*c*x + b**2*c**2*x**2) + (A*b*e - 2*A*c*d + B*b*d)*log(x + (A*b**2*e - 2*A*b*c*d + B*b**2*d - b*(A*b*e - 2*A*c*d + B*b*d))/(2*A*b*c*e - 4*A*c**2*d + 2*B*b*c*d))/b**3 - (A*b*e - 2*A*c*d + B*b*d)*log(x + (A*b**2*e - 2*A*b*c*d + B*b**2*d + b*(A*b*e - 2*A*c*d + B*b*d))/(2*A*b*c*e - 4*A*c**2*d + 2*B*b*c*d))/b**3","B",0
1150,1,128,0,0.474354," ","integrate((B*x+A)/(c*x**2+b*x)**2,x)","\frac{- A b + x \left(- 2 A c + B b\right)}{b^{3} x + b^{2} c x^{2}} + \frac{\left(- 2 A c + B b\right) \log{\left(x + \frac{- 2 A b c + B b^{2} - b \left(- 2 A c + B b\right)}{- 4 A c^{2} + 2 B b c} \right)}}{b^{3}} - \frac{\left(- 2 A c + B b\right) \log{\left(x + \frac{- 2 A b c + B b^{2} + b \left(- 2 A c + B b\right)}{- 4 A c^{2} + 2 B b c} \right)}}{b^{3}}"," ",0,"(-A*b + x*(-2*A*c + B*b))/(b**3*x + b**2*c*x**2) + (-2*A*c + B*b)*log(x + (-2*A*b*c + B*b**2 - b*(-2*A*c + B*b))/(-4*A*c**2 + 2*B*b*c))/b**3 - (-2*A*c + B*b)*log(x + (-2*A*b*c + B*b**2 + b*(-2*A*c + B*b))/(-4*A*c**2 + 2*B*b*c))/b**3","B",0
1151,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1152,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1153,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**5/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,1,881,0,77.980055," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+b*x)**3,x)","\frac{- A b^{3} c^{3} d^{4} + x^{3} \left(- 2 A b^{4} c^{2} e^{4} + 12 A b^{2} c^{4} d^{2} e^{2} - 24 A b c^{5} d^{3} e + 12 A c^{6} d^{4} + 4 B b^{5} c e^{4} - 8 B b^{4} c^{2} d e^{3} + 8 B b^{2} c^{4} d^{3} e - 6 B b c^{5} d^{4}\right) + x^{2} \left(- A b^{5} c e^{4} - 4 A b^{4} c^{2} d e^{3} + 18 A b^{3} c^{3} d^{2} e^{2} - 36 A b^{2} c^{4} d^{3} e + 18 A b c^{5} d^{4} + 3 B b^{6} e^{4} - 4 B b^{5} c d e^{3} - 6 B b^{4} c^{2} d^{2} e^{2} + 12 B b^{3} c^{3} d^{3} e - 9 B b^{2} c^{4} d^{4}\right) + x \left(- 8 A b^{3} c^{3} d^{3} e + 4 A b^{2} c^{4} d^{4} - 2 B b^{3} c^{3} d^{4}\right)}{2 b^{6} c^{3} x^{2} + 4 b^{5} c^{4} x^{3} + 2 b^{4} c^{5} x^{4}} + \frac{d^{2} \left(6 A b^{2} e^{2} - 12 A b c d e + 6 A c^{2} d^{2} + 4 B b^{2} d e - 3 B b c d^{2}\right) \log{\left(x + \frac{- 6 A b^{3} c^{2} d^{2} e^{2} + 12 A b^{2} c^{3} d^{3} e - 6 A b c^{4} d^{4} - 4 B b^{3} c^{2} d^{3} e + 3 B b^{2} c^{3} d^{4} + b c^{2} d^{2} \left(6 A b^{2} e^{2} - 12 A b c d e + 6 A c^{2} d^{2} + 4 B b^{2} d e - 3 B b c d^{2}\right)}{- 12 A b^{2} c^{3} d^{2} e^{2} + 24 A b c^{4} d^{3} e - 12 A c^{5} d^{4} + B b^{5} e^{4} - 8 B b^{2} c^{3} d^{3} e + 6 B b c^{4} d^{4}} \right)}}{b^{5}} + \frac{\left(b e - c d\right)^{2} \left(- 6 A c^{3} d^{2} + B b^{3} e^{2} + 2 B b^{2} c d e + 3 B b c^{2} d^{2}\right) \log{\left(x + \frac{- 6 A b^{3} c^{2} d^{2} e^{2} + 12 A b^{2} c^{3} d^{3} e - 6 A b c^{4} d^{4} - 4 B b^{3} c^{2} d^{3} e + 3 B b^{2} c^{3} d^{4} + \frac{b \left(b e - c d\right)^{2} \left(- 6 A c^{3} d^{2} + B b^{3} e^{2} + 2 B b^{2} c d e + 3 B b c^{2} d^{2}\right)}{c}}{- 12 A b^{2} c^{3} d^{2} e^{2} + 24 A b c^{4} d^{3} e - 12 A c^{5} d^{4} + B b^{5} e^{4} - 8 B b^{2} c^{3} d^{3} e + 6 B b c^{4} d^{4}} \right)}}{b^{5} c^{3}}"," ",0,"(-A*b**3*c**3*d**4 + x**3*(-2*A*b**4*c**2*e**4 + 12*A*b**2*c**4*d**2*e**2 - 24*A*b*c**5*d**3*e + 12*A*c**6*d**4 + 4*B*b**5*c*e**4 - 8*B*b**4*c**2*d*e**3 + 8*B*b**2*c**4*d**3*e - 6*B*b*c**5*d**4) + x**2*(-A*b**5*c*e**4 - 4*A*b**4*c**2*d*e**3 + 18*A*b**3*c**3*d**2*e**2 - 36*A*b**2*c**4*d**3*e + 18*A*b*c**5*d**4 + 3*B*b**6*e**4 - 4*B*b**5*c*d*e**3 - 6*B*b**4*c**2*d**2*e**2 + 12*B*b**3*c**3*d**3*e - 9*B*b**2*c**4*d**4) + x*(-8*A*b**3*c**3*d**3*e + 4*A*b**2*c**4*d**4 - 2*B*b**3*c**3*d**4))/(2*b**6*c**3*x**2 + 4*b**5*c**4*x**3 + 2*b**4*c**5*x**4) + d**2*(6*A*b**2*e**2 - 12*A*b*c*d*e + 6*A*c**2*d**2 + 4*B*b**2*d*e - 3*B*b*c*d**2)*log(x + (-6*A*b**3*c**2*d**2*e**2 + 12*A*b**2*c**3*d**3*e - 6*A*b*c**4*d**4 - 4*B*b**3*c**2*d**3*e + 3*B*b**2*c**3*d**4 + b*c**2*d**2*(6*A*b**2*e**2 - 12*A*b*c*d*e + 6*A*c**2*d**2 + 4*B*b**2*d*e - 3*B*b*c*d**2))/(-12*A*b**2*c**3*d**2*e**2 + 24*A*b*c**4*d**3*e - 12*A*c**5*d**4 + B*b**5*e**4 - 8*B*b**2*c**3*d**3*e + 6*B*b*c**4*d**4))/b**5 + (b*e - c*d)**2*(-6*A*c**3*d**2 + B*b**3*e**2 + 2*B*b**2*c*d*e + 3*B*b*c**2*d**2)*log(x + (-6*A*b**3*c**2*d**2*e**2 + 12*A*b**2*c**3*d**3*e - 6*A*b*c**4*d**4 - 4*B*b**3*c**2*d**3*e + 3*B*b**2*c**3*d**4 + b*(b*e - c*d)**2*(-6*A*c**3*d**2 + B*b**3*e**2 + 2*B*b**2*c*d*e + 3*B*b*c**2*d**2)/c)/(-12*A*b**2*c**3*d**2*e**2 + 24*A*b*c**4*d**3*e - 12*A*c**5*d**4 + B*b**5*e**4 - 8*B*b**2*c**3*d**3*e + 6*B*b*c**4*d**4))/(b**5*c**3)","B",0
1156,1,653,0,28.927991," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x)**3,x)","\frac{- A b^{3} c^{2} d^{3} + x^{3} \left(6 A b^{2} c^{3} d e^{2} - 18 A b c^{4} d^{2} e + 12 A c^{5} d^{3} - 2 B b^{4} c e^{3} + 6 B b^{2} c^{3} d^{2} e - 6 B b c^{4} d^{3}\right) + x^{2} \left(- A b^{4} c e^{3} + 9 A b^{3} c^{2} d e^{2} - 27 A b^{2} c^{3} d^{2} e + 18 A b c^{4} d^{3} - B b^{5} e^{3} - 3 B b^{4} c d e^{2} + 9 B b^{3} c^{2} d^{2} e - 9 B b^{2} c^{3} d^{3}\right) + x \left(- 6 A b^{3} c^{2} d^{2} e + 4 A b^{2} c^{3} d^{3} - 2 B b^{3} c^{2} d^{3}\right)}{2 b^{6} c^{2} x^{2} + 4 b^{5} c^{3} x^{3} + 2 b^{4} c^{4} x^{4}} + \frac{3 d \left(b e - c d\right) \left(A b e - 2 A c d + B b d\right) \log{\left(x + \frac{3 A b^{3} d e^{2} - 9 A b^{2} c d^{2} e + 6 A b c^{2} d^{3} + 3 B b^{3} d^{2} e - 3 B b^{2} c d^{3} - 3 b d \left(b e - c d\right) \left(A b e - 2 A c d + B b d\right)}{6 A b^{2} c d e^{2} - 18 A b c^{2} d^{2} e + 12 A c^{3} d^{3} + 6 B b^{2} c d^{2} e - 6 B b c^{2} d^{3}} \right)}}{b^{5}} - \frac{3 d \left(b e - c d\right) \left(A b e - 2 A c d + B b d\right) \log{\left(x + \frac{3 A b^{3} d e^{2} - 9 A b^{2} c d^{2} e + 6 A b c^{2} d^{3} + 3 B b^{3} d^{2} e - 3 B b^{2} c d^{3} + 3 b d \left(b e - c d\right) \left(A b e - 2 A c d + B b d\right)}{6 A b^{2} c d e^{2} - 18 A b c^{2} d^{2} e + 12 A c^{3} d^{3} + 6 B b^{2} c d^{2} e - 6 B b c^{2} d^{3}} \right)}}{b^{5}}"," ",0,"(-A*b**3*c**2*d**3 + x**3*(6*A*b**2*c**3*d*e**2 - 18*A*b*c**4*d**2*e + 12*A*c**5*d**3 - 2*B*b**4*c*e**3 + 6*B*b**2*c**3*d**2*e - 6*B*b*c**4*d**3) + x**2*(-A*b**4*c*e**3 + 9*A*b**3*c**2*d*e**2 - 27*A*b**2*c**3*d**2*e + 18*A*b*c**4*d**3 - B*b**5*e**3 - 3*B*b**4*c*d*e**2 + 9*B*b**3*c**2*d**2*e - 9*B*b**2*c**3*d**3) + x*(-6*A*b**3*c**2*d**2*e + 4*A*b**2*c**3*d**3 - 2*B*b**3*c**2*d**3))/(2*b**6*c**2*x**2 + 4*b**5*c**3*x**3 + 2*b**4*c**4*x**4) + 3*d*(b*e - c*d)*(A*b*e - 2*A*c*d + B*b*d)*log(x + (3*A*b**3*d*e**2 - 9*A*b**2*c*d**2*e + 6*A*b*c**2*d**3 + 3*B*b**3*d**2*e - 3*B*b**2*c*d**3 - 3*b*d*(b*e - c*d)*(A*b*e - 2*A*c*d + B*b*d))/(6*A*b**2*c*d*e**2 - 18*A*b*c**2*d**2*e + 12*A*c**3*d**3 + 6*B*b**2*c*d**2*e - 6*B*b*c**2*d**3))/b**5 - 3*d*(b*e - c*d)*(A*b*e - 2*A*c*d + B*b*d)*log(x + (3*A*b**3*d*e**2 - 9*A*b**2*c*d**2*e + 6*A*b*c**2*d**3 + 3*B*b**3*d**2*e - 3*B*b**2*c*d**3 + 3*b*d*(b*e - c*d)*(A*b*e - 2*A*c*d + B*b*d))/(6*A*b**2*c*d*e**2 - 18*A*b*c**2*d**2*e + 12*A*c**3*d**3 + 6*B*b**2*c*d**2*e - 6*B*b*c**2*d**3))/b**5","B",0
1157,1,660,0,10.665899," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x)**3,x)","\frac{- A b^{3} c d^{2} + x^{3} \left(2 A b^{2} c^{2} e^{2} - 12 A b c^{3} d e + 12 A c^{4} d^{2} + 4 B b^{2} c^{2} d e - 6 B b c^{3} d^{2}\right) + x^{2} \left(3 A b^{3} c e^{2} - 18 A b^{2} c^{2} d e + 18 A b c^{3} d^{2} - B b^{4} e^{2} + 6 B b^{3} c d e - 9 B b^{2} c^{2} d^{2}\right) + x \left(- 4 A b^{3} c d e + 4 A b^{2} c^{2} d^{2} - 2 B b^{3} c d^{2}\right)}{2 b^{6} c x^{2} + 4 b^{5} c^{2} x^{3} + 2 b^{4} c^{3} x^{4}} + \frac{\left(A b^{2} e^{2} - 6 A b c d e + 6 A c^{2} d^{2} + 2 B b^{2} d e - 3 B b c d^{2}\right) \log{\left(x + \frac{A b^{3} e^{2} - 6 A b^{2} c d e + 6 A b c^{2} d^{2} + 2 B b^{3} d e - 3 B b^{2} c d^{2} - b \left(A b^{2} e^{2} - 6 A b c d e + 6 A c^{2} d^{2} + 2 B b^{2} d e - 3 B b c d^{2}\right)}{2 A b^{2} c e^{2} - 12 A b c^{2} d e + 12 A c^{3} d^{2} + 4 B b^{2} c d e - 6 B b c^{2} d^{2}} \right)}}{b^{5}} - \frac{\left(A b^{2} e^{2} - 6 A b c d e + 6 A c^{2} d^{2} + 2 B b^{2} d e - 3 B b c d^{2}\right) \log{\left(x + \frac{A b^{3} e^{2} - 6 A b^{2} c d e + 6 A b c^{2} d^{2} + 2 B b^{3} d e - 3 B b^{2} c d^{2} + b \left(A b^{2} e^{2} - 6 A b c d e + 6 A c^{2} d^{2} + 2 B b^{2} d e - 3 B b c d^{2}\right)}{2 A b^{2} c e^{2} - 12 A b c^{2} d e + 12 A c^{3} d^{2} + 4 B b^{2} c d e - 6 B b c^{2} d^{2}} \right)}}{b^{5}}"," ",0,"(-A*b**3*c*d**2 + x**3*(2*A*b**2*c**2*e**2 - 12*A*b*c**3*d*e + 12*A*c**4*d**2 + 4*B*b**2*c**2*d*e - 6*B*b*c**3*d**2) + x**2*(3*A*b**3*c*e**2 - 18*A*b**2*c**2*d*e + 18*A*b*c**3*d**2 - B*b**4*e**2 + 6*B*b**3*c*d*e - 9*B*b**2*c**2*d**2) + x*(-4*A*b**3*c*d*e + 4*A*b**2*c**2*d**2 - 2*B*b**3*c*d**2))/(2*b**6*c*x**2 + 4*b**5*c**2*x**3 + 2*b**4*c**3*x**4) + (A*b**2*e**2 - 6*A*b*c*d*e + 6*A*c**2*d**2 + 2*B*b**2*d*e - 3*B*b*c*d**2)*log(x + (A*b**3*e**2 - 6*A*b**2*c*d*e + 6*A*b*c**2*d**2 + 2*B*b**3*d*e - 3*B*b**2*c*d**2 - b*(A*b**2*e**2 - 6*A*b*c*d*e + 6*A*c**2*d**2 + 2*B*b**2*d*e - 3*B*b*c*d**2))/(2*A*b**2*c*e**2 - 12*A*b*c**2*d*e + 12*A*c**3*d**2 + 4*B*b**2*c*d*e - 6*B*b*c**2*d**2))/b**5 - (A*b**2*e**2 - 6*A*b*c*d*e + 6*A*c**2*d**2 + 2*B*b**2*d*e - 3*B*b*c*d**2)*log(x + (A*b**3*e**2 - 6*A*b**2*c*d*e + 6*A*b*c**2*d**2 + 2*B*b**3*d*e - 3*B*b**2*c*d**2 + b*(A*b**2*e**2 - 6*A*b*c*d*e + 6*A*c**2*d**2 + 2*B*b**2*d*e - 3*B*b*c*d**2))/(2*A*b**2*c*e**2 - 12*A*b*c**2*d*e + 12*A*c**3*d**2 + 4*B*b**2*c*d*e - 6*B*b*c**2*d**2))/b**5","B",0
1158,1,449,0,2.866847," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x)**3,x)","\frac{- A b^{3} d + x^{3} \left(- 6 A b c^{2} e + 12 A c^{3} d + 2 B b^{2} c e - 6 B b c^{2} d\right) + x^{2} \left(- 9 A b^{2} c e + 18 A b c^{2} d + 3 B b^{3} e - 9 B b^{2} c d\right) + x \left(- 2 A b^{3} e + 4 A b^{2} c d - 2 B b^{3} d\right)}{2 b^{6} x^{2} + 4 b^{5} c x^{3} + 2 b^{4} c^{2} x^{4}} + \frac{\left(- 3 A b c e + 6 A c^{2} d + B b^{2} e - 3 B b c d\right) \log{\left(x + \frac{- 3 A b^{2} c e + 6 A b c^{2} d + B b^{3} e - 3 B b^{2} c d - b \left(- 3 A b c e + 6 A c^{2} d + B b^{2} e - 3 B b c d\right)}{- 6 A b c^{2} e + 12 A c^{3} d + 2 B b^{2} c e - 6 B b c^{2} d} \right)}}{b^{5}} - \frac{\left(- 3 A b c e + 6 A c^{2} d + B b^{2} e - 3 B b c d\right) \log{\left(x + \frac{- 3 A b^{2} c e + 6 A b c^{2} d + B b^{3} e - 3 B b^{2} c d + b \left(- 3 A b c e + 6 A c^{2} d + B b^{2} e - 3 B b c d\right)}{- 6 A b c^{2} e + 12 A c^{3} d + 2 B b^{2} c e - 6 B b c^{2} d} \right)}}{b^{5}}"," ",0,"(-A*b**3*d + x**3*(-6*A*b*c**2*e + 12*A*c**3*d + 2*B*b**2*c*e - 6*B*b*c**2*d) + x**2*(-9*A*b**2*c*e + 18*A*b*c**2*d + 3*B*b**3*e - 9*B*b**2*c*d) + x*(-2*A*b**3*e + 4*A*b**2*c*d - 2*B*b**3*d))/(2*b**6*x**2 + 4*b**5*c*x**3 + 2*b**4*c**2*x**4) + (-3*A*b*c*e + 6*A*c**2*d + B*b**2*e - 3*B*b*c*d)*log(x + (-3*A*b**2*c*e + 6*A*b*c**2*d + B*b**3*e - 3*B*b**2*c*d - b*(-3*A*b*c*e + 6*A*c**2*d + B*b**2*e - 3*B*b*c*d))/(-6*A*b*c**2*e + 12*A*c**3*d + 2*B*b**2*c*e - 6*B*b*c**2*d))/b**5 - (-3*A*b*c*e + 6*A*c**2*d + B*b**2*e - 3*B*b*c*d)*log(x + (-3*A*b**2*c*e + 6*A*b*c**2*d + B*b**3*e - 3*B*b**2*c*d + b*(-3*A*b*c*e + 6*A*c**2*d + B*b**2*e - 3*B*b*c*d))/(-6*A*b*c**2*e + 12*A*c**3*d + 2*B*b**2*c*e - 6*B*b*c**2*d))/b**5","B",0
1159,1,219,0,0.715905," ","integrate((B*x+A)/(c*x**2+b*x)**3,x)","\frac{- A b^{3} + x^{3} \left(12 A c^{3} - 6 B b c^{2}\right) + x^{2} \left(18 A b c^{2} - 9 B b^{2} c\right) + x \left(4 A b^{2} c - 2 B b^{3}\right)}{2 b^{6} x^{2} + 4 b^{5} c x^{3} + 2 b^{4} c^{2} x^{4}} - \frac{3 c \left(- 2 A c + B b\right) \log{\left(x + \frac{- 6 A b c^{2} + 3 B b^{2} c - 3 b c \left(- 2 A c + B b\right)}{- 12 A c^{3} + 6 B b c^{2}} \right)}}{b^{5}} + \frac{3 c \left(- 2 A c + B b\right) \log{\left(x + \frac{- 6 A b c^{2} + 3 B b^{2} c + 3 b c \left(- 2 A c + B b\right)}{- 12 A c^{3} + 6 B b c^{2}} \right)}}{b^{5}}"," ",0,"(-A*b**3 + x**3*(12*A*c**3 - 6*B*b*c**2) + x**2*(18*A*b*c**2 - 9*B*b**2*c) + x*(4*A*b**2*c - 2*B*b**3))/(2*b**6*x**2 + 4*b**5*c*x**3 + 2*b**4*c**2*x**4) - 3*c*(-2*A*c + B*b)*log(x + (-6*A*b*c**2 + 3*B*b**2*c - 3*b*c*(-2*A*c + B*b))/(-12*A*c**3 + 6*B*b*c**2))/b**5 + 3*c*(-2*A*c + B*b)*log(x + (-6*A*b*c**2 + 3*B*b**2*c + 3*b*c*(-2*A*c + B*b))/(-12*A*c**3 + 6*B*b*c**2))/b**5","B",0
1160,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1161,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(A + B x\right) \left(d + e x\right)^{3}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)*(d + e*x)**3, x)","F",0
1163,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(A + B x\right) \left(d + e x\right)^{2}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)*(d + e*x)**2, x)","F",0
1164,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(A + B x\right) \left(d + e x\right)\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)*(d + e*x), x)","F",0
1165,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(A + B x\right)\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x), x)","F",0
1166,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{d + e x}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x), x)","F",0
1167,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**2, x)","F",0
1168,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**3, x)","F",0
1169,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**4, x)","F",0
1170,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**5, x)","F",0
1171,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**6,x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**6, x)","F",0
1172,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right) \left(d + e x\right)^{2}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)*(d + e*x)**2, x)","F",0
1173,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right) \left(d + e x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)*(d + e*x), x)","F",0
1174,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x), x)","F",0
1175,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{d + e x}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x), x)","F",0
1176,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**2, x)","F",0
1177,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**3, x)","F",0
1178,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**4, x)","F",0
1179,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**5, x)","F",0
1180,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**6, x)","F",0
1181,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**7, x)","F",0
1182,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1183,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right) \left(d + e x\right)^{2}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)*(d + e*x)**2, x)","F",0
1184,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right) \left(d + e x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)*(d + e*x), x)","F",0
1185,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2),x)","\int \left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x), x)","F",0
1186,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/(e*x+d),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{d + e x}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/(d + e*x), x)","F",0
1187,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/(d + e*x)**2, x)","F",0
1188,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/(d + e*x)**3, x)","F",0
1189,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/(d + e*x)**4, x)","F",0
1190,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(A + B x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((x*(b + c*x))**(5/2)*(A + B*x)/(d + e*x)**5, x)","F",0
1191,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/sqrt(x*(b + c*x)), x)","F",0
1192,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/sqrt(x*(b + c*x)), x)","F",0
1193,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/sqrt(x*(b + c*x)), x)","F",0
1194,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)/sqrt(x*(b + c*x)), x)","F",0
1195,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)), x)","F",0
1196,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)**2), x)","F",0
1197,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)**3), x)","F",0
1198,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**4/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)**4), x)","F",0
1199,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/(x*(b + c*x))**(3/2), x)","F",0
1200,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/(x*(b + c*x))**(3/2), x)","F",0
1201,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/(x*(b + c*x))**(3/2), x)","F",0
1202,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(b + c*x))**(3/2), x)","F",0
1203,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((A + B*x)/((x*(b + c*x))**(3/2)*(d + e*x)), x)","F",0
1204,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)/((x*(b + c*x))**(3/2)*(d + e*x)**2), x)","F",0
1205,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((A + B*x)/((x*(b + c*x))**(3/2)*(d + e*x)**3), x)","F",0
1206,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{4}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**4/(x*(b + c*x))**(5/2), x)","F",0
1207,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/(x*(b + c*x))**(5/2), x)","F",0
1208,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/(x*(b + c*x))**(5/2), x)","F",0
1209,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/(x*(b + c*x))**(5/2), x)","F",0
1210,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(5/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(x*(b + c*x))**(5/2), x)","F",0
1211,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x)**(5/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((A + B*x)/((x*(b + c*x))**(5/2)*(d + e*x)), x)","F",0
1212,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1213,1,683,0,9.271488," ","integrate((B*x+A)*(e*x+d)**(7/2)*(c*x**2+b*x),x)","\begin{cases} - \frac{4 A b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{2 A b d^{4} x \sqrt{d + e x}}{99 e} + \frac{16 A b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{92 A b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{68 A b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{2 A b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{16 A c d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 A c d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 A c d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 A c d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 A c d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 A c d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 A c e^{3} x^{6} \sqrt{d + e x}}{13} + \frac{16 B b d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 B b d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 B b d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 B b d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 B b d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 B b d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 B b e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{32 B c d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{16 B c d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{4 B c d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{2 B c d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{320 B c d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{412 B c d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{92 B c d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{2 B c e^{3} x^{7} \sqrt{d + e x}}{15} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(\frac{A b x^{2}}{2} + \frac{A c x^{3}}{3} + \frac{B b x^{3}}{3} + \frac{B c x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*A*b*d**5*sqrt(d + e*x)/(99*e**2) + 2*A*b*d**4*x*sqrt(d + e*x)/(99*e) + 16*A*b*d**3*x**2*sqrt(d + e*x)/33 + 92*A*b*d**2*e*x**3*sqrt(d + e*x)/99 + 68*A*b*d*e**2*x**4*sqrt(d + e*x)/99 + 2*A*b*e**3*x**5*sqrt(d + e*x)/11 + 16*A*c*d**6*sqrt(d + e*x)/(1287*e**3) - 8*A*c*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*A*c*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*A*c*d**3*x**3*sqrt(d + e*x)/1287 + 916*A*c*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*A*c*d*e**2*x**5*sqrt(d + e*x)/143 + 2*A*c*e**3*x**6*sqrt(d + e*x)/13 + 16*B*b*d**6*sqrt(d + e*x)/(1287*e**3) - 8*B*b*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*B*b*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*B*b*d**3*x**3*sqrt(d + e*x)/1287 + 916*B*b*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*B*b*d*e**2*x**5*sqrt(d + e*x)/143 + 2*B*b*e**3*x**6*sqrt(d + e*x)/13 - 32*B*c*d**7*sqrt(d + e*x)/(6435*e**4) + 16*B*c*d**6*x*sqrt(d + e*x)/(6435*e**3) - 4*B*c*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 2*B*c*d**4*x**3*sqrt(d + e*x)/(1287*e) + 320*B*c*d**3*x**4*sqrt(d + e*x)/1287 + 412*B*c*d**2*e*x**5*sqrt(d + e*x)/715 + 92*B*c*d*e**2*x**6*sqrt(d + e*x)/195 + 2*B*c*e**3*x**7*sqrt(d + e*x)/15, Ne(e, 0)), (d**(7/2)*(A*b*x**2/2 + A*c*x**3/3 + B*b*x**3/3 + B*c*x**4/4), True))","A",0
1214,1,581,0,4.638993," ","integrate((B*x+A)*(e*x+d)**(5/2)*(c*x**2+b*x),x)","\begin{cases} - \frac{4 A b d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{2 A b d^{3} x \sqrt{d + e x}}{63 e} + \frac{10 A b d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{38 A b d e x^{3} \sqrt{d + e x}}{63} + \frac{2 A b e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{16 A c d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 A c d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 A c d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 A c d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 A c d e x^{4} \sqrt{d + e x}}{99} + \frac{2 A c e^{2} x^{5} \sqrt{d + e x}}{11} + \frac{16 B b d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 B b d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 B b d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 B b d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 B b d e x^{4} \sqrt{d + e x}}{99} + \frac{2 B b e^{2} x^{5} \sqrt{d + e x}}{11} - \frac{32 B c d^{6} \sqrt{d + e x}}{3003 e^{4}} + \frac{16 B c d^{5} x \sqrt{d + e x}}{3003 e^{3}} - \frac{4 B c d^{4} x^{2} \sqrt{d + e x}}{1001 e^{2}} + \frac{10 B c d^{3} x^{3} \sqrt{d + e x}}{3003 e} + \frac{106 B c d^{2} x^{4} \sqrt{d + e x}}{429} + \frac{54 B c d e x^{5} \sqrt{d + e x}}{143} + \frac{2 B c e^{2} x^{6} \sqrt{d + e x}}{13} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(\frac{A b x^{2}}{2} + \frac{A c x^{3}}{3} + \frac{B b x^{3}}{3} + \frac{B c x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*A*b*d**4*sqrt(d + e*x)/(63*e**2) + 2*A*b*d**3*x*sqrt(d + e*x)/(63*e) + 10*A*b*d**2*x**2*sqrt(d + e*x)/21 + 38*A*b*d*e*x**3*sqrt(d + e*x)/63 + 2*A*b*e**2*x**4*sqrt(d + e*x)/9 + 16*A*c*d**5*sqrt(d + e*x)/(693*e**3) - 8*A*c*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*A*c*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*A*c*d**2*x**3*sqrt(d + e*x)/693 + 46*A*c*d*e*x**4*sqrt(d + e*x)/99 + 2*A*c*e**2*x**5*sqrt(d + e*x)/11 + 16*B*b*d**5*sqrt(d + e*x)/(693*e**3) - 8*B*b*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*B*b*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*B*b*d**2*x**3*sqrt(d + e*x)/693 + 46*B*b*d*e*x**4*sqrt(d + e*x)/99 + 2*B*b*e**2*x**5*sqrt(d + e*x)/11 - 32*B*c*d**6*sqrt(d + e*x)/(3003*e**4) + 16*B*c*d**5*x*sqrt(d + e*x)/(3003*e**3) - 4*B*c*d**4*x**2*sqrt(d + e*x)/(1001*e**2) + 10*B*c*d**3*x**3*sqrt(d + e*x)/(3003*e) + 106*B*c*d**2*x**4*sqrt(d + e*x)/429 + 54*B*c*d*e*x**5*sqrt(d + e*x)/143 + 2*B*c*e**2*x**6*sqrt(d + e*x)/13, Ne(e, 0)), (d**(5/2)*(A*b*x**2/2 + A*c*x**3/3 + B*b*x**3/3 + B*c*x**4/4), True))","A",0
1215,1,434,0,17.816198," ","integrate((B*x+A)*(e*x+d)**(3/2)*(c*x**2+b*x),x)","\frac{2 A b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 A b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 A c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 A c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 B b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 B b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 B c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 B c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}}"," ",0,"2*A*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*A*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*A*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*A*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*B*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*B*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*B*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*B*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4","B",0
1216,1,146,0,4.182301," ","integrate((B*x+A)*(e*x+d)**(1/2)*(c*x**2+b*x),x)","\frac{2 \left(\frac{B c \left(d + e x\right)^{\frac{9}{2}}}{9 e^{3}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(A c e + B b e - 3 B c d\right)}{7 e^{3}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(A b e^{2} - 2 A c d e - 2 B b d e + 3 B c d^{2}\right)}{5 e^{3}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- A b d e^{2} + A c d^{2} e + B b d^{2} e - B c d^{3}\right)}{3 e^{3}}\right)}{e}"," ",0,"2*(B*c*(d + e*x)**(9/2)/(9*e**3) + (d + e*x)**(7/2)*(A*c*e + B*b*e - 3*B*c*d)/(7*e**3) + (d + e*x)**(5/2)*(A*b*e**2 - 2*A*c*d*e - 2*B*b*d*e + 3*B*c*d**2)/(5*e**3) + (d + e*x)**(3/2)*(-A*b*d*e**2 + A*c*d**2*e + B*b*d**2*e - B*c*d**3)/(3*e**3))/e","A",0
1217,1,430,0,47.604532," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 A b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 A c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 A c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 B b d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 B b \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 B c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 B c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{\frac{A b x^{2}}{2} + \frac{B c x^{4}}{4} + \frac{x^{3} \left(A c + B b\right)}{3}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*A*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*A*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*A*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*B*b*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*B*b*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*B*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*B*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3)/e, Ne(e, 0)), ((A*b*x**2/2 + B*c*x**4/4 + x**3*(A*c + B*b)/3)/sqrt(d), True))","A",0
1218,1,126,0,24.163861," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**(3/2),x)","\frac{2 B c \left(d + e x\right)^{\frac{5}{2}}}{5 e^{4}} - \frac{2 d \left(- A e + B d\right) \left(b e - c d\right)}{e^{4} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 A c e + 2 B b e - 6 B c d\right)}{3 e^{4}} + \frac{\sqrt{d + e x} \left(2 A b e^{2} - 4 A c d e - 4 B b d e + 6 B c d^{2}\right)}{e^{4}}"," ",0,"2*B*c*(d + e*x)**(5/2)/(5*e**4) - 2*d*(-A*e + B*d)*(b*e - c*d)/(e**4*sqrt(d + e*x)) + (d + e*x)**(3/2)*(2*A*c*e + 2*B*b*e - 6*B*c*d)/(3*e**4) + sqrt(d + e*x)*(2*A*b*e**2 - 4*A*c*d*e - 4*B*b*d*e + 6*B*c*d**2)/e**4","A",0
1219,1,539,0,1.556436," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{4 A b d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{6 A b e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{16 A c d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{24 A c d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{6 A c e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{16 B b d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{24 B b d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{6 B b e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{32 B c d^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{48 B c d^{2} e x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 B c d e^{2} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{2 B c e^{3} x^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{\frac{A b x^{2}}{2} + \frac{A c x^{3}}{3} + \frac{B b x^{3}}{3} + \frac{B c x^{4}}{4}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*A*b*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 6*A*b*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 16*A*c*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 24*A*c*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 6*A*c*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 16*B*b*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 24*B*b*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 6*B*b*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 32*B*c*d**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 48*B*c*d**2*e*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*B*c*d*e**2*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 2*B*c*e**3*x**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)), Ne(e, 0)), ((A*b*x**2/2 + A*c*x**3/3 + B*b*x**3/3 + B*c*x**4/4)/d**(5/2), True))","A",0
1220,1,784,0,3.426551," ","integrate((B*x+A)*(c*x**2+b*x)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{4 A b d e^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{10 A b e^{3} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{16 A c d^{2} e}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{40 A c d e^{2} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{30 A c e^{3} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{16 B b d^{2} e}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{40 B b d e^{2} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{30 B b e^{3} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{96 B c d^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{240 B c d^{2} e x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{180 B c d e^{2} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{30 B c e^{3} x^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{\frac{A b x^{2}}{2} + \frac{A c x^{3}}{3} + \frac{B b x^{3}}{3} + \frac{B c x^{4}}{4}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*A*b*d*e**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 10*A*b*e**3*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 16*A*c*d**2*e/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 40*A*c*d*e**2*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 30*A*c*e**3*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 16*B*b*d**2*e/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 40*B*b*d*e**2*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 30*B*b*e**3*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 96*B*c*d**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 240*B*c*d**2*e*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 180*B*c*d*e**2*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 30*B*c*e**3*x**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)), Ne(e, 0)), ((A*b*x**2/2 + A*c*x**3/3 + B*b*x**3/3 + B*c*x**4/4)/d**(7/2), True))","A",0
1221,1,1352,0,15.939325," ","integrate((B*x+A)*(e*x+d)**(7/2)*(c*x**2+b*x)**2,x)","\begin{cases} \frac{16 A b^{2} d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 A b^{2} d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 A b^{2} d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 A b^{2} d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 A b^{2} d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 A b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 A b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{64 A b c d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{32 A b c d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{8 A b c d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{4 A b c d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{640 A b c d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{824 A b c d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{184 A b c d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{4 A b c e^{3} x^{7} \sqrt{d + e x}}{15} + \frac{256 A c^{2} d^{8} \sqrt{d + e x}}{109395 e^{5}} - \frac{128 A c^{2} d^{7} x \sqrt{d + e x}}{109395 e^{4}} + \frac{32 A c^{2} d^{6} x^{2} \sqrt{d + e x}}{36465 e^{3}} - \frac{16 A c^{2} d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{14 A c^{2} d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{2424 A c^{2} d^{3} x^{5} \sqrt{d + e x}}{12155} + \frac{1604 A c^{2} d^{2} e x^{6} \sqrt{d + e x}}{3315} + \frac{104 A c^{2} d e^{2} x^{7} \sqrt{d + e x}}{255} + \frac{2 A c^{2} e^{3} x^{8} \sqrt{d + e x}}{17} - \frac{32 B b^{2} d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{16 B b^{2} d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{4 B b^{2} d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{2 B b^{2} d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{320 B b^{2} d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{412 B b^{2} d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{92 B b^{2} d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{2 B b^{2} e^{3} x^{7} \sqrt{d + e x}}{15} + \frac{512 B b c d^{8} \sqrt{d + e x}}{109395 e^{5}} - \frac{256 B b c d^{7} x \sqrt{d + e x}}{109395 e^{4}} + \frac{64 B b c d^{6} x^{2} \sqrt{d + e x}}{36465 e^{3}} - \frac{32 B b c d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{28 B b c d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{4848 B b c d^{3} x^{5} \sqrt{d + e x}}{12155} + \frac{3208 B b c d^{2} e x^{6} \sqrt{d + e x}}{3315} + \frac{208 B b c d e^{2} x^{7} \sqrt{d + e x}}{255} + \frac{4 B b c e^{3} x^{8} \sqrt{d + e x}}{17} - \frac{512 B c^{2} d^{9} \sqrt{d + e x}}{415701 e^{6}} + \frac{256 B c^{2} d^{8} x \sqrt{d + e x}}{415701 e^{5}} - \frac{64 B c^{2} d^{7} x^{2} \sqrt{d + e x}}{138567 e^{4}} + \frac{160 B c^{2} d^{6} x^{3} \sqrt{d + e x}}{415701 e^{3}} - \frac{140 B c^{2} d^{5} x^{4} \sqrt{d + e x}}{415701 e^{2}} + \frac{14 B c^{2} d^{4} x^{5} \sqrt{d + e x}}{46189 e} + \frac{2096 B c^{2} d^{3} x^{6} \sqrt{d + e x}}{12597} + \frac{404 B c^{2} d^{2} e x^{7} \sqrt{d + e x}}{969} + \frac{116 B c^{2} d e^{2} x^{8} \sqrt{d + e x}}{323} + \frac{2 B c^{2} e^{3} x^{9} \sqrt{d + e x}}{19} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(\frac{A b^{2} x^{3}}{3} + \frac{A b c x^{4}}{2} + \frac{A c^{2} x^{5}}{5} + \frac{B b^{2} x^{4}}{4} + \frac{2 B b c x^{5}}{5} + \frac{B c^{2} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*A*b**2*d**6*sqrt(d + e*x)/(1287*e**3) - 8*A*b**2*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*A*b**2*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*A*b**2*d**3*x**3*sqrt(d + e*x)/1287 + 916*A*b**2*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*A*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 2*A*b**2*e**3*x**6*sqrt(d + e*x)/13 - 64*A*b*c*d**7*sqrt(d + e*x)/(6435*e**4) + 32*A*b*c*d**6*x*sqrt(d + e*x)/(6435*e**3) - 8*A*b*c*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 4*A*b*c*d**4*x**3*sqrt(d + e*x)/(1287*e) + 640*A*b*c*d**3*x**4*sqrt(d + e*x)/1287 + 824*A*b*c*d**2*e*x**5*sqrt(d + e*x)/715 + 184*A*b*c*d*e**2*x**6*sqrt(d + e*x)/195 + 4*A*b*c*e**3*x**7*sqrt(d + e*x)/15 + 256*A*c**2*d**8*sqrt(d + e*x)/(109395*e**5) - 128*A*c**2*d**7*x*sqrt(d + e*x)/(109395*e**4) + 32*A*c**2*d**6*x**2*sqrt(d + e*x)/(36465*e**3) - 16*A*c**2*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 14*A*c**2*d**4*x**4*sqrt(d + e*x)/(21879*e) + 2424*A*c**2*d**3*x**5*sqrt(d + e*x)/12155 + 1604*A*c**2*d**2*e*x**6*sqrt(d + e*x)/3315 + 104*A*c**2*d*e**2*x**7*sqrt(d + e*x)/255 + 2*A*c**2*e**3*x**8*sqrt(d + e*x)/17 - 32*B*b**2*d**7*sqrt(d + e*x)/(6435*e**4) + 16*B*b**2*d**6*x*sqrt(d + e*x)/(6435*e**3) - 4*B*b**2*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 2*B*b**2*d**4*x**3*sqrt(d + e*x)/(1287*e) + 320*B*b**2*d**3*x**4*sqrt(d + e*x)/1287 + 412*B*b**2*d**2*e*x**5*sqrt(d + e*x)/715 + 92*B*b**2*d*e**2*x**6*sqrt(d + e*x)/195 + 2*B*b**2*e**3*x**7*sqrt(d + e*x)/15 + 512*B*b*c*d**8*sqrt(d + e*x)/(109395*e**5) - 256*B*b*c*d**7*x*sqrt(d + e*x)/(109395*e**4) + 64*B*b*c*d**6*x**2*sqrt(d + e*x)/(36465*e**3) - 32*B*b*c*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 28*B*b*c*d**4*x**4*sqrt(d + e*x)/(21879*e) + 4848*B*b*c*d**3*x**5*sqrt(d + e*x)/12155 + 3208*B*b*c*d**2*e*x**6*sqrt(d + e*x)/3315 + 208*B*b*c*d*e**2*x**7*sqrt(d + e*x)/255 + 4*B*b*c*e**3*x**8*sqrt(d + e*x)/17 - 512*B*c**2*d**9*sqrt(d + e*x)/(415701*e**6) + 256*B*c**2*d**8*x*sqrt(d + e*x)/(415701*e**5) - 64*B*c**2*d**7*x**2*sqrt(d + e*x)/(138567*e**4) + 160*B*c**2*d**6*x**3*sqrt(d + e*x)/(415701*e**3) - 140*B*c**2*d**5*x**4*sqrt(d + e*x)/(415701*e**2) + 14*B*c**2*d**4*x**5*sqrt(d + e*x)/(46189*e) + 2096*B*c**2*d**3*x**6*sqrt(d + e*x)/12597 + 404*B*c**2*d**2*e*x**7*sqrt(d + e*x)/969 + 116*B*c**2*d*e**2*x**8*sqrt(d + e*x)/323 + 2*B*c**2*e**3*x**9*sqrt(d + e*x)/19, Ne(e, 0)), (d**(7/2)*(A*b**2*x**3/3 + A*b*c*x**4/2 + A*c**2*x**5/5 + B*b**2*x**4/4 + 2*B*b*c*x**5/5 + B*c**2*x**6/6), True))","A",0
1222,1,1556,0,52.785019," ","integrate((B*x+A)*(e*x+d)**(5/2)*(c*x**2+b*x)**2,x)","\frac{2 A b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 A b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 A b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{4 A b c d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 A b c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{4 A b c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 A c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 A c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 A c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 B b^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 B b^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 B b^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{4 B b c d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{8 B b c d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{4 B b c \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 B c^{2} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{4 B c^{2} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 B c^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}}"," ",0,"2*A*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*A*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*A*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 4*A*b*c*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*A*b*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 4*A*b*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*A*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*A*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*A*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*B*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*B*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*B*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 4*B*b*c*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 8*B*b*c*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 4*B*b*c*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*B*c**2*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 4*B*c**2*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*B*c**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6","B",0
1223,1,937,0,33.457753," ","integrate((B*x+A)*(e*x+d)**(3/2)*(c*x**2+b*x)**2,x)","\frac{2 A b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 A b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{4 A b c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 A b c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 A c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{2 A c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 B b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 B b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{4 B b c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 B b c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 B c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{2 B c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}}"," ",0,"2*A*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*A*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 4*A*b*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*A*b*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*A*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 2*A*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*B*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*B*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 4*B*b*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*B*b*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*B*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 2*B*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6","B",0
1224,1,377,0,7.013049," ","integrate((B*x+A)*(e*x+d)**(1/2)*(c*x**2+b*x)**2,x)","\frac{2 \left(\frac{B c^{2} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{5}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(A c^{2} e + 2 B b c e - 5 B c^{2} d\right)}{11 e^{5}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(2 A b c e^{2} - 4 A c^{2} d e + B b^{2} e^{2} - 8 B b c d e + 10 B c^{2} d^{2}\right)}{9 e^{5}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(A b^{2} e^{3} - 6 A b c d e^{2} + 6 A c^{2} d^{2} e - 3 B b^{2} d e^{2} + 12 B b c d^{2} e - 10 B c^{2} d^{3}\right)}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 2 A b^{2} d e^{3} + 6 A b c d^{2} e^{2} - 4 A c^{2} d^{3} e + 3 B b^{2} d^{2} e^{2} - 8 B b c d^{3} e + 5 B c^{2} d^{4}\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A b^{2} d^{2} e^{3} - 2 A b c d^{3} e^{2} + A c^{2} d^{4} e - B b^{2} d^{3} e^{2} + 2 B b c d^{4} e - B c^{2} d^{5}\right)}{3 e^{5}}\right)}{e}"," ",0,"2*(B*c**2*(d + e*x)**(13/2)/(13*e**5) + (d + e*x)**(11/2)*(A*c**2*e + 2*B*b*c*e - 5*B*c**2*d)/(11*e**5) + (d + e*x)**(9/2)*(2*A*b*c*e**2 - 4*A*c**2*d*e + B*b**2*e**2 - 8*B*b*c*d*e + 10*B*c**2*d**2)/(9*e**5) + (d + e*x)**(7/2)*(A*b**2*e**3 - 6*A*b*c*d*e**2 + 6*A*c**2*d**2*e - 3*B*b**2*d*e**2 + 12*B*b*c*d**2*e - 10*B*c**2*d**3)/(7*e**5) + (d + e*x)**(5/2)*(-2*A*b**2*d*e**3 + 6*A*b*c*d**2*e**2 - 4*A*c**2*d**3*e + 3*B*b**2*d**2*e**2 - 8*B*b*c*d**3*e + 5*B*c**2*d**4)/(5*e**5) + (d + e*x)**(3/2)*(A*b**2*d**2*e**3 - 2*A*b*c*d**3*e**2 + A*c**2*d**4*e - B*b**2*d**3*e**2 + 2*B*b*c*d**4*e - B*c**2*d**5)/(3*e**5))/e","A",0
1225,1,944,0,106.601155," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 A b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{4 A b c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{4 A b c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 A c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 A c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 B b^{2} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 B b^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{4 B b c d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{4 B b c \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 B c^{2} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{2 B c^{2} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}}}{e} & \text{for}\: e \neq 0 \\\frac{\frac{A b^{2} x^{3}}{3} + \frac{B c^{2} x^{6}}{6} + \frac{x^{5} \left(A c^{2} + 2 B b c\right)}{5} + \frac{x^{4} \left(2 A b c + B b^{2}\right)}{4}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*A*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 4*A*b*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 4*A*b*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*A*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*A*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*B*b**2*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*B*b**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 4*B*b*c*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 4*B*b*c*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*B*c**2*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 2*B*c**2*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5)/e, Ne(e, 0)), ((A*b**2*x**3/3 + B*c**2*x**6/6 + x**5*(A*c**2 + 2*B*b*c)/5 + x**4*(2*A*b*c + B*b**2)/4)/sqrt(d), True))","A",0
1226,1,321,0,62.034680," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**(3/2),x)","\frac{2 B c^{2} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{6}} + \frac{2 d^{2} \left(- A e + B d\right) \left(b e - c d\right)^{2}}{e^{6} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(2 A c^{2} e + 4 B b c e - 10 B c^{2} d\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(4 A b c e^{2} - 8 A c^{2} d e + 2 B b^{2} e^{2} - 16 B b c d e + 20 B c^{2} d^{2}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 A b^{2} e^{3} - 12 A b c d e^{2} + 12 A c^{2} d^{2} e - 6 B b^{2} d e^{2} + 24 B b c d^{2} e - 20 B c^{2} d^{3}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(- 4 A b^{2} d e^{3} + 12 A b c d^{2} e^{2} - 8 A c^{2} d^{3} e + 6 B b^{2} d^{2} e^{2} - 16 B b c d^{3} e + 10 B c^{2} d^{4}\right)}{e^{6}}"," ",0,"2*B*c**2*(d + e*x)**(9/2)/(9*e**6) + 2*d**2*(-A*e + B*d)*(b*e - c*d)**2/(e**6*sqrt(d + e*x)) + (d + e*x)**(7/2)*(2*A*c**2*e + 4*B*b*c*e - 10*B*c**2*d)/(7*e**6) + (d + e*x)**(5/2)*(4*A*b*c*e**2 - 8*A*c**2*d*e + 2*B*b**2*e**2 - 16*B*b*c*d*e + 20*B*c**2*d**2)/(5*e**6) + (d + e*x)**(3/2)*(2*A*b**2*e**3 - 12*A*b*c*d*e**2 + 12*A*c**2*d**2*e - 6*B*b**2*d*e**2 + 24*B*b*c*d**2*e - 20*B*c**2*d**3)/(3*e**6) + sqrt(d + e*x)*(-4*A*b**2*d*e**3 + 12*A*b*c*d**2*e**2 - 8*A*c**2*d**3*e + 6*B*b**2*d**2*e**2 - 16*B*b*c*d**3*e + 10*B*c**2*d**4)/e**6","A",0
1227,1,292,0,75.510567," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**(5/2),x)","\frac{2 B c^{2} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{6}} + \frac{2 d^{2} \left(- A e + B d\right) \left(b e - c d\right)^{2}}{3 e^{6} \left(d + e x\right)^{\frac{3}{2}}} - \frac{2 d \left(b e - c d\right) \left(- 2 A b e^{2} + 4 A c d e + 3 B b d e - 5 B c d^{2}\right)}{e^{6} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 A c^{2} e + 4 B b c e - 10 B c^{2} d\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(4 A b c e^{2} - 8 A c^{2} d e + 2 B b^{2} e^{2} - 16 B b c d e + 20 B c^{2} d^{2}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(2 A b^{2} e^{3} - 12 A b c d e^{2} + 12 A c^{2} d^{2} e - 6 B b^{2} d e^{2} + 24 B b c d^{2} e - 20 B c^{2} d^{3}\right)}{e^{6}}"," ",0,"2*B*c**2*(d + e*x)**(7/2)/(7*e**6) + 2*d**2*(-A*e + B*d)*(b*e - c*d)**2/(3*e**6*(d + e*x)**(3/2)) - 2*d*(b*e - c*d)*(-2*A*b*e**2 + 4*A*c*d*e + 3*B*b*d*e - 5*B*c*d**2)/(e**6*sqrt(d + e*x)) + (d + e*x)**(5/2)*(2*A*c**2*e + 4*B*b*c*e - 10*B*c**2*d)/(5*e**6) + (d + e*x)**(3/2)*(4*A*b*c*e**2 - 8*A*c**2*d*e + 2*B*b**2*e**2 - 16*B*b*c*d*e + 20*B*c**2*d**2)/(3*e**6) + sqrt(d + e*x)*(2*A*b**2*e**3 - 12*A*b*c*d*e**2 + 12*A*c**2*d**2*e - 6*B*b**2*d*e**2 + 24*B*b*c*d**2*e - 20*B*c**2*d**3)/e**6","A",0
1228,1,1833,0,4.863459," ","integrate((B*x+A)*(c*x**2+b*x)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{16 A b^{2} d^{2} e^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{40 A b^{2} d e^{4} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{30 A b^{2} e^{5} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{192 A b c d^{3} e^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{480 A b c d^{2} e^{3} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{360 A b c d e^{4} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{60 A b c e^{5} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{256 A c^{2} d^{4} e}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{640 A c^{2} d^{3} e^{2} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{480 A c^{2} d^{2} e^{3} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{80 A c^{2} d e^{4} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{10 A c^{2} e^{5} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{96 B b^{2} d^{3} e^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{240 B b^{2} d^{2} e^{3} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{180 B b^{2} d e^{4} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{30 B b^{2} e^{5} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{512 B b c d^{4} e}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{1280 B b c d^{3} e^{2} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{960 B b c d^{2} e^{3} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{160 B b c d e^{4} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{20 B b c e^{5} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{512 B c^{2} d^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1280 B c^{2} d^{4} e x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{960 B c^{2} d^{3} e^{2} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{160 B c^{2} d^{2} e^{3} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{20 B c^{2} d e^{4} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{6 B c^{2} e^{5} x^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{\frac{A b^{2} x^{3}}{3} + \frac{A b c x^{4}}{2} + \frac{A c^{2} x^{5}}{5} + \frac{B b^{2} x^{4}}{4} + \frac{2 B b c x^{5}}{5} + \frac{B c^{2} x^{6}}{6}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*A*b**2*d**2*e**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 40*A*b**2*d*e**4*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 30*A*b**2*e**5*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 192*A*b*c*d**3*e**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 480*A*b*c*d**2*e**3*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 360*A*b*c*d*e**4*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 60*A*b*c*e**5*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 256*A*c**2*d**4*e/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 640*A*c**2*d**3*e**2*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 480*A*c**2*d**2*e**3*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 80*A*c**2*d*e**4*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 10*A*c**2*e**5*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 96*B*b**2*d**3*e**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 240*B*b**2*d**2*e**3*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 180*B*b**2*d*e**4*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 30*B*b**2*e**5*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 512*B*b*c*d**4*e/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 1280*B*b*c*d**3*e**2*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 960*B*b*c*d**2*e**3*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 160*B*b*c*d*e**4*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 20*B*b*c*e**5*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 512*B*c**2*d**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1280*B*c**2*d**4*e*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 960*B*c**2*d**3*e**2*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 160*B*c**2*d**2*e**3*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 20*B*c**2*d*e**4*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 6*B*c**2*e**5*x**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)), Ne(e, 0)), ((A*b**2*x**3/3 + A*b*c*x**4/2 + A*c**2*x**5/5 + B*b**2*x**4/4 + 2*B*b*c*x**5/5 + B*c**2*x**6/6)/d**(7/2), True))","A",0
1229,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(c*x**2+b*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,1,199,0,136.765060," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x),x)","\frac{2 A d^{3} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} + \frac{2 B \left(d + e x\right)^{\frac{5}{2}}}{5 c} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 A c e - 2 B b e + 2 B c d\right)}{3 c^{2}} + \frac{\sqrt{d + e x} \left(- 2 A b c e^{2} + 4 A c^{2} d e + 2 B b^{2} e^{2} - 4 B b c d e + 2 B c^{2} d^{2}\right)}{c^{3}} - \frac{2 \left(- A c + B b\right) \left(b e - c d\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c^{4} \sqrt{\frac{b e - c d}{c}}}"," ",0,"2*A*d**3*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) + 2*B*(d + e*x)**(5/2)/(5*c) + (d + e*x)**(3/2)*(2*A*c*e - 2*B*b*e + 2*B*c*d)/(3*c**2) + sqrt(d + e*x)*(-2*A*b*c*e**2 + 4*A*c**2*d*e + 2*B*b**2*e**2 - 4*B*b*c*d*e + 2*B*c**2*d**2)/c**3 - 2*(-A*c + B*b)*(b*e - c*d)**3*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c**4*sqrt((b*e - c*d)/c))","A",0
1231,1,134,0,82.049130," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x),x)","\frac{2 A d^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} + \frac{2 B \left(d + e x\right)^{\frac{3}{2}}}{3 c} + \frac{\sqrt{d + e x} \left(2 A c e - 2 B b e + 2 B c d\right)}{c^{2}} + \frac{2 \left(- A c + B b\right) \left(b e - c d\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c^{3} \sqrt{\frac{b e - c d}{c}}}"," ",0,"2*A*d**2*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) + 2*B*(d + e*x)**(3/2)/(3*c) + sqrt(d + e*x)*(2*A*c*e - 2*B*b*e + 2*B*c*d)/c**2 + 2*(-A*c + B*b)*(b*e - c*d)**2*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c**3*sqrt((b*e - c*d)/c))","A",0
1232,1,104,0,17.771165," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x),x)","\frac{2 \left(\frac{A d e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b \sqrt{- d}} + \frac{B e \sqrt{d + e x}}{c} - \frac{e \left(- A c + B b\right) \left(b e - c d\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b c^{2} \sqrt{\frac{b e - c d}{c}}}\right)}{e}"," ",0,"2*(A*d*e*atan(sqrt(d + e*x)/sqrt(-d))/(b*sqrt(-d)) + B*e*sqrt(d + e*x)/c - e*(-A*c + B*b)*(b*e - c*d)*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*c**2*sqrt((b*e - c*d)/c)))/e","A",0
1233,1,87,0,69.748174," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x),x)","\frac{2 A \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d}} \sqrt{d + e x}} \right)}}{b d \sqrt{- \frac{1}{d}}} - \frac{2 \left(- A c + B b\right) \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{c}{b e - c d}} \sqrt{d + e x}} \right)}}{b \sqrt{\frac{c}{b e - c d}} \left(b e - c d\right)}"," ",0,"2*A*atan(1/(sqrt(-1/d)*sqrt(d + e*x)))/(b*d*sqrt(-1/d)) - 2*(-A*c + B*b)*atan(1/(sqrt(c/(b*e - c*d))*sqrt(d + e*x)))/(b*sqrt(c/(b*e - c*d))*(b*e - c*d))","A",0
1234,1,107,0,61.492259," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x),x)","\frac{2 A \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d \sqrt{- d}} - \frac{2 \left(- A e + B d\right)}{d \sqrt{d + e x} \left(b e - c d\right)} - \frac{2 \left(- A c + B b\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)}"," ",0,"2*A*atan(sqrt(d + e*x)/sqrt(-d))/(b*d*sqrt(-d)) - 2*(-A*e + B*d)/(d*sqrt(d + e*x)*(b*e - c*d)) - 2*(-A*c + B*b)*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d))","A",0
1235,1,160,0,66.515665," ","integrate((B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x),x)","\frac{2 A \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d^{2} \sqrt{- d}} - \frac{2 \left(- A e + B d\right)}{3 d \left(d + e x\right)^{\frac{3}{2}} \left(b e - c d\right)} + \frac{2 \left(A b e^{2} - 2 A c d e + B c d^{2}\right)}{d^{2} \sqrt{d + e x} \left(b e - c d\right)^{2}} + \frac{2 c \left(- A c + B b\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)^{2}}"," ",0,"2*A*atan(sqrt(d + e*x)/sqrt(-d))/(b*d**2*sqrt(-d)) - 2*(-A*e + B*d)/(3*d*(d + e*x)**(3/2)*(b*e - c*d)) + 2*(A*b*e**2 - 2*A*c*d*e + B*c*d**2)/(d**2*sqrt(d + e*x)*(b*e - c*d)**2) + 2*c*(-A*c + B*b)*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d)**2)","A",0
1236,1,228,0,78.316088," ","integrate((B*x+A)/(e*x+d)**(7/2)/(c*x**2+b*x),x)","\frac{2 A \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d^{3} \sqrt{- d}} - \frac{2 \left(- A e + B d\right)}{5 d \left(d + e x\right)^{\frac{5}{2}} \left(b e - c d\right)} + \frac{2 \left(A b e^{2} - 2 A c d e + B c d^{2}\right)}{3 d^{2} \left(d + e x\right)^{\frac{3}{2}} \left(b e - c d\right)^{2}} + \frac{2 \left(A b^{2} e^{3} - 3 A b c d e^{2} + 3 A c^{2} d^{2} e - B c^{2} d^{3}\right)}{d^{3} \sqrt{d + e x} \left(b e - c d\right)^{3}} - \frac{2 c^{2} \left(- A c + B b\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)^{3}}"," ",0,"2*A*atan(sqrt(d + e*x)/sqrt(-d))/(b*d**3*sqrt(-d)) - 2*(-A*e + B*d)/(5*d*(d + e*x)**(5/2)*(b*e - c*d)) + 2*(A*b*e**2 - 2*A*c*d*e + B*c*d**2)/(3*d**2*(d + e*x)**(3/2)*(b*e - c*d)**2) + 2*(A*b**2*e**3 - 3*A*b*c*d*e**2 + 3*A*c**2*d**2*e - B*c**2*d**3)/(d**3*sqrt(d + e*x)*(b*e - c*d)**3) - 2*c**2*(-A*c + B*b)*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d)**3)","A",0
1237,1,311,0,92.505955," ","integrate((B*x+A)/(e*x+d)**(9/2)/(c*x**2+b*x),x)","\frac{2 A \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b d^{4} \sqrt{- d}} - \frac{2 \left(- A e + B d\right)}{7 d \left(d + e x\right)^{\frac{7}{2}} \left(b e - c d\right)} + \frac{2 \left(A b e^{2} - 2 A c d e + B c d^{2}\right)}{5 d^{2} \left(d + e x\right)^{\frac{5}{2}} \left(b e - c d\right)^{2}} + \frac{2 \left(A b^{2} e^{3} - 3 A b c d e^{2} + 3 A c^{2} d^{2} e - B c^{2} d^{3}\right)}{3 d^{3} \left(d + e x\right)^{\frac{3}{2}} \left(b e - c d\right)^{3}} + \frac{2 \left(A b^{3} e^{4} - 4 A b^{2} c d e^{3} + 6 A b c^{2} d^{2} e^{2} - 4 A c^{3} d^{3} e + B c^{3} d^{4}\right)}{d^{4} \sqrt{d + e x} \left(b e - c d\right)^{4}} + \frac{2 c^{3} \left(- A c + B b\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e - c d}{c}}} \right)}}{b \sqrt{\frac{b e - c d}{c}} \left(b e - c d\right)^{4}}"," ",0,"2*A*atan(sqrt(d + e*x)/sqrt(-d))/(b*d**4*sqrt(-d)) - 2*(-A*e + B*d)/(7*d*(d + e*x)**(7/2)*(b*e - c*d)) + 2*(A*b*e**2 - 2*A*c*d*e + B*c*d**2)/(5*d**2*(d + e*x)**(5/2)*(b*e - c*d)**2) + 2*(A*b**2*e**3 - 3*A*b*c*d*e**2 + 3*A*c**2*d**2*e - B*c**2*d**3)/(3*d**3*(d + e*x)**(3/2)*(b*e - c*d)**3) + 2*(A*b**3*e**4 - 4*A*b**2*c*d*e**3 + 6*A*b*c**2*d**2*e**2 - 4*A*c**3*d**3*e + B*c**3*d**4)/(d**4*sqrt(d + e*x)*(b*e - c*d)**4) + 2*c**3*(-A*c + B*b)*atan(sqrt(d + e*x)/sqrt((b*e - c*d)/c))/(b*sqrt((b*e - c*d)/c)*(b*e - c*d)**4)","A",0
1238,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(9/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,1,1431,0,147.846234," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x)**2,x)","\frac{2 A c^{2} d e \sqrt{d + e x}}{2 b^{4} e^{2} - 2 b^{3} c d e + 2 b^{3} c e^{2} x - 2 b^{2} c^{2} d e x} - \frac{2 A c e^{2} \sqrt{d + e x}}{2 b^{3} e^{2} - 2 b^{2} c d e + 2 b^{2} c e^{2} x - 2 b c^{2} d e x} + \frac{A c e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{A c e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{A c^{2} d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} + \frac{A c^{2} d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} - \frac{A d e \sqrt{\frac{1}{d^{3}}} \log{\left(- d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} + \frac{A d e \sqrt{\frac{1}{d^{3}}} \log{\left(d^{2} \sqrt{\frac{1}{d^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} - \frac{2 A e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{2} \sqrt{\frac{b e}{c} - d}} + \frac{2 A e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{2} \sqrt{- d}} - \frac{A \sqrt{d + e x}}{b^{2} x} + \frac{4 A c d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{3} \sqrt{\frac{b e}{c} - d}} - \frac{4 A c d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{3} \sqrt{- d}} - \frac{2 B c d e \sqrt{d + e x}}{2 b^{3} e^{2} - 2 b^{2} c d e + 2 b^{2} c e^{2} x - 2 b c^{2} d e x} - \frac{B e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{B e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{2 B e^{2} \sqrt{d + e x}}{2 b^{2} e^{2} - 2 b c d e + 2 b c e^{2} x - 2 c^{2} d e x} + \frac{B c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(- b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{B c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} \log{\left(b^{2} e^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} - 2 b c d e \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + c^{2} d^{2} \sqrt{- \frac{1}{c \left(b e - c d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{2 B d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{b e}{c} - d}} \right)}}{b^{2} \sqrt{\frac{b e}{c} - d}} + \frac{2 B d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{b^{2} \sqrt{- d}}"," ",0,"2*A*c**2*d*e*sqrt(d + e*x)/(2*b**4*e**2 - 2*b**3*c*d*e + 2*b**3*c*e**2*x - 2*b**2*c**2*d*e*x) - 2*A*c*e**2*sqrt(d + e*x)/(2*b**3*e**2 - 2*b**2*c*d*e + 2*b**2*c*e**2*x - 2*b*c**2*d*e*x) + A*c*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b) - A*c*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b) - A*c**2*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b**2) + A*c**2*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b**2) - A*d*e*sqrt(d**(-3))*log(-d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**2) + A*d*e*sqrt(d**(-3))*log(d**2*sqrt(d**(-3)) + sqrt(d + e*x))/(2*b**2) - 2*A*e*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**2*sqrt(b*e/c - d)) + 2*A*e*atan(sqrt(d + e*x)/sqrt(-d))/(b**2*sqrt(-d)) - A*sqrt(d + e*x)/(b**2*x) + 4*A*c*d*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**3*sqrt(b*e/c - d)) - 4*A*c*d*atan(sqrt(d + e*x)/sqrt(-d))/(b**3*sqrt(-d)) - 2*B*c*d*e*sqrt(d + e*x)/(2*b**3*e**2 - 2*b**2*c*d*e + 2*b**2*c*e**2*x - 2*b*c**2*d*e*x) - B*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/2 + B*e**2*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/2 + 2*B*e**2*sqrt(d + e*x)/(2*b**2*e**2 - 2*b*c*d*e + 2*b*c*e**2*x - 2*c**2*d*e*x) + B*c*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(-b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) + 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) - c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b) - B*c*d*e*sqrt(-1/(c*(b*e - c*d)**3))*log(b**2*e**2*sqrt(-1/(c*(b*e - c*d)**3)) - 2*b*c*d*e*sqrt(-1/(c*(b*e - c*d)**3)) + c**2*d**2*sqrt(-1/(c*(b*e - c*d)**3)) + sqrt(d + e*x))/(2*b) - 2*B*d*atan(sqrt(d + e*x)/sqrt(b*e/c - d))/(b**2*sqrt(b*e/c - d)) + 2*B*d*atan(sqrt(d + e*x)/sqrt(-d))/(b**2*sqrt(-d))","B",0
1243,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1244,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1245,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1246,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(c*x**2+b*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(9/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1248,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1250,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1251,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1252,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1253,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1254,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)*(c*x**2+b*x)**(1/2),x)","\int \sqrt{x \left(b + c x\right)} \left(A + B x\right) \sqrt{d + e x}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)*sqrt(d + e*x), x)","F",0
1256,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/sqrt(d + e*x), x)","F",0
1257,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**(3/2), x)","F",0
1258,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**(5/2), x)","F",0
1259,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\sqrt{x \left(b + c x\right)} \left(A + B x\right)}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(x*(b + c*x))*(A + B*x)/(d + e*x)**(7/2), x)","F",0
1260,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1261,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**(3/2), x)","F",0
1262,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**(5/2), x)","F",0
1263,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(A + B x\right)}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((x*(b + c*x))**(3/2)*(A + B*x)/(d + e*x)**(7/2), x)","F",0
1264,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{\frac{5}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**(5/2)/sqrt(x*(b + c*x)), x)","F",0
1265,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{\frac{3}{2}}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**(3/2)/sqrt(x*(b + c*x)), x)","F",0
1266,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\sqrt{x \left(b + c x\right)}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/sqrt(x*(b + c*x)), x)","F",0
1267,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*sqrt(d + e*x)), x)","F",0
1268,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)**(3/2)), x)","F",0
1269,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)**(5/2)), x)","F",0
1270,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(c*x**2+b*x)**(1/2),x)","\int \frac{A + B x}{\sqrt{x \left(b + c x\right)} \left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(x*(b + c*x))*(d + e*x)**(7/2)), x)","F",0
1271,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1273,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1274,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/(x*(b + c*x))**(3/2), x)","F",0
1275,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)/((x*(b + c*x))**(3/2)*sqrt(d + e*x)), x)","F",0
1276,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x)**(3/2),x)","\int \frac{A + B x}{\left(x \left(b + c x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((x*(b + c*x))**(3/2)*(d + e*x)**(3/2)), x)","F",0
1277,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1278,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1279,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1280,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1281,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1282,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1283,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1284,1,287,0,0.112953," ","integrate((B*x+A)*(e*x+d)**5*(c*x**2+a),x)","A a d^{5} x + \frac{B c e^{5} x^{9}}{9} + x^{8} \left(\frac{A c e^{5}}{8} + \frac{5 B c d e^{4}}{8}\right) + x^{7} \left(\frac{5 A c d e^{4}}{7} + \frac{B a e^{5}}{7} + \frac{10 B c d^{2} e^{3}}{7}\right) + x^{6} \left(\frac{A a e^{5}}{6} + \frac{5 A c d^{2} e^{3}}{3} + \frac{5 B a d e^{4}}{6} + \frac{5 B c d^{3} e^{2}}{3}\right) + x^{5} \left(A a d e^{4} + 2 A c d^{3} e^{2} + 2 B a d^{2} e^{3} + B c d^{4} e\right) + x^{4} \left(\frac{5 A a d^{2} e^{3}}{2} + \frac{5 A c d^{4} e}{4} + \frac{5 B a d^{3} e^{2}}{2} + \frac{B c d^{5}}{4}\right) + x^{3} \left(\frac{10 A a d^{3} e^{2}}{3} + \frac{A c d^{5}}{3} + \frac{5 B a d^{4} e}{3}\right) + x^{2} \left(\frac{5 A a d^{4} e}{2} + \frac{B a d^{5}}{2}\right)"," ",0,"A*a*d**5*x + B*c*e**5*x**9/9 + x**8*(A*c*e**5/8 + 5*B*c*d*e**4/8) + x**7*(5*A*c*d*e**4/7 + B*a*e**5/7 + 10*B*c*d**2*e**3/7) + x**6*(A*a*e**5/6 + 5*A*c*d**2*e**3/3 + 5*B*a*d*e**4/6 + 5*B*c*d**3*e**2/3) + x**5*(A*a*d*e**4 + 2*A*c*d**3*e**2 + 2*B*a*d**2*e**3 + B*c*d**4*e) + x**4*(5*A*a*d**2*e**3/2 + 5*A*c*d**4*e/4 + 5*B*a*d**3*e**2/2 + B*c*d**5/4) + x**3*(10*A*a*d**3*e**2/3 + A*c*d**5/3 + 5*B*a*d**4*e/3) + x**2*(5*A*a*d**4*e/2 + B*a*d**5/2)","B",0
1285,1,226,0,0.102060," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+a),x)","A a d^{4} x + \frac{B c e^{4} x^{8}}{8} + x^{7} \left(\frac{A c e^{4}}{7} + \frac{4 B c d e^{3}}{7}\right) + x^{6} \left(\frac{2 A c d e^{3}}{3} + \frac{B a e^{4}}{6} + B c d^{2} e^{2}\right) + x^{5} \left(\frac{A a e^{4}}{5} + \frac{6 A c d^{2} e^{2}}{5} + \frac{4 B a d e^{3}}{5} + \frac{4 B c d^{3} e}{5}\right) + x^{4} \left(A a d e^{3} + A c d^{3} e + \frac{3 B a d^{2} e^{2}}{2} + \frac{B c d^{4}}{4}\right) + x^{3} \left(2 A a d^{2} e^{2} + \frac{A c d^{4}}{3} + \frac{4 B a d^{3} e}{3}\right) + x^{2} \left(2 A a d^{3} e + \frac{B a d^{4}}{2}\right)"," ",0,"A*a*d**4*x + B*c*e**4*x**8/8 + x**7*(A*c*e**4/7 + 4*B*c*d*e**3/7) + x**6*(2*A*c*d*e**3/3 + B*a*e**4/6 + B*c*d**2*e**2) + x**5*(A*a*e**4/5 + 6*A*c*d**2*e**2/5 + 4*B*a*d*e**3/5 + 4*B*c*d**3*e/5) + x**4*(A*a*d*e**3 + A*c*d**3*e + 3*B*a*d**2*e**2/2 + B*c*d**4/4) + x**3*(2*A*a*d**2*e**2 + A*c*d**4/3 + 4*B*a*d**3*e/3) + x**2*(2*A*a*d**3*e + B*a*d**4/2)","B",0
1286,1,173,0,0.092846," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+a),x)","A a d^{3} x + \frac{B c e^{3} x^{7}}{7} + x^{6} \left(\frac{A c e^{3}}{6} + \frac{B c d e^{2}}{2}\right) + x^{5} \left(\frac{3 A c d e^{2}}{5} + \frac{B a e^{3}}{5} + \frac{3 B c d^{2} e}{5}\right) + x^{4} \left(\frac{A a e^{3}}{4} + \frac{3 A c d^{2} e}{4} + \frac{3 B a d e^{2}}{4} + \frac{B c d^{3}}{4}\right) + x^{3} \left(A a d e^{2} + \frac{A c d^{3}}{3} + B a d^{2} e\right) + x^{2} \left(\frac{3 A a d^{2} e}{2} + \frac{B a d^{3}}{2}\right)"," ",0,"A*a*d**3*x + B*c*e**3*x**7/7 + x**6*(A*c*e**3/6 + B*c*d*e**2/2) + x**5*(3*A*c*d*e**2/5 + B*a*e**3/5 + 3*B*c*d**2*e/5) + x**4*(A*a*e**3/4 + 3*A*c*d**2*e/4 + 3*B*a*d*e**2/4 + B*c*d**3/4) + x**3*(A*a*d*e**2 + A*c*d**3/3 + B*a*d**2*e) + x**2*(3*A*a*d**2*e/2 + B*a*d**3/2)","A",0
1287,1,119,0,0.084242," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+a),x)","A a d^{2} x + \frac{B c e^{2} x^{6}}{6} + x^{5} \left(\frac{A c e^{2}}{5} + \frac{2 B c d e}{5}\right) + x^{4} \left(\frac{A c d e}{2} + \frac{B a e^{2}}{4} + \frac{B c d^{2}}{4}\right) + x^{3} \left(\frac{A a e^{2}}{3} + \frac{A c d^{2}}{3} + \frac{2 B a d e}{3}\right) + x^{2} \left(A a d e + \frac{B a d^{2}}{2}\right)"," ",0,"A*a*d**2*x + B*c*e**2*x**6/6 + x**5*(A*c*e**2/5 + 2*B*c*d*e/5) + x**4*(A*c*d*e/2 + B*a*e**2/4 + B*c*d**2/4) + x**3*(A*a*e**2/3 + A*c*d**2/3 + 2*B*a*d*e/3) + x**2*(A*a*d*e + B*a*d**2/2)","A",0
1288,1,66,0,0.072164," ","integrate((B*x+A)*(e*x+d)*(c*x**2+a),x)","A a d x + \frac{B c e x^{5}}{5} + x^{4} \left(\frac{A c e}{4} + \frac{B c d}{4}\right) + x^{3} \left(\frac{A c d}{3} + \frac{B a e}{3}\right) + x^{2} \left(\frac{A a e}{2} + \frac{B a d}{2}\right)"," ",0,"A*a*d*x + B*c*e*x**5/5 + x**4*(A*c*e/4 + B*c*d/4) + x**3*(A*c*d/3 + B*a*e/3) + x**2*(A*a*e/2 + B*a*d/2)","A",0
1289,1,29,0,0.063164," ","integrate((B*x+A)*(c*x**2+a),x)","A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4}"," ",0,"A*a*x + A*c*x**3/3 + B*a*x**2/2 + B*c*x**4/4","A",0
1290,1,82,0,0.328192," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d),x)","\frac{B c x^{3}}{3 e} + x^{2} \left(\frac{A c}{2 e} - \frac{B c d}{2 e^{2}}\right) + x \left(- \frac{A c d}{e^{2}} + \frac{B a}{e} + \frac{B c d^{2}}{e^{3}}\right) - \frac{\left(- A e + B d\right) \left(a e^{2} + c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x**3/(3*e) + x**2*(A*c/(2*e) - B*c*d/(2*e**2)) + x*(-A*c*d/e**2 + B*a/e + B*c*d**2/e**3) - (-A*e + B*d)*(a*e**2 + c*d**2)*log(d + e*x)/e**4","A",0
1291,1,104,0,0.587588," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**2,x)","\frac{B c x^{2}}{2 e^{2}} + x \left(\frac{A c}{e^{2}} - \frac{2 B c d}{e^{3}}\right) + \frac{- A a e^{3} - A c d^{2} e + B a d e^{2} + B c d^{3}}{d e^{4} + e^{5} x} + \frac{\left(- 2 A c d e + B a e^{2} + 3 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x**2/(2*e**2) + x*(A*c/e**2 - 2*B*c*d/e**3) + (-A*a*e**3 - A*c*d**2*e + B*a*d*e**2 + B*c*d**3)/(d*e**4 + e**5*x) + (-2*A*c*d*e + B*a*e**2 + 3*B*c*d**2)*log(d + e*x)/e**4","A",0
1292,1,117,0,1.267418," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**3,x)","\frac{B c x}{e^{3}} - \frac{c \left(- A e + 3 B d\right) \log{\left(d + e x \right)}}{e^{4}} + \frac{- A a e^{3} + 3 A c d^{2} e - B a d e^{2} - 5 B c d^{3} + x \left(4 A c d e^{2} - 2 B a e^{3} - 6 B c d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}}"," ",0,"B*c*x/e**3 - c*(-A*e + 3*B*d)*log(d + e*x)/e**4 + (-A*a*e**3 + 3*A*c*d**2*e - B*a*d*e**2 - 5*B*c*d**3 + x*(4*A*c*d*e**2 - 2*B*a*e**3 - 6*B*c*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2)","A",0
1293,1,138,0,2.604900," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**4,x)","\frac{B c \log{\left(d + e x \right)}}{e^{4}} + \frac{- 2 A a e^{3} - 2 A c d^{2} e - B a d e^{2} + 11 B c d^{3} + x^{2} \left(- 6 A c e^{3} + 18 B c d e^{2}\right) + x \left(- 6 A c d e^{2} - 3 B a e^{3} + 27 B c d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"B*c*log(d + e*x)/e**4 + (-2*A*a*e**3 - 2*A*c*d**2*e - B*a*d*e**2 + 11*B*c*d**3 + x**2*(-6*A*c*e**3 + 18*B*c*d*e**2) + x*(-6*A*c*d*e**2 - 3*B*a*e**3 + 27*B*c*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
1294,1,150,0,4.894027," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**5,x)","\frac{- 3 A a e^{3} - A c d^{2} e - B a d e^{2} - 3 B c d^{3} - 12 B c e^{3} x^{3} + x^{2} \left(- 6 A c e^{3} - 18 B c d e^{2}\right) + x \left(- 4 A c d e^{2} - 4 B a e^{3} - 12 B c d^{2} e\right)}{12 d^{4} e^{4} + 48 d^{3} e^{5} x + 72 d^{2} e^{6} x^{2} + 48 d e^{7} x^{3} + 12 e^{8} x^{4}}"," ",0,"(-3*A*a*e**3 - A*c*d**2*e - B*a*d*e**2 - 3*B*c*d**3 - 12*B*c*e**3*x**3 + x**2*(-6*A*c*e**3 - 18*B*c*d*e**2) + x*(-4*A*c*d*e**2 - 4*B*a*e**3 - 12*B*c*d**2*e))/(12*d**4*e**4 + 48*d**3*e**5*x + 72*d**2*e**6*x**2 + 48*d*e**7*x**3 + 12*e**8*x**4)","A",0
1295,1,165,0,8.413603," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**6,x)","\frac{- 12 A a e^{3} - 2 A c d^{2} e - 3 B a d e^{2} - 3 B c d^{3} - 30 B c e^{3} x^{3} + x^{2} \left(- 20 A c e^{3} - 30 B c d e^{2}\right) + x \left(- 10 A c d e^{2} - 15 B a e^{3} - 15 B c d^{2} e\right)}{60 d^{5} e^{4} + 300 d^{4} e^{5} x + 600 d^{3} e^{6} x^{2} + 600 d^{2} e^{7} x^{3} + 300 d e^{8} x^{4} + 60 e^{9} x^{5}}"," ",0,"(-12*A*a*e**3 - 2*A*c*d**2*e - 3*B*a*d*e**2 - 3*B*c*d**3 - 30*B*c*e**3*x**3 + x**2*(-20*A*c*e**3 - 30*B*c*d*e**2) + x*(-10*A*c*d*e**2 - 15*B*a*e**3 - 15*B*c*d**2*e))/(60*d**5*e**4 + 300*d**4*e**5*x + 600*d**3*e**6*x**2 + 600*d**2*e**7*x**3 + 300*d*e**8*x**4 + 60*e**9*x**5)","A",0
1296,1,173,0,13.569868," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**7,x)","\frac{- 10 A a e^{3} - A c d^{2} e - 2 B a d e^{2} - B c d^{3} - 20 B c e^{3} x^{3} + x^{2} \left(- 15 A c e^{3} - 15 B c d e^{2}\right) + x \left(- 6 A c d e^{2} - 12 B a e^{3} - 6 B c d^{2} e\right)}{60 d^{6} e^{4} + 360 d^{5} e^{5} x + 900 d^{4} e^{6} x^{2} + 1200 d^{3} e^{7} x^{3} + 900 d^{2} e^{8} x^{4} + 360 d e^{9} x^{5} + 60 e^{10} x^{6}}"," ",0,"(-10*A*a*e**3 - A*c*d**2*e - 2*B*a*d*e**2 - B*c*d**3 - 20*B*c*e**3*x**3 + x**2*(-15*A*c*e**3 - 15*B*c*d*e**2) + x*(-6*A*c*d*e**2 - 12*B*a*e**3 - 6*B*c*d**2*e))/(60*d**6*e**4 + 360*d**5*e**5*x + 900*d**4*e**6*x**2 + 1200*d**3*e**7*x**3 + 900*d**2*e**8*x**4 + 360*d*e**9*x**5 + 60*e**10*x**6)","A",0
1297,1,495,0,0.137081," ","integrate((B*x+A)*(e*x+d)**5*(c*x**2+a)**2,x)","A a^{2} d^{5} x + \frac{B c^{2} e^{5} x^{11}}{11} + x^{10} \left(\frac{A c^{2} e^{5}}{10} + \frac{B c^{2} d e^{4}}{2}\right) + x^{9} \left(\frac{5 A c^{2} d e^{4}}{9} + \frac{2 B a c e^{5}}{9} + \frac{10 B c^{2} d^{2} e^{3}}{9}\right) + x^{8} \left(\frac{A a c e^{5}}{4} + \frac{5 A c^{2} d^{2} e^{3}}{4} + \frac{5 B a c d e^{4}}{4} + \frac{5 B c^{2} d^{3} e^{2}}{4}\right) + x^{7} \left(\frac{10 A a c d e^{4}}{7} + \frac{10 A c^{2} d^{3} e^{2}}{7} + \frac{B a^{2} e^{5}}{7} + \frac{20 B a c d^{2} e^{3}}{7} + \frac{5 B c^{2} d^{4} e}{7}\right) + x^{6} \left(\frac{A a^{2} e^{5}}{6} + \frac{10 A a c d^{2} e^{3}}{3} + \frac{5 A c^{2} d^{4} e}{6} + \frac{5 B a^{2} d e^{4}}{6} + \frac{10 B a c d^{3} e^{2}}{3} + \frac{B c^{2} d^{5}}{6}\right) + x^{5} \left(A a^{2} d e^{4} + 4 A a c d^{3} e^{2} + \frac{A c^{2} d^{5}}{5} + 2 B a^{2} d^{2} e^{3} + 2 B a c d^{4} e\right) + x^{4} \left(\frac{5 A a^{2} d^{2} e^{3}}{2} + \frac{5 A a c d^{4} e}{2} + \frac{5 B a^{2} d^{3} e^{2}}{2} + \frac{B a c d^{5}}{2}\right) + x^{3} \left(\frac{10 A a^{2} d^{3} e^{2}}{3} + \frac{2 A a c d^{5}}{3} + \frac{5 B a^{2} d^{4} e}{3}\right) + x^{2} \left(\frac{5 A a^{2} d^{4} e}{2} + \frac{B a^{2} d^{5}}{2}\right)"," ",0,"A*a**2*d**5*x + B*c**2*e**5*x**11/11 + x**10*(A*c**2*e**5/10 + B*c**2*d*e**4/2) + x**9*(5*A*c**2*d*e**4/9 + 2*B*a*c*e**5/9 + 10*B*c**2*d**2*e**3/9) + x**8*(A*a*c*e**5/4 + 5*A*c**2*d**2*e**3/4 + 5*B*a*c*d*e**4/4 + 5*B*c**2*d**3*e**2/4) + x**7*(10*A*a*c*d*e**4/7 + 10*A*c**2*d**3*e**2/7 + B*a**2*e**5/7 + 20*B*a*c*d**2*e**3/7 + 5*B*c**2*d**4*e/7) + x**6*(A*a**2*e**5/6 + 10*A*a*c*d**2*e**3/3 + 5*A*c**2*d**4*e/6 + 5*B*a**2*d*e**4/6 + 10*B*a*c*d**3*e**2/3 + B*c**2*d**5/6) + x**5*(A*a**2*d*e**4 + 4*A*a*c*d**3*e**2 + A*c**2*d**5/5 + 2*B*a**2*d**2*e**3 + 2*B*a*c*d**4*e) + x**4*(5*A*a**2*d**2*e**3/2 + 5*A*a*c*d**4*e/2 + 5*B*a**2*d**3*e**2/2 + B*a*c*d**5/2) + x**3*(10*A*a**2*d**3*e**2/3 + 2*A*a*c*d**5/3 + 5*B*a**2*d**4*e/3) + x**2*(5*A*a**2*d**4*e/2 + B*a**2*d**5/2)","B",0
1298,1,398,0,0.124578," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+a)**2,x)","A a^{2} d^{4} x + \frac{B c^{2} e^{4} x^{10}}{10} + x^{9} \left(\frac{A c^{2} e^{4}}{9} + \frac{4 B c^{2} d e^{3}}{9}\right) + x^{8} \left(\frac{A c^{2} d e^{3}}{2} + \frac{B a c e^{4}}{4} + \frac{3 B c^{2} d^{2} e^{2}}{4}\right) + x^{7} \left(\frac{2 A a c e^{4}}{7} + \frac{6 A c^{2} d^{2} e^{2}}{7} + \frac{8 B a c d e^{3}}{7} + \frac{4 B c^{2} d^{3} e}{7}\right) + x^{6} \left(\frac{4 A a c d e^{3}}{3} + \frac{2 A c^{2} d^{3} e}{3} + \frac{B a^{2} e^{4}}{6} + 2 B a c d^{2} e^{2} + \frac{B c^{2} d^{4}}{6}\right) + x^{5} \left(\frac{A a^{2} e^{4}}{5} + \frac{12 A a c d^{2} e^{2}}{5} + \frac{A c^{2} d^{4}}{5} + \frac{4 B a^{2} d e^{3}}{5} + \frac{8 B a c d^{3} e}{5}\right) + x^{4} \left(A a^{2} d e^{3} + 2 A a c d^{3} e + \frac{3 B a^{2} d^{2} e^{2}}{2} + \frac{B a c d^{4}}{2}\right) + x^{3} \left(2 A a^{2} d^{2} e^{2} + \frac{2 A a c d^{4}}{3} + \frac{4 B a^{2} d^{3} e}{3}\right) + x^{2} \left(2 A a^{2} d^{3} e + \frac{B a^{2} d^{4}}{2}\right)"," ",0,"A*a**2*d**4*x + B*c**2*e**4*x**10/10 + x**9*(A*c**2*e**4/9 + 4*B*c**2*d*e**3/9) + x**8*(A*c**2*d*e**3/2 + B*a*c*e**4/4 + 3*B*c**2*d**2*e**2/4) + x**7*(2*A*a*c*e**4/7 + 6*A*c**2*d**2*e**2/7 + 8*B*a*c*d*e**3/7 + 4*B*c**2*d**3*e/7) + x**6*(4*A*a*c*d*e**3/3 + 2*A*c**2*d**3*e/3 + B*a**2*e**4/6 + 2*B*a*c*d**2*e**2 + B*c**2*d**4/6) + x**5*(A*a**2*e**4/5 + 12*A*a*c*d**2*e**2/5 + A*c**2*d**4/5 + 4*B*a**2*d*e**3/5 + 8*B*a*c*d**3*e/5) + x**4*(A*a**2*d*e**3 + 2*A*a*c*d**3*e + 3*B*a**2*d**2*e**2/2 + B*a*c*d**4/2) + x**3*(2*A*a**2*d**2*e**2 + 2*A*a*c*d**4/3 + 4*B*a**2*d**3*e/3) + x**2*(2*A*a**2*d**3*e + B*a**2*d**4/2)","A",0
1299,1,303,0,0.112425," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+a)**2,x)","A a^{2} d^{3} x + \frac{B c^{2} e^{3} x^{9}}{9} + x^{8} \left(\frac{A c^{2} e^{3}}{8} + \frac{3 B c^{2} d e^{2}}{8}\right) + x^{7} \left(\frac{3 A c^{2} d e^{2}}{7} + \frac{2 B a c e^{3}}{7} + \frac{3 B c^{2} d^{2} e}{7}\right) + x^{6} \left(\frac{A a c e^{3}}{3} + \frac{A c^{2} d^{2} e}{2} + B a c d e^{2} + \frac{B c^{2} d^{3}}{6}\right) + x^{5} \left(\frac{6 A a c d e^{2}}{5} + \frac{A c^{2} d^{3}}{5} + \frac{B a^{2} e^{3}}{5} + \frac{6 B a c d^{2} e}{5}\right) + x^{4} \left(\frac{A a^{2} e^{3}}{4} + \frac{3 A a c d^{2} e}{2} + \frac{3 B a^{2} d e^{2}}{4} + \frac{B a c d^{3}}{2}\right) + x^{3} \left(A a^{2} d e^{2} + \frac{2 A a c d^{3}}{3} + B a^{2} d^{2} e\right) + x^{2} \left(\frac{3 A a^{2} d^{2} e}{2} + \frac{B a^{2} d^{3}}{2}\right)"," ",0,"A*a**2*d**3*x + B*c**2*e**3*x**9/9 + x**8*(A*c**2*e**3/8 + 3*B*c**2*d*e**2/8) + x**7*(3*A*c**2*d*e**2/7 + 2*B*a*c*e**3/7 + 3*B*c**2*d**2*e/7) + x**6*(A*a*c*e**3/3 + A*c**2*d**2*e/2 + B*a*c*d*e**2 + B*c**2*d**3/6) + x**5*(6*A*a*c*d*e**2/5 + A*c**2*d**3/5 + B*a**2*e**3/5 + 6*B*a*c*d**2*e/5) + x**4*(A*a**2*e**3/4 + 3*A*a*c*d**2*e/2 + 3*B*a**2*d*e**2/4 + B*a*c*d**3/2) + x**3*(A*a**2*d*e**2 + 2*A*a*c*d**3/3 + B*a**2*d**2*e) + x**2*(3*A*a**2*d**2*e/2 + B*a**2*d**3/2)","A",0
1300,1,211,0,0.100587," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+a)**2,x)","A a^{2} d^{2} x + \frac{B c^{2} e^{2} x^{8}}{8} + x^{7} \left(\frac{A c^{2} e^{2}}{7} + \frac{2 B c^{2} d e}{7}\right) + x^{6} \left(\frac{A c^{2} d e}{3} + \frac{B a c e^{2}}{3} + \frac{B c^{2} d^{2}}{6}\right) + x^{5} \left(\frac{2 A a c e^{2}}{5} + \frac{A c^{2} d^{2}}{5} + \frac{4 B a c d e}{5}\right) + x^{4} \left(A a c d e + \frac{B a^{2} e^{2}}{4} + \frac{B a c d^{2}}{2}\right) + x^{3} \left(\frac{A a^{2} e^{2}}{3} + \frac{2 A a c d^{2}}{3} + \frac{2 B a^{2} d e}{3}\right) + x^{2} \left(A a^{2} d e + \frac{B a^{2} d^{2}}{2}\right)"," ",0,"A*a**2*d**2*x + B*c**2*e**2*x**8/8 + x**7*(A*c**2*e**2/7 + 2*B*c**2*d*e/7) + x**6*(A*c**2*d*e/3 + B*a*c*e**2/3 + B*c**2*d**2/6) + x**5*(2*A*a*c*e**2/5 + A*c**2*d**2/5 + 4*B*a*c*d*e/5) + x**4*(A*a*c*d*e + B*a**2*e**2/4 + B*a*c*d**2/2) + x**3*(A*a**2*e**2/3 + 2*A*a*c*d**2/3 + 2*B*a**2*d*e/3) + x**2*(A*a**2*d*e + B*a**2*d**2/2)","A",0
1301,1,124,0,0.084504," ","integrate((B*x+A)*(e*x+d)*(c*x**2+a)**2,x)","A a^{2} d x + \frac{B c^{2} e x^{7}}{7} + x^{6} \left(\frac{A c^{2} e}{6} + \frac{B c^{2} d}{6}\right) + x^{5} \left(\frac{A c^{2} d}{5} + \frac{2 B a c e}{5}\right) + x^{4} \left(\frac{A a c e}{2} + \frac{B a c d}{2}\right) + x^{3} \left(\frac{2 A a c d}{3} + \frac{B a^{2} e}{3}\right) + x^{2} \left(\frac{A a^{2} e}{2} + \frac{B a^{2} d}{2}\right)"," ",0,"A*a**2*d*x + B*c**2*e*x**7/7 + x**6*(A*c**2*e/6 + B*c**2*d/6) + x**5*(A*c**2*d/5 + 2*B*a*c*e/5) + x**4*(A*a*c*e/2 + B*a*c*d/2) + x**3*(2*A*a*c*d/3 + B*a**2*e/3) + x**2*(A*a**2*e/2 + B*a**2*d/2)","A",0
1302,1,58,0,0.072514," ","integrate((B*x+A)*(c*x**2+a)**2,x)","A a^{2} x + \frac{2 A a c x^{3}}{3} + \frac{A c^{2} x^{5}}{5} + \frac{B a^{2} x^{2}}{2} + \frac{B a c x^{4}}{2} + \frac{B c^{2} x^{6}}{6}"," ",0,"A*a**2*x + 2*A*a*c*x**3/3 + A*c**2*x**5/5 + B*a**2*x**2/2 + B*a*c*x**4/2 + B*c**2*x**6/6","A",0
1303,1,207,0,0.576028," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d),x)","\frac{B c^{2} x^{5}}{5 e} + x^{4} \left(\frac{A c^{2}}{4 e} - \frac{B c^{2} d}{4 e^{2}}\right) + x^{3} \left(- \frac{A c^{2} d}{3 e^{2}} + \frac{2 B a c}{3 e} + \frac{B c^{2} d^{2}}{3 e^{3}}\right) + x^{2} \left(\frac{A a c}{e} + \frac{A c^{2} d^{2}}{2 e^{3}} - \frac{B a c d}{e^{2}} - \frac{B c^{2} d^{3}}{2 e^{4}}\right) + x \left(- \frac{2 A a c d}{e^{2}} - \frac{A c^{2} d^{3}}{e^{4}} + \frac{B a^{2}}{e} + \frac{2 B a c d^{2}}{e^{3}} + \frac{B c^{2} d^{4}}{e^{5}}\right) - \frac{\left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**5/(5*e) + x**4*(A*c**2/(4*e) - B*c**2*d/(4*e**2)) + x**3*(-A*c**2*d/(3*e**2) + 2*B*a*c/(3*e) + B*c**2*d**2/(3*e**3)) + x**2*(A*a*c/e + A*c**2*d**2/(2*e**3) - B*a*c*d/e**2 - B*c**2*d**3/(2*e**4)) + x*(-2*A*a*c*d/e**2 - A*c**2*d**3/e**4 + B*a**2/e + 2*B*a*c*d**2/e**3 + B*c**2*d**4/e**5) - (-A*e + B*d)*(a*e**2 + c*d**2)**2*log(d + e*x)/e**6","A",0
1304,1,246,0,1.190853," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**2,x)","\frac{B c^{2} x^{4}}{4 e^{2}} + x^{3} \left(\frac{A c^{2}}{3 e^{2}} - \frac{2 B c^{2} d}{3 e^{3}}\right) + x^{2} \left(- \frac{A c^{2} d}{e^{3}} + \frac{B a c}{e^{2}} + \frac{3 B c^{2} d^{2}}{2 e^{4}}\right) + x \left(\frac{2 A a c}{e^{2}} + \frac{3 A c^{2} d^{2}}{e^{4}} - \frac{4 B a c d}{e^{3}} - \frac{4 B c^{2} d^{3}}{e^{5}}\right) + \frac{- A a^{2} e^{5} - 2 A a c d^{2} e^{3} - A c^{2} d^{4} e + B a^{2} d e^{4} + 2 B a c d^{3} e^{2} + B c^{2} d^{5}}{d e^{6} + e^{7} x} + \frac{\left(a e^{2} + c d^{2}\right) \left(- 4 A c d e + B a e^{2} + 5 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**4/(4*e**2) + x**3*(A*c**2/(3*e**2) - 2*B*c**2*d/(3*e**3)) + x**2*(-A*c**2*d/e**3 + B*a*c/e**2 + 3*B*c**2*d**2/(2*e**4)) + x*(2*A*a*c/e**2 + 3*A*c**2*d**2/e**4 - 4*B*a*c*d/e**3 - 4*B*c**2*d**3/e**5) + (-A*a**2*e**5 - 2*A*a*c*d**2*e**3 - A*c**2*d**4*e + B*a**2*d*e**4 + 2*B*a*c*d**3*e**2 + B*c**2*d**5)/(d*e**6 + e**7*x) + (a*e**2 + c*d**2)*(-4*A*c*d*e + B*a*e**2 + 5*B*c*d**2)*log(d + e*x)/e**6","A",0
1305,1,282,0,3.333446," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**3,x)","\frac{B c^{2} x^{3}}{3 e^{3}} - \frac{2 c \left(- A a e^{3} - 3 A c d^{2} e + 3 B a d e^{2} + 5 B c d^{3}\right) \log{\left(d + e x \right)}}{e^{6}} + x^{2} \left(\frac{A c^{2}}{2 e^{3}} - \frac{3 B c^{2} d}{2 e^{4}}\right) + x \left(- \frac{3 A c^{2} d}{e^{4}} + \frac{2 B a c}{e^{3}} + \frac{6 B c^{2} d^{2}}{e^{5}}\right) + \frac{- A a^{2} e^{5} + 6 A a c d^{2} e^{3} + 7 A c^{2} d^{4} e - B a^{2} d e^{4} - 10 B a c d^{3} e^{2} - 9 B c^{2} d^{5} + x \left(8 A a c d e^{4} + 8 A c^{2} d^{3} e^{2} - 2 B a^{2} e^{5} - 12 B a c d^{2} e^{3} - 10 B c^{2} d^{4} e\right)}{2 d^{2} e^{6} + 4 d e^{7} x + 2 e^{8} x^{2}}"," ",0,"B*c**2*x**3/(3*e**3) - 2*c*(-A*a*e**3 - 3*A*c*d**2*e + 3*B*a*d*e**2 + 5*B*c*d**3)*log(d + e*x)/e**6 + x**2*(A*c**2/(2*e**3) - 3*B*c**2*d/(2*e**4)) + x*(-3*A*c**2*d/e**4 + 2*B*a*c/e**3 + 6*B*c**2*d**2/e**5) + (-A*a**2*e**5 + 6*A*a*c*d**2*e**3 + 7*A*c**2*d**4*e - B*a**2*d*e**4 - 10*B*a*c*d**3*e**2 - 9*B*c**2*d**5 + x*(8*A*a*c*d*e**4 + 8*A*c**2*d**3*e**2 - 2*B*a**2*e**5 - 12*B*a*c*d**2*e**3 - 10*B*c**2*d**4*e))/(2*d**2*e**6 + 4*d*e**7*x + 2*e**8*x**2)","A",0
1306,1,294,0,9.161136," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**4,x)","\frac{B c^{2} x^{2}}{2 e^{4}} + \frac{2 c \left(- 2 A c d e + B a e^{2} + 5 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{6}} + x \left(\frac{A c^{2}}{e^{4}} - \frac{4 B c^{2} d}{e^{5}}\right) + \frac{- 2 A a^{2} e^{5} - 4 A a c d^{2} e^{3} - 26 A c^{2} d^{4} e - B a^{2} d e^{4} + 22 B a c d^{3} e^{2} + 47 B c^{2} d^{5} + x^{2} \left(- 12 A a c e^{5} - 36 A c^{2} d^{2} e^{3} + 36 B a c d e^{4} + 60 B c^{2} d^{3} e^{2}\right) + x \left(- 12 A a c d e^{4} - 60 A c^{2} d^{3} e^{2} - 3 B a^{2} e^{5} + 54 B a c d^{2} e^{3} + 105 B c^{2} d^{4} e\right)}{6 d^{3} e^{6} + 18 d^{2} e^{7} x + 18 d e^{8} x^{2} + 6 e^{9} x^{3}}"," ",0,"B*c**2*x**2/(2*e**4) + 2*c*(-2*A*c*d*e + B*a*e**2 + 5*B*c*d**2)*log(d + e*x)/e**6 + x*(A*c**2/e**4 - 4*B*c**2*d/e**5) + (-2*A*a**2*e**5 - 4*A*a*c*d**2*e**3 - 26*A*c**2*d**4*e - B*a**2*d*e**4 + 22*B*a*c*d**3*e**2 + 47*B*c**2*d**5 + x**2*(-12*A*a*c*e**5 - 36*A*c**2*d**2*e**3 + 36*B*a*c*d*e**4 + 60*B*c**2*d**3*e**2) + x*(-12*A*a*c*d*e**4 - 60*A*c**2*d**3*e**2 - 3*B*a**2*e**5 + 54*B*a*c*d**2*e**3 + 105*B*c**2*d**4*e))/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3)","A",0
1307,1,304,0,21.565801," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**5,x)","\frac{B c^{2} x}{e^{5}} - \frac{c^{2} \left(- A e + 5 B d\right) \log{\left(d + e x \right)}}{e^{6}} + \frac{- 3 A a^{2} e^{5} - 2 A a c d^{2} e^{3} + 25 A c^{2} d^{4} e - B a^{2} d e^{4} - 6 B a c d^{3} e^{2} - 77 B c^{2} d^{5} + x^{3} \left(48 A c^{2} d e^{4} - 24 B a c e^{5} - 120 B c^{2} d^{2} e^{3}\right) + x^{2} \left(- 12 A a c e^{5} + 108 A c^{2} d^{2} e^{3} - 36 B a c d e^{4} - 300 B c^{2} d^{3} e^{2}\right) + x \left(- 8 A a c d e^{4} + 88 A c^{2} d^{3} e^{2} - 4 B a^{2} e^{5} - 24 B a c d^{2} e^{3} - 260 B c^{2} d^{4} e\right)}{12 d^{4} e^{6} + 48 d^{3} e^{7} x + 72 d^{2} e^{8} x^{2} + 48 d e^{9} x^{3} + 12 e^{10} x^{4}}"," ",0,"B*c**2*x/e**5 - c**2*(-A*e + 5*B*d)*log(d + e*x)/e**6 + (-3*A*a**2*e**5 - 2*A*a*c*d**2*e**3 + 25*A*c**2*d**4*e - B*a**2*d*e**4 - 6*B*a*c*d**3*e**2 - 77*B*c**2*d**5 + x**3*(48*A*c**2*d*e**4 - 24*B*a*c*e**5 - 120*B*c**2*d**2*e**3) + x**2*(-12*A*a*c*e**5 + 108*A*c**2*d**2*e**3 - 36*B*a*c*d*e**4 - 300*B*c**2*d**3*e**2) + x*(-8*A*a*c*d*e**4 + 88*A*c**2*d**3*e**2 - 4*B*a**2*e**5 - 24*B*a*c*d**2*e**3 - 260*B*c**2*d**4*e))/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4)","A",0
1308,1,326,0,54.056751," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**6,x)","\frac{B c^{2} \log{\left(d + e x \right)}}{e^{6}} + \frac{- 12 A a^{2} e^{5} - 4 A a c d^{2} e^{3} - 12 A c^{2} d^{4} e - 3 B a^{2} d e^{4} - 6 B a c d^{3} e^{2} + 137 B c^{2} d^{5} + x^{4} \left(- 60 A c^{2} e^{5} + 300 B c^{2} d e^{4}\right) + x^{3} \left(- 120 A c^{2} d e^{4} - 60 B a c e^{5} + 900 B c^{2} d^{2} e^{3}\right) + x^{2} \left(- 40 A a c e^{5} - 120 A c^{2} d^{2} e^{3} - 60 B a c d e^{4} + 1100 B c^{2} d^{3} e^{2}\right) + x \left(- 20 A a c d e^{4} - 60 A c^{2} d^{3} e^{2} - 15 B a^{2} e^{5} - 30 B a c d^{2} e^{3} + 625 B c^{2} d^{4} e\right)}{60 d^{5} e^{6} + 300 d^{4} e^{7} x + 600 d^{3} e^{8} x^{2} + 600 d^{2} e^{9} x^{3} + 300 d e^{10} x^{4} + 60 e^{11} x^{5}}"," ",0,"B*c**2*log(d + e*x)/e**6 + (-12*A*a**2*e**5 - 4*A*a*c*d**2*e**3 - 12*A*c**2*d**4*e - 3*B*a**2*d*e**4 - 6*B*a*c*d**3*e**2 + 137*B*c**2*d**5 + x**4*(-60*A*c**2*e**5 + 300*B*c**2*d*e**4) + x**3*(-120*A*c**2*d*e**4 - 60*B*a*c*e**5 + 900*B*c**2*d**2*e**3) + x**2*(-40*A*a*c*e**5 - 120*A*c**2*d**2*e**3 - 60*B*a*c*d*e**4 + 1100*B*c**2*d**3*e**2) + x*(-20*A*a*c*d*e**4 - 60*A*c**2*d**3*e**2 - 15*B*a**2*e**5 - 30*B*a*c*d**2*e**3 + 625*B*c**2*d**4*e))/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5)","A",0
1309,1,337,0,125.889271," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**7,x)","\frac{- 5 A a^{2} e^{5} - A a c d^{2} e^{3} - A c^{2} d^{4} e - B a^{2} d e^{4} - B a c d^{3} e^{2} - 5 B c^{2} d^{5} - 30 B c^{2} e^{5} x^{5} + x^{4} \left(- 15 A c^{2} e^{5} - 75 B c^{2} d e^{4}\right) + x^{3} \left(- 20 A c^{2} d e^{4} - 20 B a c e^{5} - 100 B c^{2} d^{2} e^{3}\right) + x^{2} \left(- 15 A a c e^{5} - 15 A c^{2} d^{2} e^{3} - 15 B a c d e^{4} - 75 B c^{2} d^{3} e^{2}\right) + x \left(- 6 A a c d e^{4} - 6 A c^{2} d^{3} e^{2} - 6 B a^{2} e^{5} - 6 B a c d^{2} e^{3} - 30 B c^{2} d^{4} e\right)}{30 d^{6} e^{6} + 180 d^{5} e^{7} x + 450 d^{4} e^{8} x^{2} + 600 d^{3} e^{9} x^{3} + 450 d^{2} e^{10} x^{4} + 180 d e^{11} x^{5} + 30 e^{12} x^{6}}"," ",0,"(-5*A*a**2*e**5 - A*a*c*d**2*e**3 - A*c**2*d**4*e - B*a**2*d*e**4 - B*a*c*d**3*e**2 - 5*B*c**2*d**5 - 30*B*c**2*e**5*x**5 + x**4*(-15*A*c**2*e**5 - 75*B*c**2*d*e**4) + x**3*(-20*A*c**2*d*e**4 - 20*B*a*c*e**5 - 100*B*c**2*d**2*e**3) + x**2*(-15*A*a*c*e**5 - 15*A*c**2*d**2*e**3 - 15*B*a*c*d*e**4 - 75*B*c**2*d**3*e**2) + x*(-6*A*a*c*d*e**4 - 6*A*c**2*d**3*e**2 - 6*B*a**2*e**5 - 6*B*a*c*d**2*e**3 - 30*B*c**2*d**4*e))/(30*d**6*e**6 + 180*d**5*e**7*x + 450*d**4*e**8*x**2 + 600*d**3*e**9*x**3 + 450*d**2*e**10*x**4 + 180*d*e**11*x**5 + 30*e**12*x**6)","A",0
1310,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1311,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,1,694,0,0.163323," ","integrate((B*x+A)*(e*x+d)**5*(c*x**2+a)**3,x)","A a^{3} d^{5} x + \frac{B c^{3} e^{5} x^{13}}{13} + x^{12} \left(\frac{A c^{3} e^{5}}{12} + \frac{5 B c^{3} d e^{4}}{12}\right) + x^{11} \left(\frac{5 A c^{3} d e^{4}}{11} + \frac{3 B a c^{2} e^{5}}{11} + \frac{10 B c^{3} d^{2} e^{3}}{11}\right) + x^{10} \left(\frac{3 A a c^{2} e^{5}}{10} + A c^{3} d^{2} e^{3} + \frac{3 B a c^{2} d e^{4}}{2} + B c^{3} d^{3} e^{2}\right) + x^{9} \left(\frac{5 A a c^{2} d e^{4}}{3} + \frac{10 A c^{3} d^{3} e^{2}}{9} + \frac{B a^{2} c e^{5}}{3} + \frac{10 B a c^{2} d^{2} e^{3}}{3} + \frac{5 B c^{3} d^{4} e}{9}\right) + x^{8} \left(\frac{3 A a^{2} c e^{5}}{8} + \frac{15 A a c^{2} d^{2} e^{3}}{4} + \frac{5 A c^{3} d^{4} e}{8} + \frac{15 B a^{2} c d e^{4}}{8} + \frac{15 B a c^{2} d^{3} e^{2}}{4} + \frac{B c^{3} d^{5}}{8}\right) + x^{7} \left(\frac{15 A a^{2} c d e^{4}}{7} + \frac{30 A a c^{2} d^{3} e^{2}}{7} + \frac{A c^{3} d^{5}}{7} + \frac{B a^{3} e^{5}}{7} + \frac{30 B a^{2} c d^{2} e^{3}}{7} + \frac{15 B a c^{2} d^{4} e}{7}\right) + x^{6} \left(\frac{A a^{3} e^{5}}{6} + 5 A a^{2} c d^{2} e^{3} + \frac{5 A a c^{2} d^{4} e}{2} + \frac{5 B a^{3} d e^{4}}{6} + 5 B a^{2} c d^{3} e^{2} + \frac{B a c^{2} d^{5}}{2}\right) + x^{5} \left(A a^{3} d e^{4} + 6 A a^{2} c d^{3} e^{2} + \frac{3 A a c^{2} d^{5}}{5} + 2 B a^{3} d^{2} e^{3} + 3 B a^{2} c d^{4} e\right) + x^{4} \left(\frac{5 A a^{3} d^{2} e^{3}}{2} + \frac{15 A a^{2} c d^{4} e}{4} + \frac{5 B a^{3} d^{3} e^{2}}{2} + \frac{3 B a^{2} c d^{5}}{4}\right) + x^{3} \left(\frac{10 A a^{3} d^{3} e^{2}}{3} + A a^{2} c d^{5} + \frac{5 B a^{3} d^{4} e}{3}\right) + x^{2} \left(\frac{5 A a^{3} d^{4} e}{2} + \frac{B a^{3} d^{5}}{2}\right)"," ",0,"A*a**3*d**5*x + B*c**3*e**5*x**13/13 + x**12*(A*c**3*e**5/12 + 5*B*c**3*d*e**4/12) + x**11*(5*A*c**3*d*e**4/11 + 3*B*a*c**2*e**5/11 + 10*B*c**3*d**2*e**3/11) + x**10*(3*A*a*c**2*e**5/10 + A*c**3*d**2*e**3 + 3*B*a*c**2*d*e**4/2 + B*c**3*d**3*e**2) + x**9*(5*A*a*c**2*d*e**4/3 + 10*A*c**3*d**3*e**2/9 + B*a**2*c*e**5/3 + 10*B*a*c**2*d**2*e**3/3 + 5*B*c**3*d**4*e/9) + x**8*(3*A*a**2*c*e**5/8 + 15*A*a*c**2*d**2*e**3/4 + 5*A*c**3*d**4*e/8 + 15*B*a**2*c*d*e**4/8 + 15*B*a*c**2*d**3*e**2/4 + B*c**3*d**5/8) + x**7*(15*A*a**2*c*d*e**4/7 + 30*A*a*c**2*d**3*e**2/7 + A*c**3*d**5/7 + B*a**3*e**5/7 + 30*B*a**2*c*d**2*e**3/7 + 15*B*a*c**2*d**4*e/7) + x**6*(A*a**3*e**5/6 + 5*A*a**2*c*d**2*e**3 + 5*A*a*c**2*d**4*e/2 + 5*B*a**3*d*e**4/6 + 5*B*a**2*c*d**3*e**2 + B*a*c**2*d**5/2) + x**5*(A*a**3*d*e**4 + 6*A*a**2*c*d**3*e**2 + 3*A*a*c**2*d**5/5 + 2*B*a**3*d**2*e**3 + 3*B*a**2*c*d**4*e) + x**4*(5*A*a**3*d**2*e**3/2 + 15*A*a**2*c*d**4*e/4 + 5*B*a**3*d**3*e**2/2 + 3*B*a**2*c*d**5/4) + x**3*(10*A*a**3*d**3*e**2/3 + A*a**2*c*d**5 + 5*B*a**3*d**4*e/3) + x**2*(5*A*a**3*d**4*e/2 + B*a**3*d**5/2)","B",0
1314,1,564,0,0.151938," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+a)**3,x)","A a^{3} d^{4} x + \frac{B c^{3} e^{4} x^{12}}{12} + x^{11} \left(\frac{A c^{3} e^{4}}{11} + \frac{4 B c^{3} d e^{3}}{11}\right) + x^{10} \left(\frac{2 A c^{3} d e^{3}}{5} + \frac{3 B a c^{2} e^{4}}{10} + \frac{3 B c^{3} d^{2} e^{2}}{5}\right) + x^{9} \left(\frac{A a c^{2} e^{4}}{3} + \frac{2 A c^{3} d^{2} e^{2}}{3} + \frac{4 B a c^{2} d e^{3}}{3} + \frac{4 B c^{3} d^{3} e}{9}\right) + x^{8} \left(\frac{3 A a c^{2} d e^{3}}{2} + \frac{A c^{3} d^{3} e}{2} + \frac{3 B a^{2} c e^{4}}{8} + \frac{9 B a c^{2} d^{2} e^{2}}{4} + \frac{B c^{3} d^{4}}{8}\right) + x^{7} \left(\frac{3 A a^{2} c e^{4}}{7} + \frac{18 A a c^{2} d^{2} e^{2}}{7} + \frac{A c^{3} d^{4}}{7} + \frac{12 B a^{2} c d e^{3}}{7} + \frac{12 B a c^{2} d^{3} e}{7}\right) + x^{6} \left(2 A a^{2} c d e^{3} + 2 A a c^{2} d^{3} e + \frac{B a^{3} e^{4}}{6} + 3 B a^{2} c d^{2} e^{2} + \frac{B a c^{2} d^{4}}{2}\right) + x^{5} \left(\frac{A a^{3} e^{4}}{5} + \frac{18 A a^{2} c d^{2} e^{2}}{5} + \frac{3 A a c^{2} d^{4}}{5} + \frac{4 B a^{3} d e^{3}}{5} + \frac{12 B a^{2} c d^{3} e}{5}\right) + x^{4} \left(A a^{3} d e^{3} + 3 A a^{2} c d^{3} e + \frac{3 B a^{3} d^{2} e^{2}}{2} + \frac{3 B a^{2} c d^{4}}{4}\right) + x^{3} \left(2 A a^{3} d^{2} e^{2} + A a^{2} c d^{4} + \frac{4 B a^{3} d^{3} e}{3}\right) + x^{2} \left(2 A a^{3} d^{3} e + \frac{B a^{3} d^{4}}{2}\right)"," ",0,"A*a**3*d**4*x + B*c**3*e**4*x**12/12 + x**11*(A*c**3*e**4/11 + 4*B*c**3*d*e**3/11) + x**10*(2*A*c**3*d*e**3/5 + 3*B*a*c**2*e**4/10 + 3*B*c**3*d**2*e**2/5) + x**9*(A*a*c**2*e**4/3 + 2*A*c**3*d**2*e**2/3 + 4*B*a*c**2*d*e**3/3 + 4*B*c**3*d**3*e/9) + x**8*(3*A*a*c**2*d*e**3/2 + A*c**3*d**3*e/2 + 3*B*a**2*c*e**4/8 + 9*B*a*c**2*d**2*e**2/4 + B*c**3*d**4/8) + x**7*(3*A*a**2*c*e**4/7 + 18*A*a*c**2*d**2*e**2/7 + A*c**3*d**4/7 + 12*B*a**2*c*d*e**3/7 + 12*B*a*c**2*d**3*e/7) + x**6*(2*A*a**2*c*d*e**3 + 2*A*a*c**2*d**3*e + B*a**3*e**4/6 + 3*B*a**2*c*d**2*e**2 + B*a*c**2*d**4/2) + x**5*(A*a**3*e**4/5 + 18*A*a**2*c*d**2*e**2/5 + 3*A*a*c**2*d**4/5 + 4*B*a**3*d*e**3/5 + 12*B*a**2*c*d**3*e/5) + x**4*(A*a**3*d*e**3 + 3*A*a**2*c*d**3*e + 3*B*a**3*d**2*e**2/2 + 3*B*a**2*c*d**4/4) + x**3*(2*A*a**3*d**2*e**2 + A*a**2*c*d**4 + 4*B*a**3*d**3*e/3) + x**2*(2*A*a**3*d**3*e + B*a**3*d**4/2)","A",0
1315,1,435,0,0.136509," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+a)**3,x)","A a^{3} d^{3} x + \frac{B c^{3} e^{3} x^{11}}{11} + x^{10} \left(\frac{A c^{3} e^{3}}{10} + \frac{3 B c^{3} d e^{2}}{10}\right) + x^{9} \left(\frac{A c^{3} d e^{2}}{3} + \frac{B a c^{2} e^{3}}{3} + \frac{B c^{3} d^{2} e}{3}\right) + x^{8} \left(\frac{3 A a c^{2} e^{3}}{8} + \frac{3 A c^{3} d^{2} e}{8} + \frac{9 B a c^{2} d e^{2}}{8} + \frac{B c^{3} d^{3}}{8}\right) + x^{7} \left(\frac{9 A a c^{2} d e^{2}}{7} + \frac{A c^{3} d^{3}}{7} + \frac{3 B a^{2} c e^{3}}{7} + \frac{9 B a c^{2} d^{2} e}{7}\right) + x^{6} \left(\frac{A a^{2} c e^{3}}{2} + \frac{3 A a c^{2} d^{2} e}{2} + \frac{3 B a^{2} c d e^{2}}{2} + \frac{B a c^{2} d^{3}}{2}\right) + x^{5} \left(\frac{9 A a^{2} c d e^{2}}{5} + \frac{3 A a c^{2} d^{3}}{5} + \frac{B a^{3} e^{3}}{5} + \frac{9 B a^{2} c d^{2} e}{5}\right) + x^{4} \left(\frac{A a^{3} e^{3}}{4} + \frac{9 A a^{2} c d^{2} e}{4} + \frac{3 B a^{3} d e^{2}}{4} + \frac{3 B a^{2} c d^{3}}{4}\right) + x^{3} \left(A a^{3} d e^{2} + A a^{2} c d^{3} + B a^{3} d^{2} e\right) + x^{2} \left(\frac{3 A a^{3} d^{2} e}{2} + \frac{B a^{3} d^{3}}{2}\right)"," ",0,"A*a**3*d**3*x + B*c**3*e**3*x**11/11 + x**10*(A*c**3*e**3/10 + 3*B*c**3*d*e**2/10) + x**9*(A*c**3*d*e**2/3 + B*a*c**2*e**3/3 + B*c**3*d**2*e/3) + x**8*(3*A*a*c**2*e**3/8 + 3*A*c**3*d**2*e/8 + 9*B*a*c**2*d*e**2/8 + B*c**3*d**3/8) + x**7*(9*A*a*c**2*d*e**2/7 + A*c**3*d**3/7 + 3*B*a**2*c*e**3/7 + 9*B*a*c**2*d**2*e/7) + x**6*(A*a**2*c*e**3/2 + 3*A*a*c**2*d**2*e/2 + 3*B*a**2*c*d*e**2/2 + B*a*c**2*d**3/2) + x**5*(9*A*a**2*c*d*e**2/5 + 3*A*a*c**2*d**3/5 + B*a**3*e**3/5 + 9*B*a**2*c*d**2*e/5) + x**4*(A*a**3*e**3/4 + 9*A*a**2*c*d**2*e/4 + 3*B*a**3*d*e**2/4 + 3*B*a**2*c*d**3/4) + x**3*(A*a**3*d*e**2 + A*a**2*c*d**3 + B*a**3*d**2*e) + x**2*(3*A*a**3*d**2*e/2 + B*a**3*d**3/2)","A",0
1316,1,306,0,0.114171," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+a)**3,x)","A a^{3} d^{2} x + \frac{B c^{3} e^{2} x^{10}}{10} + x^{9} \left(\frac{A c^{3} e^{2}}{9} + \frac{2 B c^{3} d e}{9}\right) + x^{8} \left(\frac{A c^{3} d e}{4} + \frac{3 B a c^{2} e^{2}}{8} + \frac{B c^{3} d^{2}}{8}\right) + x^{7} \left(\frac{3 A a c^{2} e^{2}}{7} + \frac{A c^{3} d^{2}}{7} + \frac{6 B a c^{2} d e}{7}\right) + x^{6} \left(A a c^{2} d e + \frac{B a^{2} c e^{2}}{2} + \frac{B a c^{2} d^{2}}{2}\right) + x^{5} \left(\frac{3 A a^{2} c e^{2}}{5} + \frac{3 A a c^{2} d^{2}}{5} + \frac{6 B a^{2} c d e}{5}\right) + x^{4} \left(\frac{3 A a^{2} c d e}{2} + \frac{B a^{3} e^{2}}{4} + \frac{3 B a^{2} c d^{2}}{4}\right) + x^{3} \left(\frac{A a^{3} e^{2}}{3} + A a^{2} c d^{2} + \frac{2 B a^{3} d e}{3}\right) + x^{2} \left(A a^{3} d e + \frac{B a^{3} d^{2}}{2}\right)"," ",0,"A*a**3*d**2*x + B*c**3*e**2*x**10/10 + x**9*(A*c**3*e**2/9 + 2*B*c**3*d*e/9) + x**8*(A*c**3*d*e/4 + 3*B*a*c**2*e**2/8 + B*c**3*d**2/8) + x**7*(3*A*a*c**2*e**2/7 + A*c**3*d**2/7 + 6*B*a*c**2*d*e/7) + x**6*(A*a*c**2*d*e + B*a**2*c*e**2/2 + B*a*c**2*d**2/2) + x**5*(3*A*a**2*c*e**2/5 + 3*A*a*c**2*d**2/5 + 6*B*a**2*c*d*e/5) + x**4*(3*A*a**2*c*d*e/2 + B*a**3*e**2/4 + 3*B*a**2*c*d**2/4) + x**3*(A*a**3*e**2/3 + A*a**2*c*d**2 + 2*B*a**3*d*e/3) + x**2*(A*a**3*d*e + B*a**3*d**2/2)","A",0
1317,1,182,0,0.094337," ","integrate((B*x+A)*(e*x+d)*(c*x**2+a)**3,x)","A a^{3} d x + \frac{B c^{3} e x^{9}}{9} + x^{8} \left(\frac{A c^{3} e}{8} + \frac{B c^{3} d}{8}\right) + x^{7} \left(\frac{A c^{3} d}{7} + \frac{3 B a c^{2} e}{7}\right) + x^{6} \left(\frac{A a c^{2} e}{2} + \frac{B a c^{2} d}{2}\right) + x^{5} \left(\frac{3 A a c^{2} d}{5} + \frac{3 B a^{2} c e}{5}\right) + x^{4} \left(\frac{3 A a^{2} c e}{4} + \frac{3 B a^{2} c d}{4}\right) + x^{3} \left(A a^{2} c d + \frac{B a^{3} e}{3}\right) + x^{2} \left(\frac{A a^{3} e}{2} + \frac{B a^{3} d}{2}\right)"," ",0,"A*a**3*d*x + B*c**3*e*x**9/9 + x**8*(A*c**3*e/8 + B*c**3*d/8) + x**7*(A*c**3*d/7 + 3*B*a*c**2*e/7) + x**6*(A*a*c**2*e/2 + B*a*c**2*d/2) + x**5*(3*A*a*c**2*d/5 + 3*B*a**2*c*e/5) + x**4*(3*A*a**2*c*e/4 + 3*B*a**2*c*d/4) + x**3*(A*a**2*c*d + B*a**3*e/3) + x**2*(A*a**3*e/2 + B*a**3*d/2)","A",0
1318,1,85,0,0.077476," ","integrate((B*x+A)*(c*x**2+a)**3,x)","A a^{3} x + A a^{2} c x^{3} + \frac{3 A a c^{2} x^{5}}{5} + \frac{A c^{3} x^{7}}{7} + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} c x^{4}}{4} + \frac{B a c^{2} x^{6}}{2} + \frac{B c^{3} x^{8}}{8}"," ",0,"A*a**3*x + A*a**2*c*x**3 + 3*A*a*c**2*x**5/5 + A*c**3*x**7/7 + B*a**3*x**2/2 + 3*B*a**2*c*x**4/4 + B*a*c**2*x**6/2 + B*c**3*x**8/8","A",0
1319,1,410,0,0.918566," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d),x)","\frac{B c^{3} x^{7}}{7 e} + x^{6} \left(\frac{A c^{3}}{6 e} - \frac{B c^{3} d}{6 e^{2}}\right) + x^{5} \left(- \frac{A c^{3} d}{5 e^{2}} + \frac{3 B a c^{2}}{5 e} + \frac{B c^{3} d^{2}}{5 e^{3}}\right) + x^{4} \left(\frac{3 A a c^{2}}{4 e} + \frac{A c^{3} d^{2}}{4 e^{3}} - \frac{3 B a c^{2} d}{4 e^{2}} - \frac{B c^{3} d^{3}}{4 e^{4}}\right) + x^{3} \left(- \frac{A a c^{2} d}{e^{2}} - \frac{A c^{3} d^{3}}{3 e^{4}} + \frac{B a^{2} c}{e} + \frac{B a c^{2} d^{2}}{e^{3}} + \frac{B c^{3} d^{4}}{3 e^{5}}\right) + x^{2} \left(\frac{3 A a^{2} c}{2 e} + \frac{3 A a c^{2} d^{2}}{2 e^{3}} + \frac{A c^{3} d^{4}}{2 e^{5}} - \frac{3 B a^{2} c d}{2 e^{2}} - \frac{3 B a c^{2} d^{3}}{2 e^{4}} - \frac{B c^{3} d^{5}}{2 e^{6}}\right) + x \left(- \frac{3 A a^{2} c d}{e^{2}} - \frac{3 A a c^{2} d^{3}}{e^{4}} - \frac{A c^{3} d^{5}}{e^{6}} + \frac{B a^{3}}{e} + \frac{3 B a^{2} c d^{2}}{e^{3}} + \frac{3 B a c^{2} d^{4}}{e^{5}} + \frac{B c^{3} d^{6}}{e^{7}}\right) - \frac{\left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{8}}"," ",0,"B*c**3*x**7/(7*e) + x**6*(A*c**3/(6*e) - B*c**3*d/(6*e**2)) + x**5*(-A*c**3*d/(5*e**2) + 3*B*a*c**2/(5*e) + B*c**3*d**2/(5*e**3)) + x**4*(3*A*a*c**2/(4*e) + A*c**3*d**2/(4*e**3) - 3*B*a*c**2*d/(4*e**2) - B*c**3*d**3/(4*e**4)) + x**3*(-A*a*c**2*d/e**2 - A*c**3*d**3/(3*e**4) + B*a**2*c/e + B*a*c**2*d**2/e**3 + B*c**3*d**4/(3*e**5)) + x**2*(3*A*a**2*c/(2*e) + 3*A*a*c**2*d**2/(2*e**3) + A*c**3*d**4/(2*e**5) - 3*B*a**2*c*d/(2*e**2) - 3*B*a*c**2*d**3/(2*e**4) - B*c**3*d**5/(2*e**6)) + x*(-3*A*a**2*c*d/e**2 - 3*A*a*c**2*d**3/e**4 - A*c**3*d**5/e**6 + B*a**3/e + 3*B*a**2*c*d**2/e**3 + 3*B*a*c**2*d**4/e**5 + B*c**3*d**6/e**7) - (-A*e + B*d)*(a*e**2 + c*d**2)**3*log(d + e*x)/e**8","A",0
1320,1,454,0,1.958099," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**2,x)","\frac{B c^{3} x^{6}}{6 e^{2}} + x^{5} \left(\frac{A c^{3}}{5 e^{2}} - \frac{2 B c^{3} d}{5 e^{3}}\right) + x^{4} \left(- \frac{A c^{3} d}{2 e^{3}} + \frac{3 B a c^{2}}{4 e^{2}} + \frac{3 B c^{3} d^{2}}{4 e^{4}}\right) + x^{3} \left(\frac{A a c^{2}}{e^{2}} + \frac{A c^{3} d^{2}}{e^{4}} - \frac{2 B a c^{2} d}{e^{3}} - \frac{4 B c^{3} d^{3}}{3 e^{5}}\right) + x^{2} \left(- \frac{3 A a c^{2} d}{e^{3}} - \frac{2 A c^{3} d^{3}}{e^{5}} + \frac{3 B a^{2} c}{2 e^{2}} + \frac{9 B a c^{2} d^{2}}{2 e^{4}} + \frac{5 B c^{3} d^{4}}{2 e^{6}}\right) + x \left(\frac{3 A a^{2} c}{e^{2}} + \frac{9 A a c^{2} d^{2}}{e^{4}} + \frac{5 A c^{3} d^{4}}{e^{6}} - \frac{6 B a^{2} c d}{e^{3}} - \frac{12 B a c^{2} d^{3}}{e^{5}} - \frac{6 B c^{3} d^{5}}{e^{7}}\right) + \frac{- A a^{3} e^{7} - 3 A a^{2} c d^{2} e^{5} - 3 A a c^{2} d^{4} e^{3} - A c^{3} d^{6} e + B a^{3} d e^{6} + 3 B a^{2} c d^{3} e^{4} + 3 B a c^{2} d^{5} e^{2} + B c^{3} d^{7}}{d e^{8} + e^{9} x} + \frac{\left(a e^{2} + c d^{2}\right)^{2} \left(- 6 A c d e + B a e^{2} + 7 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"B*c**3*x**6/(6*e**2) + x**5*(A*c**3/(5*e**2) - 2*B*c**3*d/(5*e**3)) + x**4*(-A*c**3*d/(2*e**3) + 3*B*a*c**2/(4*e**2) + 3*B*c**3*d**2/(4*e**4)) + x**3*(A*a*c**2/e**2 + A*c**3*d**2/e**4 - 2*B*a*c**2*d/e**3 - 4*B*c**3*d**3/(3*e**5)) + x**2*(-3*A*a*c**2*d/e**3 - 2*A*c**3*d**3/e**5 + 3*B*a**2*c/(2*e**2) + 9*B*a*c**2*d**2/(2*e**4) + 5*B*c**3*d**4/(2*e**6)) + x*(3*A*a**2*c/e**2 + 9*A*a*c**2*d**2/e**4 + 5*A*c**3*d**4/e**6 - 6*B*a**2*c*d/e**3 - 12*B*a*c**2*d**3/e**5 - 6*B*c**3*d**5/e**7) + (-A*a**3*e**7 - 3*A*a**2*c*d**2*e**5 - 3*A*a*c**2*d**4*e**3 - A*c**3*d**6*e + B*a**3*d*e**6 + 3*B*a**2*c*d**3*e**4 + 3*B*a*c**2*d**5*e**2 + B*c**3*d**7)/(d*e**8 + e**9*x) + (a*e**2 + c*d**2)**2*(-6*A*c*d*e + B*a*e**2 + 7*B*c*d**2)*log(d + e*x)/e**8","A",0
1321,1,490,0,6.096389," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**3,x)","\frac{B c^{3} x^{5}}{5 e^{3}} - \frac{3 c \left(a e^{2} + c d^{2}\right) \left(- A a e^{3} - 5 A c d^{2} e + 3 B a d e^{2} + 7 B c d^{3}\right) \log{\left(d + e x \right)}}{e^{8}} + x^{4} \left(\frac{A c^{3}}{4 e^{3}} - \frac{3 B c^{3} d}{4 e^{4}}\right) + x^{3} \left(- \frac{A c^{3} d}{e^{4}} + \frac{B a c^{2}}{e^{3}} + \frac{2 B c^{3} d^{2}}{e^{5}}\right) + x^{2} \left(\frac{3 A a c^{2}}{2 e^{3}} + \frac{3 A c^{3} d^{2}}{e^{5}} - \frac{9 B a c^{2} d}{2 e^{4}} - \frac{5 B c^{3} d^{3}}{e^{6}}\right) + x \left(- \frac{9 A a c^{2} d}{e^{4}} - \frac{10 A c^{3} d^{3}}{e^{6}} + \frac{3 B a^{2} c}{e^{3}} + \frac{18 B a c^{2} d^{2}}{e^{5}} + \frac{15 B c^{3} d^{4}}{e^{7}}\right) + \frac{- A a^{3} e^{7} + 9 A a^{2} c d^{2} e^{5} + 21 A a c^{2} d^{4} e^{3} + 11 A c^{3} d^{6} e - B a^{3} d e^{6} - 15 B a^{2} c d^{3} e^{4} - 27 B a c^{2} d^{5} e^{2} - 13 B c^{3} d^{7} + x \left(12 A a^{2} c d e^{6} + 24 A a c^{2} d^{3} e^{4} + 12 A c^{3} d^{5} e^{2} - 2 B a^{3} e^{7} - 18 B a^{2} c d^{2} e^{5} - 30 B a c^{2} d^{4} e^{3} - 14 B c^{3} d^{6} e\right)}{2 d^{2} e^{8} + 4 d e^{9} x + 2 e^{10} x^{2}}"," ",0,"B*c**3*x**5/(5*e**3) - 3*c*(a*e**2 + c*d**2)*(-A*a*e**3 - 5*A*c*d**2*e + 3*B*a*d*e**2 + 7*B*c*d**3)*log(d + e*x)/e**8 + x**4*(A*c**3/(4*e**3) - 3*B*c**3*d/(4*e**4)) + x**3*(-A*c**3*d/e**4 + B*a*c**2/e**3 + 2*B*c**3*d**2/e**5) + x**2*(3*A*a*c**2/(2*e**3) + 3*A*c**3*d**2/e**5 - 9*B*a*c**2*d/(2*e**4) - 5*B*c**3*d**3/e**6) + x*(-9*A*a*c**2*d/e**4 - 10*A*c**3*d**3/e**6 + 3*B*a**2*c/e**3 + 18*B*a*c**2*d**2/e**5 + 15*B*c**3*d**4/e**7) + (-A*a**3*e**7 + 9*A*a**2*c*d**2*e**5 + 21*A*a*c**2*d**4*e**3 + 11*A*c**3*d**6*e - B*a**3*d*e**6 - 15*B*a**2*c*d**3*e**4 - 27*B*a*c**2*d**5*e**2 - 13*B*c**3*d**7 + x*(12*A*a**2*c*d*e**6 + 24*A*a*c**2*d**3*e**4 + 12*A*c**3*d**5*e**2 - 2*B*a**3*e**7 - 18*B*a**2*c*d**2*e**5 - 30*B*a*c**2*d**4*e**3 - 14*B*c**3*d**6*e))/(2*d**2*e**8 + 4*d*e**9*x + 2*e**10*x**2)","A",0
1322,1,530,0,18.980229," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**4,x)","\frac{B c^{3} x^{4}}{4 e^{4}} + \frac{c \left(- 12 A a c d e^{3} - 20 A c^{2} d^{3} e + 3 B a^{2} e^{4} + 30 B a c d^{2} e^{2} + 35 B c^{2} d^{4}\right) \log{\left(d + e x \right)}}{e^{8}} + x^{3} \left(\frac{A c^{3}}{3 e^{4}} - \frac{4 B c^{3} d}{3 e^{5}}\right) + x^{2} \left(- \frac{2 A c^{3} d}{e^{5}} + \frac{3 B a c^{2}}{2 e^{4}} + \frac{5 B c^{3} d^{2}}{e^{6}}\right) + x \left(\frac{3 A a c^{2}}{e^{4}} + \frac{10 A c^{3} d^{2}}{e^{6}} - \frac{12 B a c^{2} d}{e^{5}} - \frac{20 B c^{3} d^{3}}{e^{7}}\right) + \frac{- 2 A a^{3} e^{7} - 6 A a^{2} c d^{2} e^{5} - 78 A a c^{2} d^{4} e^{3} - 74 A c^{3} d^{6} e - B a^{3} d e^{6} + 33 B a^{2} c d^{3} e^{4} + 141 B a c^{2} d^{5} e^{2} + 107 B c^{3} d^{7} + x^{2} \left(- 18 A a^{2} c e^{7} - 108 A a c^{2} d^{2} e^{5} - 90 A c^{3} d^{4} e^{3} + 54 B a^{2} c d e^{6} + 180 B a c^{2} d^{3} e^{4} + 126 B c^{3} d^{5} e^{2}\right) + x \left(- 18 A a^{2} c d e^{6} - 180 A a c^{2} d^{3} e^{4} - 162 A c^{3} d^{5} e^{2} - 3 B a^{3} e^{7} + 81 B a^{2} c d^{2} e^{5} + 315 B a c^{2} d^{4} e^{3} + 231 B c^{3} d^{6} e\right)}{6 d^{3} e^{8} + 18 d^{2} e^{9} x + 18 d e^{10} x^{2} + 6 e^{11} x^{3}}"," ",0,"B*c**3*x**4/(4*e**4) + c*(-12*A*a*c*d*e**3 - 20*A*c**2*d**3*e + 3*B*a**2*e**4 + 30*B*a*c*d**2*e**2 + 35*B*c**2*d**4)*log(d + e*x)/e**8 + x**3*(A*c**3/(3*e**4) - 4*B*c**3*d/(3*e**5)) + x**2*(-2*A*c**3*d/e**5 + 3*B*a*c**2/(2*e**4) + 5*B*c**3*d**2/e**6) + x*(3*A*a*c**2/e**4 + 10*A*c**3*d**2/e**6 - 12*B*a*c**2*d/e**5 - 20*B*c**3*d**3/e**7) + (-2*A*a**3*e**7 - 6*A*a**2*c*d**2*e**5 - 78*A*a*c**2*d**4*e**3 - 74*A*c**3*d**6*e - B*a**3*d*e**6 + 33*B*a**2*c*d**3*e**4 + 141*B*a*c**2*d**5*e**2 + 107*B*c**3*d**7 + x**2*(-18*A*a**2*c*e**7 - 108*A*a*c**2*d**2*e**5 - 90*A*c**3*d**4*e**3 + 54*B*a**2*c*d*e**6 + 180*B*a*c**2*d**3*e**4 + 126*B*c**3*d**5*e**2) + x*(-18*A*a**2*c*d*e**6 - 180*A*a*c**2*d**3*e**4 - 162*A*c**3*d**5*e**2 - 3*B*a**3*e**7 + 81*B*a**2*c*d**2*e**5 + 315*B*a*c**2*d**4*e**3 + 231*B*c**3*d**6*e))/(6*d**3*e**8 + 18*d**2*e**9*x + 18*d*e**10*x**2 + 6*e**11*x**3)","A",0
1323,1,537,0,63.111076," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**5,x)","\frac{B c^{3} x^{3}}{3 e^{5}} - \frac{c^{2} \left(- 3 A a e^{3} - 15 A c d^{2} e + 15 B a d e^{2} + 35 B c d^{3}\right) \log{\left(d + e x \right)}}{e^{8}} + x^{2} \left(\frac{A c^{3}}{2 e^{5}} - \frac{5 B c^{3} d}{2 e^{6}}\right) + x \left(- \frac{5 A c^{3} d}{e^{6}} + \frac{3 B a c^{2}}{e^{5}} + \frac{15 B c^{3} d^{2}}{e^{7}}\right) + \frac{- 3 A a^{3} e^{7} - 3 A a^{2} c d^{2} e^{5} + 75 A a c^{2} d^{4} e^{3} + 171 A c^{3} d^{6} e - B a^{3} d e^{6} - 9 B a^{2} c d^{3} e^{4} - 231 B a c^{2} d^{5} e^{2} - 319 B c^{3} d^{7} + x^{3} \left(144 A a c^{2} d e^{6} + 240 A c^{3} d^{3} e^{4} - 36 B a^{2} c e^{7} - 360 B a c^{2} d^{2} e^{5} - 420 B c^{3} d^{4} e^{3}\right) + x^{2} \left(- 18 A a^{2} c e^{7} + 324 A a c^{2} d^{2} e^{5} + 630 A c^{3} d^{4} e^{3} - 54 B a^{2} c d e^{6} - 900 B a c^{2} d^{3} e^{4} - 1134 B c^{3} d^{5} e^{2}\right) + x \left(- 12 A a^{2} c d e^{6} + 264 A a c^{2} d^{3} e^{4} + 564 A c^{3} d^{5} e^{2} - 4 B a^{3} e^{7} - 36 B a^{2} c d^{2} e^{5} - 780 B a c^{2} d^{4} e^{3} - 1036 B c^{3} d^{6} e\right)}{12 d^{4} e^{8} + 48 d^{3} e^{9} x + 72 d^{2} e^{10} x^{2} + 48 d e^{11} x^{3} + 12 e^{12} x^{4}}"," ",0,"B*c**3*x**3/(3*e**5) - c**2*(-3*A*a*e**3 - 15*A*c*d**2*e + 15*B*a*d*e**2 + 35*B*c*d**3)*log(d + e*x)/e**8 + x**2*(A*c**3/(2*e**5) - 5*B*c**3*d/(2*e**6)) + x*(-5*A*c**3*d/e**6 + 3*B*a*c**2/e**5 + 15*B*c**3*d**2/e**7) + (-3*A*a**3*e**7 - 3*A*a**2*c*d**2*e**5 + 75*A*a*c**2*d**4*e**3 + 171*A*c**3*d**6*e - B*a**3*d*e**6 - 9*B*a**2*c*d**3*e**4 - 231*B*a*c**2*d**5*e**2 - 319*B*c**3*d**7 + x**3*(144*A*a*c**2*d*e**6 + 240*A*c**3*d**3*e**4 - 36*B*a**2*c*e**7 - 360*B*a*c**2*d**2*e**5 - 420*B*c**3*d**4*e**3) + x**2*(-18*A*a**2*c*e**7 + 324*A*a*c**2*d**2*e**5 + 630*A*c**3*d**4*e**3 - 54*B*a**2*c*d*e**6 - 900*B*a*c**2*d**3*e**4 - 1134*B*c**3*d**5*e**2) + x*(-12*A*a**2*c*d*e**6 + 264*A*a*c**2*d**3*e**4 + 564*A*c**3*d**5*e**2 - 4*B*a**3*e**7 - 36*B*a**2*c*d**2*e**5 - 780*B*a*c**2*d**4*e**3 - 1036*B*c**3*d**6*e))/(12*d**4*e**8 + 48*d**3*e**9*x + 72*d**2*e**10*x**2 + 48*d*e**11*x**3 + 12*e**12*x**4)","A",0
1324,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1325,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1326,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,1,908,0,3.504734," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+a),x)","\frac{B e^{4} x^{4}}{4 c} + x^{3} \left(\frac{A e^{4}}{3 c} + \frac{4 B d e^{3}}{3 c}\right) + x^{2} \left(\frac{2 A d e^{3}}{c} - \frac{B a e^{4}}{2 c^{2}} + \frac{3 B d^{2} e^{2}}{c}\right) + x \left(- \frac{A a e^{4}}{c^{2}} + \frac{6 A d^{2} e^{2}}{c} - \frac{4 B a d e^{3}}{c^{2}} + \frac{4 B d^{3} e}{c}\right) + \left(\frac{- 4 A a c d e^{3} + 4 A c^{2} d^{3} e + B a^{2} e^{4} - 6 B a c d^{2} e^{2} + B c^{2} d^{4}}{2 c^{3}} - \frac{\sqrt{- a c^{7}} \left(A a^{2} e^{4} - 6 A a c d^{2} e^{2} + A c^{2} d^{4} + 4 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{2 a c^{6}}\right) \log{\left(x + \frac{4 A a^{2} c d e^{3} - 4 A a c^{2} d^{3} e - B a^{3} e^{4} + 6 B a^{2} c d^{2} e^{2} - B a c^{2} d^{4} + 2 a c^{3} \left(\frac{- 4 A a c d e^{3} + 4 A c^{2} d^{3} e + B a^{2} e^{4} - 6 B a c d^{2} e^{2} + B c^{2} d^{4}}{2 c^{3}} - \frac{\sqrt{- a c^{7}} \left(A a^{2} e^{4} - 6 A a c d^{2} e^{2} + A c^{2} d^{4} + 4 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{2 a c^{6}}\right)}{A a^{2} c e^{4} - 6 A a c^{2} d^{2} e^{2} + A c^{3} d^{4} + 4 B a^{2} c d e^{3} - 4 B a c^{2} d^{3} e} \right)} + \left(\frac{- 4 A a c d e^{3} + 4 A c^{2} d^{3} e + B a^{2} e^{4} - 6 B a c d^{2} e^{2} + B c^{2} d^{4}}{2 c^{3}} + \frac{\sqrt{- a c^{7}} \left(A a^{2} e^{4} - 6 A a c d^{2} e^{2} + A c^{2} d^{4} + 4 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{2 a c^{6}}\right) \log{\left(x + \frac{4 A a^{2} c d e^{3} - 4 A a c^{2} d^{3} e - B a^{3} e^{4} + 6 B a^{2} c d^{2} e^{2} - B a c^{2} d^{4} + 2 a c^{3} \left(\frac{- 4 A a c d e^{3} + 4 A c^{2} d^{3} e + B a^{2} e^{4} - 6 B a c d^{2} e^{2} + B c^{2} d^{4}}{2 c^{3}} + \frac{\sqrt{- a c^{7}} \left(A a^{2} e^{4} - 6 A a c d^{2} e^{2} + A c^{2} d^{4} + 4 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{2 a c^{6}}\right)}{A a^{2} c e^{4} - 6 A a c^{2} d^{2} e^{2} + A c^{3} d^{4} + 4 B a^{2} c d e^{3} - 4 B a c^{2} d^{3} e} \right)}"," ",0,"B*e**4*x**4/(4*c) + x**3*(A*e**4/(3*c) + 4*B*d*e**3/(3*c)) + x**2*(2*A*d*e**3/c - B*a*e**4/(2*c**2) + 3*B*d**2*e**2/c) + x*(-A*a*e**4/c**2 + 6*A*d**2*e**2/c - 4*B*a*d*e**3/c**2 + 4*B*d**3*e/c) + ((-4*A*a*c*d*e**3 + 4*A*c**2*d**3*e + B*a**2*e**4 - 6*B*a*c*d**2*e**2 + B*c**2*d**4)/(2*c**3) - sqrt(-a*c**7)*(A*a**2*e**4 - 6*A*a*c*d**2*e**2 + A*c**2*d**4 + 4*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(2*a*c**6))*log(x + (4*A*a**2*c*d*e**3 - 4*A*a*c**2*d**3*e - B*a**3*e**4 + 6*B*a**2*c*d**2*e**2 - B*a*c**2*d**4 + 2*a*c**3*((-4*A*a*c*d*e**3 + 4*A*c**2*d**3*e + B*a**2*e**4 - 6*B*a*c*d**2*e**2 + B*c**2*d**4)/(2*c**3) - sqrt(-a*c**7)*(A*a**2*e**4 - 6*A*a*c*d**2*e**2 + A*c**2*d**4 + 4*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(2*a*c**6)))/(A*a**2*c*e**4 - 6*A*a*c**2*d**2*e**2 + A*c**3*d**4 + 4*B*a**2*c*d*e**3 - 4*B*a*c**2*d**3*e)) + ((-4*A*a*c*d*e**3 + 4*A*c**2*d**3*e + B*a**2*e**4 - 6*B*a*c*d**2*e**2 + B*c**2*d**4)/(2*c**3) + sqrt(-a*c**7)*(A*a**2*e**4 - 6*A*a*c*d**2*e**2 + A*c**2*d**4 + 4*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(2*a*c**6))*log(x + (4*A*a**2*c*d*e**3 - 4*A*a*c**2*d**3*e - B*a**3*e**4 + 6*B*a**2*c*d**2*e**2 - B*a*c**2*d**4 + 2*a*c**3*((-4*A*a*c*d*e**3 + 4*A*c**2*d**3*e + B*a**2*e**4 - 6*B*a*c*d**2*e**2 + B*c**2*d**4)/(2*c**3) + sqrt(-a*c**7)*(A*a**2*e**4 - 6*A*a*c*d**2*e**2 + A*c**2*d**4 + 4*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(2*a*c**6)))/(A*a**2*c*e**4 - 6*A*a*c**2*d**2*e**2 + A*c**3*d**4 + 4*B*a**2*c*d*e**3 - 4*B*a*c**2*d**3*e))","B",0
1331,1,641,0,2.146461," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+a),x)","\frac{B e^{3} x^{3}}{3 c} + x^{2} \left(\frac{A e^{3}}{2 c} + \frac{3 B d e^{2}}{2 c}\right) + x \left(\frac{3 A d e^{2}}{c} - \frac{B a e^{3}}{c^{2}} + \frac{3 B d^{2} e}{c}\right) + \left(- \frac{A a e^{3} - 3 A c d^{2} e + 3 B a d e^{2} - B c d^{3}}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e\right)}{2 a c^{5}}\right) \log{\left(x + \frac{A a^{2} e^{3} - 3 A a c d^{2} e + 3 B a^{2} d e^{2} - B a c d^{3} + 2 a c^{2} \left(- \frac{A a e^{3} - 3 A c d^{2} e + 3 B a d e^{2} - B c d^{3}}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e\right)}{2 a c^{5}}\right)}{- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e} \right)} + \left(- \frac{A a e^{3} - 3 A c d^{2} e + 3 B a d e^{2} - B c d^{3}}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e\right)}{2 a c^{5}}\right) \log{\left(x + \frac{A a^{2} e^{3} - 3 A a c d^{2} e + 3 B a^{2} d e^{2} - B a c d^{3} + 2 a c^{2} \left(- \frac{A a e^{3} - 3 A c d^{2} e + 3 B a d e^{2} - B c d^{3}}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e\right)}{2 a c^{5}}\right)}{- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e} \right)}"," ",0,"B*e**3*x**3/(3*c) + x**2*(A*e**3/(2*c) + 3*B*d*e**2/(2*c)) + x*(3*A*d*e**2/c - B*a*e**3/c**2 + 3*B*d**2*e/c) + (-(A*a*e**3 - 3*A*c*d**2*e + 3*B*a*d*e**2 - B*c*d**3)/(2*c**2) - sqrt(-a*c**5)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e)/(2*a*c**5))*log(x + (A*a**2*e**3 - 3*A*a*c*d**2*e + 3*B*a**2*d*e**2 - B*a*c*d**3 + 2*a*c**2*(-(A*a*e**3 - 3*A*c*d**2*e + 3*B*a*d*e**2 - B*c*d**3)/(2*c**2) - sqrt(-a*c**5)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e)/(2*a*c**5)))/(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e)) + (-(A*a*e**3 - 3*A*c*d**2*e + 3*B*a*d*e**2 - B*c*d**3)/(2*c**2) + sqrt(-a*c**5)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e)/(2*a*c**5))*log(x + (A*a**2*e**3 - 3*A*a*c*d**2*e + 3*B*a**2*d*e**2 - B*a*c*d**3 + 2*a*c**2*(-(A*a*e**3 - 3*A*c*d**2*e + 3*B*a*d*e**2 - B*c*d**3)/(2*c**2) + sqrt(-a*c**5)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e)/(2*a*c**5)))/(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e))","B",0
1332,1,425,0,1.406811," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+a),x)","\frac{B e^{2} x^{2}}{2 c} + x \left(\frac{A e^{2}}{c} + \frac{2 B d e}{c}\right) + \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2}}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(A a e^{2} - A c d^{2} + 2 B a d e\right)}{2 a c^{4}}\right) \log{\left(x + \frac{2 A a c d e - B a^{2} e^{2} + B a c d^{2} - 2 a c^{2} \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2}}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(A a e^{2} - A c d^{2} + 2 B a d e\right)}{2 a c^{4}}\right)}{A a c e^{2} - A c^{2} d^{2} + 2 B a c d e} \right)} + \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2}}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(A a e^{2} - A c d^{2} + 2 B a d e\right)}{2 a c^{4}}\right) \log{\left(x + \frac{2 A a c d e - B a^{2} e^{2} + B a c d^{2} - 2 a c^{2} \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2}}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(A a e^{2} - A c d^{2} + 2 B a d e\right)}{2 a c^{4}}\right)}{A a c e^{2} - A c^{2} d^{2} + 2 B a c d e} \right)}"," ",0,"B*e**2*x**2/(2*c) + x*(A*e**2/c + 2*B*d*e/c) + (-(-2*A*c*d*e + B*a*e**2 - B*c*d**2)/(2*c**2) - sqrt(-a*c**5)*(A*a*e**2 - A*c*d**2 + 2*B*a*d*e)/(2*a*c**4))*log(x + (2*A*a*c*d*e - B*a**2*e**2 + B*a*c*d**2 - 2*a*c**2*(-(-2*A*c*d*e + B*a*e**2 - B*c*d**2)/(2*c**2) - sqrt(-a*c**5)*(A*a*e**2 - A*c*d**2 + 2*B*a*d*e)/(2*a*c**4)))/(A*a*c*e**2 - A*c**2*d**2 + 2*B*a*c*d*e)) + (-(-2*A*c*d*e + B*a*e**2 - B*c*d**2)/(2*c**2) + sqrt(-a*c**5)*(A*a*e**2 - A*c*d**2 + 2*B*a*d*e)/(2*a*c**4))*log(x + (2*A*a*c*d*e - B*a**2*e**2 + B*a*c*d**2 - 2*a*c**2*(-(-2*A*c*d*e + B*a*e**2 - B*c*d**2)/(2*c**2) + sqrt(-a*c**5)*(A*a*e**2 - A*c*d**2 + 2*B*a*d*e)/(2*a*c**4)))/(A*a*c*e**2 - A*c**2*d**2 + 2*B*a*c*d*e))","B",0
1333,1,212,0,0.726489," ","integrate((B*x+A)*(e*x+d)/(c*x**2+a),x)","\frac{B e x}{c} + \left(\frac{A e + B d}{2 c} - \frac{\sqrt{- a c^{3}} \left(- A c d + B a e\right)}{2 a c^{3}}\right) \log{\left(x + \frac{A a e + B a d - 2 a c \left(\frac{A e + B d}{2 c} - \frac{\sqrt{- a c^{3}} \left(- A c d + B a e\right)}{2 a c^{3}}\right)}{- A c d + B a e} \right)} + \left(\frac{A e + B d}{2 c} + \frac{\sqrt{- a c^{3}} \left(- A c d + B a e\right)}{2 a c^{3}}\right) \log{\left(x + \frac{A a e + B a d - 2 a c \left(\frac{A e + B d}{2 c} + \frac{\sqrt{- a c^{3}} \left(- A c d + B a e\right)}{2 a c^{3}}\right)}{- A c d + B a e} \right)}"," ",0,"B*e*x/c + ((A*e + B*d)/(2*c) - sqrt(-a*c**3)*(-A*c*d + B*a*e)/(2*a*c**3))*log(x + (A*a*e + B*a*d - 2*a*c*((A*e + B*d)/(2*c) - sqrt(-a*c**3)*(-A*c*d + B*a*e)/(2*a*c**3)))/(-A*c*d + B*a*e)) + ((A*e + B*d)/(2*c) + sqrt(-a*c**3)*(-A*c*d + B*a*e)/(2*a*c**3))*log(x + (A*a*e + B*a*d - 2*a*c*((A*e + B*d)/(2*c) + sqrt(-a*c**3)*(-A*c*d + B*a*e)/(2*a*c**3)))/(-A*c*d + B*a*e))","B",0
1334,1,124,0,0.259644," ","integrate((B*x+A)/(c*x**2+a),x)","\left(- \frac{A \sqrt{- a c^{3}}}{2 a c^{2}} + \frac{B}{2 c}\right) \log{\left(x + \frac{- B a + 2 a c \left(- \frac{A \sqrt{- a c^{3}}}{2 a c^{2}} + \frac{B}{2 c}\right)}{A c} \right)} + \left(\frac{A \sqrt{- a c^{3}}}{2 a c^{2}} + \frac{B}{2 c}\right) \log{\left(x + \frac{- B a + 2 a c \left(\frac{A \sqrt{- a c^{3}}}{2 a c^{2}} + \frac{B}{2 c}\right)}{A c} \right)}"," ",0,"(-A*sqrt(-a*c**3)/(2*a*c**2) + B/(2*c))*log(x + (-B*a + 2*a*c*(-A*sqrt(-a*c**3)/(2*a*c**2) + B/(2*c)))/(A*c)) + (A*sqrt(-a*c**3)/(2*a*c**2) + B/(2*c))*log(x + (-B*a + 2*a*c*(A*sqrt(-a*c**3)/(2*a*c**2) + B/(2*c)))/(A*c))","B",0
1335,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1336,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1337,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1338,1,1091,0,14.772202," ","integrate((B*x+A)*(e*x+d)**5/(c*x**2+a)**2,x)","\frac{B e^{5} x^{3}}{3 c^{2}} + x^{2} \left(\frac{A e^{5}}{2 c^{2}} + \frac{5 B d e^{4}}{2 c^{2}}\right) + x \left(\frac{5 A d e^{4}}{c^{2}} - \frac{2 B a e^{5}}{c^{3}} + \frac{10 B d^{2} e^{3}}{c^{2}}\right) + \left(- \frac{e^{2} \left(A a e^{3} - 5 A c d^{2} e + 5 B a d e^{2} - 5 B c d^{3}\right)}{c^{3}} - \frac{\sqrt{- a^{3} c^{7}} \left(- 15 A a^{2} c d e^{4} + 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} + 5 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} + 5 B a c^{2} d^{4} e\right)}{4 a^{3} c^{7}}\right) \log{\left(x + \frac{4 A a^{3} e^{5} - 20 A a^{2} c d^{2} e^{3} + 20 B a^{3} d e^{4} - 20 B a^{2} c d^{3} e^{2} + 4 a^{2} c^{3} \left(- \frac{e^{2} \left(A a e^{3} - 5 A c d^{2} e + 5 B a d e^{2} - 5 B c d^{3}\right)}{c^{3}} - \frac{\sqrt{- a^{3} c^{7}} \left(- 15 A a^{2} c d e^{4} + 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} + 5 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} + 5 B a c^{2} d^{4} e\right)}{4 a^{3} c^{7}}\right)}{- 15 A a^{2} c d e^{4} + 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} + 5 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} + 5 B a c^{2} d^{4} e} \right)} + \left(- \frac{e^{2} \left(A a e^{3} - 5 A c d^{2} e + 5 B a d e^{2} - 5 B c d^{3}\right)}{c^{3}} + \frac{\sqrt{- a^{3} c^{7}} \left(- 15 A a^{2} c d e^{4} + 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} + 5 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} + 5 B a c^{2} d^{4} e\right)}{4 a^{3} c^{7}}\right) \log{\left(x + \frac{4 A a^{3} e^{5} - 20 A a^{2} c d^{2} e^{3} + 20 B a^{3} d e^{4} - 20 B a^{2} c d^{3} e^{2} + 4 a^{2} c^{3} \left(- \frac{e^{2} \left(A a e^{3} - 5 A c d^{2} e + 5 B a d e^{2} - 5 B c d^{3}\right)}{c^{3}} + \frac{\sqrt{- a^{3} c^{7}} \left(- 15 A a^{2} c d e^{4} + 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} + 5 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} + 5 B a c^{2} d^{4} e\right)}{4 a^{3} c^{7}}\right)}{- 15 A a^{2} c d e^{4} + 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} + 5 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} + 5 B a c^{2} d^{4} e} \right)} + \frac{- A a^{3} e^{5} + 10 A a^{2} c d^{2} e^{3} - 5 A a c^{2} d^{4} e - 5 B a^{3} d e^{4} + 10 B a^{2} c d^{3} e^{2} - B a c^{2} d^{5} + x \left(5 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} + A c^{3} d^{5} - B a^{3} e^{5} + 10 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e\right)}{2 a^{2} c^{3} + 2 a c^{4} x^{2}}"," ",0,"B*e**5*x**3/(3*c**2) + x**2*(A*e**5/(2*c**2) + 5*B*d*e**4/(2*c**2)) + x*(5*A*d*e**4/c**2 - 2*B*a*e**5/c**3 + 10*B*d**2*e**3/c**2) + (-e**2*(A*a*e**3 - 5*A*c*d**2*e + 5*B*a*d*e**2 - 5*B*c*d**3)/c**3 - sqrt(-a**3*c**7)*(-15*A*a**2*c*d*e**4 + 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 + 5*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 + 5*B*a*c**2*d**4*e)/(4*a**3*c**7))*log(x + (4*A*a**3*e**5 - 20*A*a**2*c*d**2*e**3 + 20*B*a**3*d*e**4 - 20*B*a**2*c*d**3*e**2 + 4*a**2*c**3*(-e**2*(A*a*e**3 - 5*A*c*d**2*e + 5*B*a*d*e**2 - 5*B*c*d**3)/c**3 - sqrt(-a**3*c**7)*(-15*A*a**2*c*d*e**4 + 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 + 5*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 + 5*B*a*c**2*d**4*e)/(4*a**3*c**7)))/(-15*A*a**2*c*d*e**4 + 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 + 5*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 + 5*B*a*c**2*d**4*e)) + (-e**2*(A*a*e**3 - 5*A*c*d**2*e + 5*B*a*d*e**2 - 5*B*c*d**3)/c**3 + sqrt(-a**3*c**7)*(-15*A*a**2*c*d*e**4 + 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 + 5*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 + 5*B*a*c**2*d**4*e)/(4*a**3*c**7))*log(x + (4*A*a**3*e**5 - 20*A*a**2*c*d**2*e**3 + 20*B*a**3*d*e**4 - 20*B*a**2*c*d**3*e**2 + 4*a**2*c**3*(-e**2*(A*a*e**3 - 5*A*c*d**2*e + 5*B*a*d*e**2 - 5*B*c*d**3)/c**3 + sqrt(-a**3*c**7)*(-15*A*a**2*c*d*e**4 + 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 + 5*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 + 5*B*a*c**2*d**4*e)/(4*a**3*c**7)))/(-15*A*a**2*c*d*e**4 + 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 + 5*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 + 5*B*a*c**2*d**4*e)) + (-A*a**3*e**5 + 10*A*a**2*c*d**2*e**3 - 5*A*a*c**2*d**4*e - 5*B*a**3*d*e**4 + 10*B*a**2*c*d**3*e**2 - B*a*c**2*d**5 + x*(5*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 + A*c**3*d**5 - B*a**3*e**5 + 10*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e))/(2*a**2*c**3 + 2*a*c**4*x**2)","B",0
1339,1,836,0,10.536260," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+a)**2,x)","\frac{B e^{4} x^{2}}{2 c^{2}} + x \left(\frac{A e^{4}}{c^{2}} + \frac{4 B d e^{3}}{c^{2}}\right) + \left(- \frac{e^{2} \left(- 2 A c d e + B a e^{2} - 3 B c d^{2}\right)}{c^{3}} - \frac{\sqrt{- a^{3} c^{7}} \left(3 A a^{2} e^{4} - 6 A a c d^{2} e^{2} - A c^{2} d^{4} + 12 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{4 a^{3} c^{6}}\right) \log{\left(x + \frac{8 A a^{2} c d e^{3} - 4 B a^{3} e^{4} + 12 B a^{2} c d^{2} e^{2} - 4 a^{2} c^{3} \left(- \frac{e^{2} \left(- 2 A c d e + B a e^{2} - 3 B c d^{2}\right)}{c^{3}} - \frac{\sqrt{- a^{3} c^{7}} \left(3 A a^{2} e^{4} - 6 A a c d^{2} e^{2} - A c^{2} d^{4} + 12 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{4 a^{3} c^{6}}\right)}{3 A a^{2} c e^{4} - 6 A a c^{2} d^{2} e^{2} - A c^{3} d^{4} + 12 B a^{2} c d e^{3} - 4 B a c^{2} d^{3} e} \right)} + \left(- \frac{e^{2} \left(- 2 A c d e + B a e^{2} - 3 B c d^{2}\right)}{c^{3}} + \frac{\sqrt{- a^{3} c^{7}} \left(3 A a^{2} e^{4} - 6 A a c d^{2} e^{2} - A c^{2} d^{4} + 12 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{4 a^{3} c^{6}}\right) \log{\left(x + \frac{8 A a^{2} c d e^{3} - 4 B a^{3} e^{4} + 12 B a^{2} c d^{2} e^{2} - 4 a^{2} c^{3} \left(- \frac{e^{2} \left(- 2 A c d e + B a e^{2} - 3 B c d^{2}\right)}{c^{3}} + \frac{\sqrt{- a^{3} c^{7}} \left(3 A a^{2} e^{4} - 6 A a c d^{2} e^{2} - A c^{2} d^{4} + 12 B a^{2} d e^{3} - 4 B a c d^{3} e\right)}{4 a^{3} c^{6}}\right)}{3 A a^{2} c e^{4} - 6 A a c^{2} d^{2} e^{2} - A c^{3} d^{4} + 12 B a^{2} c d e^{3} - 4 B a c^{2} d^{3} e} \right)} + \frac{4 A a^{2} c d e^{3} - 4 A a c^{2} d^{3} e - B a^{3} e^{4} + 6 B a^{2} c d^{2} e^{2} - B a c^{2} d^{4} + x \left(A a^{2} c e^{4} - 6 A a c^{2} d^{2} e^{2} + A c^{3} d^{4} + 4 B a^{2} c d e^{3} - 4 B a c^{2} d^{3} e\right)}{2 a^{2} c^{3} + 2 a c^{4} x^{2}}"," ",0,"B*e**4*x**2/(2*c**2) + x*(A*e**4/c**2 + 4*B*d*e**3/c**2) + (-e**2*(-2*A*c*d*e + B*a*e**2 - 3*B*c*d**2)/c**3 - sqrt(-a**3*c**7)*(3*A*a**2*e**4 - 6*A*a*c*d**2*e**2 - A*c**2*d**4 + 12*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(4*a**3*c**6))*log(x + (8*A*a**2*c*d*e**3 - 4*B*a**3*e**4 + 12*B*a**2*c*d**2*e**2 - 4*a**2*c**3*(-e**2*(-2*A*c*d*e + B*a*e**2 - 3*B*c*d**2)/c**3 - sqrt(-a**3*c**7)*(3*A*a**2*e**4 - 6*A*a*c*d**2*e**2 - A*c**2*d**4 + 12*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(4*a**3*c**6)))/(3*A*a**2*c*e**4 - 6*A*a*c**2*d**2*e**2 - A*c**3*d**4 + 12*B*a**2*c*d*e**3 - 4*B*a*c**2*d**3*e)) + (-e**2*(-2*A*c*d*e + B*a*e**2 - 3*B*c*d**2)/c**3 + sqrt(-a**3*c**7)*(3*A*a**2*e**4 - 6*A*a*c*d**2*e**2 - A*c**2*d**4 + 12*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(4*a**3*c**6))*log(x + (8*A*a**2*c*d*e**3 - 4*B*a**3*e**4 + 12*B*a**2*c*d**2*e**2 - 4*a**2*c**3*(-e**2*(-2*A*c*d*e + B*a*e**2 - 3*B*c*d**2)/c**3 + sqrt(-a**3*c**7)*(3*A*a**2*e**4 - 6*A*a*c*d**2*e**2 - A*c**2*d**4 + 12*B*a**2*d*e**3 - 4*B*a*c*d**3*e)/(4*a**3*c**6)))/(3*A*a**2*c*e**4 - 6*A*a*c**2*d**2*e**2 - A*c**3*d**4 + 12*B*a**2*c*d*e**3 - 4*B*a*c**2*d**3*e)) + (4*A*a**2*c*d*e**3 - 4*A*a*c**2*d**3*e - B*a**3*e**4 + 6*B*a**2*c*d**2*e**2 - B*a*c**2*d**4 + x*(A*a**2*c*e**4 - 6*A*a*c**2*d**2*e**2 + A*c**3*d**4 + 4*B*a**2*c*d*e**3 - 4*B*a*c**2*d**3*e))/(2*a**2*c**3 + 2*a*c**4*x**2)","B",0
1340,1,583,0,6.041238," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+a)**2,x)","\frac{B e^{3} x}{c^{2}} + \left(\frac{e^{2} \left(A e + 3 B d\right)}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e\right)}{4 a^{3} c^{5}}\right) \log{\left(x + \frac{2 A a^{2} e^{3} + 6 B a^{2} d e^{2} - 4 a^{2} c^{2} \left(\frac{e^{2} \left(A e + 3 B d\right)}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e\right)}{4 a^{3} c^{5}}\right)}{- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e} \right)} + \left(\frac{e^{2} \left(A e + 3 B d\right)}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e\right)}{4 a^{3} c^{5}}\right) \log{\left(x + \frac{2 A a^{2} e^{3} + 6 B a^{2} d e^{2} - 4 a^{2} c^{2} \left(\frac{e^{2} \left(A e + 3 B d\right)}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e\right)}{4 a^{3} c^{5}}\right)}{- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e} \right)} + \frac{A a^{2} e^{3} - 3 A a c d^{2} e + 3 B a^{2} d e^{2} - B a c d^{3} + x \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e\right)}{2 a^{2} c^{2} + 2 a c^{3} x^{2}}"," ",0,"B*e**3*x/c**2 + (e**2*(A*e + 3*B*d)/(2*c**2) - sqrt(-a**3*c**5)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e)/(4*a**3*c**5))*log(x + (2*A*a**2*e**3 + 6*B*a**2*d*e**2 - 4*a**2*c**2*(e**2*(A*e + 3*B*d)/(2*c**2) - sqrt(-a**3*c**5)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e)/(4*a**3*c**5)))/(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e)) + (e**2*(A*e + 3*B*d)/(2*c**2) + sqrt(-a**3*c**5)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e)/(4*a**3*c**5))*log(x + (2*A*a**2*e**3 + 6*B*a**2*d*e**2 - 4*a**2*c**2*(e**2*(A*e + 3*B*d)/(2*c**2) + sqrt(-a**3*c**5)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e)/(4*a**3*c**5)))/(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e)) + (A*a**2*e**3 - 3*A*a*c*d**2*e + 3*B*a**2*d*e**2 - B*a*c*d**3 + x*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e))/(2*a**2*c**2 + 2*a*c**3*x**2)","B",0
1341,1,382,0,2.959728," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+a)**2,x)","\left(\frac{B e^{2}}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(A a e^{2} + A c d^{2} + 2 B a d e\right)}{4 a^{3} c^{4}}\right) \log{\left(x + \frac{- 2 B a^{2} e^{2} + 4 a^{2} c^{2} \left(\frac{B e^{2}}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(A a e^{2} + A c d^{2} + 2 B a d e\right)}{4 a^{3} c^{4}}\right)}{A a c e^{2} + A c^{2} d^{2} + 2 B a c d e} \right)} + \left(\frac{B e^{2}}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(A a e^{2} + A c d^{2} + 2 B a d e\right)}{4 a^{3} c^{4}}\right) \log{\left(x + \frac{- 2 B a^{2} e^{2} + 4 a^{2} c^{2} \left(\frac{B e^{2}}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(A a e^{2} + A c d^{2} + 2 B a d e\right)}{4 a^{3} c^{4}}\right)}{A a c e^{2} + A c^{2} d^{2} + 2 B a c d e} \right)} + \frac{- 2 A a c d e + B a^{2} e^{2} - B a c d^{2} + x \left(- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e\right)}{2 a^{2} c^{2} + 2 a c^{3} x^{2}}"," ",0,"(B*e**2/(2*c**2) - sqrt(-a**3*c**5)*(A*a*e**2 + A*c*d**2 + 2*B*a*d*e)/(4*a**3*c**4))*log(x + (-2*B*a**2*e**2 + 4*a**2*c**2*(B*e**2/(2*c**2) - sqrt(-a**3*c**5)*(A*a*e**2 + A*c*d**2 + 2*B*a*d*e)/(4*a**3*c**4)))/(A*a*c*e**2 + A*c**2*d**2 + 2*B*a*c*d*e)) + (B*e**2/(2*c**2) + sqrt(-a**3*c**5)*(A*a*e**2 + A*c*d**2 + 2*B*a*d*e)/(4*a**3*c**4))*log(x + (-2*B*a**2*e**2 + 4*a**2*c**2*(B*e**2/(2*c**2) + sqrt(-a**3*c**5)*(A*a*e**2 + A*c*d**2 + 2*B*a*d*e)/(4*a**3*c**4)))/(A*a*c*e**2 + A*c**2*d**2 + 2*B*a*c*d*e)) + (-2*A*a*c*d*e + B*a**2*e**2 - B*a*c*d**2 + x*(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e))/(2*a**2*c**2 + 2*a*c**3*x**2)","B",0
1342,1,133,0,0.922928," ","integrate((B*x+A)*(e*x+d)/(c*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \left(A c d + B a e\right) \log{\left(- a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \left(A c d + B a e\right) \log{\left(a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x \right)}}{4} + \frac{- A a e - B a d + x \left(A c d - B a e\right)}{2 a^{2} c + 2 a c^{2} x^{2}}"," ",0,"-sqrt(-1/(a**3*c**3))*(A*c*d + B*a*e)*log(-a**2*c*sqrt(-1/(a**3*c**3)) + x)/4 + sqrt(-1/(a**3*c**3))*(A*c*d + B*a*e)*log(a**2*c*sqrt(-1/(a**3*c**3)) + x)/4 + (-A*a*e - B*a*d + x*(A*c*d - B*a*e))/(2*a**2*c + 2*a*c**2*x**2)","A",0
1343,1,90,0,0.298314," ","integrate((B*x+A)/(c*x**2+a)**2,x)","A \left(- \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} c}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} c}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} c}} + x \right)}}{4}\right) + \frac{A c x - B a}{2 a^{2} c + 2 a c^{2} x^{2}}"," ",0,"A*(-sqrt(-1/(a**3*c))*log(-a**2*sqrt(-1/(a**3*c)) + x)/4 + sqrt(-1/(a**3*c))*log(a**2*sqrt(-1/(a**3*c)) + x)/4) + (A*c*x - B*a)/(2*a**2*c + 2*a*c**2*x**2)","A",0
1344,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1345,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1346,1,1044,0,97.928113," ","integrate((B*x+A)*(e*x+d)**5/(c*x**2+a)**3,x)","\frac{B e^{5} x}{c^{3}} + \left(\frac{e^{4} \left(A e + 5 B d\right)}{2 c^{3}} - \frac{\sqrt{- a^{5} c^{7}} \left(- 15 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} - 3 A c^{3} d^{5} + 15 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e\right)}{16 a^{5} c^{7}}\right) \log{\left(x + \frac{8 A a^{3} e^{5} + 40 B a^{3} d e^{4} - 16 a^{3} c^{3} \left(\frac{e^{4} \left(A e + 5 B d\right)}{2 c^{3}} - \frac{\sqrt{- a^{5} c^{7}} \left(- 15 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} - 3 A c^{3} d^{5} + 15 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e\right)}{16 a^{5} c^{7}}\right)}{- 15 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} - 3 A c^{3} d^{5} + 15 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e} \right)} + \left(\frac{e^{4} \left(A e + 5 B d\right)}{2 c^{3}} + \frac{\sqrt{- a^{5} c^{7}} \left(- 15 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} - 3 A c^{3} d^{5} + 15 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e\right)}{16 a^{5} c^{7}}\right) \log{\left(x + \frac{8 A a^{3} e^{5} + 40 B a^{3} d e^{4} - 16 a^{3} c^{3} \left(\frac{e^{4} \left(A e + 5 B d\right)}{2 c^{3}} + \frac{\sqrt{- a^{5} c^{7}} \left(- 15 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} - 3 A c^{3} d^{5} + 15 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e\right)}{16 a^{5} c^{7}}\right)}{- 15 A a^{2} c d e^{4} - 10 A a c^{2} d^{3} e^{2} - 3 A c^{3} d^{5} + 15 B a^{3} e^{5} - 30 B a^{2} c d^{2} e^{3} - 5 B a c^{2} d^{4} e} \right)} + \frac{6 A a^{4} e^{5} - 20 A a^{3} c d^{2} e^{3} - 10 A a^{2} c^{2} d^{4} e + 30 B a^{4} d e^{4} - 20 B a^{3} c d^{3} e^{2} - 2 B a^{2} c^{2} d^{5} + x^{3} \left(- 25 A a^{2} c^{2} d e^{4} + 10 A a c^{3} d^{3} e^{2} + 3 A c^{4} d^{5} + 9 B a^{3} c e^{5} - 50 B a^{2} c^{2} d^{2} e^{3} + 5 B a c^{3} d^{4} e\right) + x^{2} \left(8 A a^{3} c e^{5} - 40 A a^{2} c^{2} d^{2} e^{3} + 40 B a^{3} c d e^{4} - 40 B a^{2} c^{2} d^{3} e^{2}\right) + x \left(- 15 A a^{3} c d e^{4} - 10 A a^{2} c^{2} d^{3} e^{2} + 5 A a c^{3} d^{5} + 7 B a^{4} e^{5} - 30 B a^{3} c d^{2} e^{3} - 5 B a^{2} c^{2} d^{4} e\right)}{8 a^{4} c^{3} + 16 a^{3} c^{4} x^{2} + 8 a^{2} c^{5} x^{4}}"," ",0,"B*e**5*x/c**3 + (e**4*(A*e + 5*B*d)/(2*c**3) - sqrt(-a**5*c**7)*(-15*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 - 3*A*c**3*d**5 + 15*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e)/(16*a**5*c**7))*log(x + (8*A*a**3*e**5 + 40*B*a**3*d*e**4 - 16*a**3*c**3*(e**4*(A*e + 5*B*d)/(2*c**3) - sqrt(-a**5*c**7)*(-15*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 - 3*A*c**3*d**5 + 15*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e)/(16*a**5*c**7)))/(-15*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 - 3*A*c**3*d**5 + 15*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e)) + (e**4*(A*e + 5*B*d)/(2*c**3) + sqrt(-a**5*c**7)*(-15*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 - 3*A*c**3*d**5 + 15*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e)/(16*a**5*c**7))*log(x + (8*A*a**3*e**5 + 40*B*a**3*d*e**4 - 16*a**3*c**3*(e**4*(A*e + 5*B*d)/(2*c**3) + sqrt(-a**5*c**7)*(-15*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 - 3*A*c**3*d**5 + 15*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e)/(16*a**5*c**7)))/(-15*A*a**2*c*d*e**4 - 10*A*a*c**2*d**3*e**2 - 3*A*c**3*d**5 + 15*B*a**3*e**5 - 30*B*a**2*c*d**2*e**3 - 5*B*a*c**2*d**4*e)) + (6*A*a**4*e**5 - 20*A*a**3*c*d**2*e**3 - 10*A*a**2*c**2*d**4*e + 30*B*a**4*d*e**4 - 20*B*a**3*c*d**3*e**2 - 2*B*a**2*c**2*d**5 + x**3*(-25*A*a**2*c**2*d*e**4 + 10*A*a*c**3*d**3*e**2 + 3*A*c**4*d**5 + 9*B*a**3*c*e**5 - 50*B*a**2*c**2*d**2*e**3 + 5*B*a*c**3*d**4*e) + x**2*(8*A*a**3*c*e**5 - 40*A*a**2*c**2*d**2*e**3 + 40*B*a**3*c*d*e**4 - 40*B*a**2*c**2*d**3*e**2) + x*(-15*A*a**3*c*d*e**4 - 10*A*a**2*c**2*d**3*e**2 + 5*A*a*c**3*d**5 + 7*B*a**4*e**5 - 30*B*a**3*c*d**2*e**3 - 5*B*a**2*c**2*d**4*e))/(8*a**4*c**3 + 16*a**3*c**4*x**2 + 8*a**2*c**5*x**4)","B",0
1347,1,816,0,46.138697," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+a)**3,x)","\left(\frac{B e^{4}}{2 c^{3}} - \frac{\sqrt{- a^{5} c^{7}} \left(3 A a^{2} e^{4} + 6 A a c d^{2} e^{2} + 3 A c^{2} d^{4} + 12 B a^{2} d e^{3} + 4 B a c d^{3} e\right)}{16 a^{5} c^{6}}\right) \log{\left(x + \frac{- 8 B a^{3} e^{4} + 16 a^{3} c^{3} \left(\frac{B e^{4}}{2 c^{3}} - \frac{\sqrt{- a^{5} c^{7}} \left(3 A a^{2} e^{4} + 6 A a c d^{2} e^{2} + 3 A c^{2} d^{4} + 12 B a^{2} d e^{3} + 4 B a c d^{3} e\right)}{16 a^{5} c^{6}}\right)}{3 A a^{2} c e^{4} + 6 A a c^{2} d^{2} e^{2} + 3 A c^{3} d^{4} + 12 B a^{2} c d e^{3} + 4 B a c^{2} d^{3} e} \right)} + \left(\frac{B e^{4}}{2 c^{3}} + \frac{\sqrt{- a^{5} c^{7}} \left(3 A a^{2} e^{4} + 6 A a c d^{2} e^{2} + 3 A c^{2} d^{4} + 12 B a^{2} d e^{3} + 4 B a c d^{3} e\right)}{16 a^{5} c^{6}}\right) \log{\left(x + \frac{- 8 B a^{3} e^{4} + 16 a^{3} c^{3} \left(\frac{B e^{4}}{2 c^{3}} + \frac{\sqrt{- a^{5} c^{7}} \left(3 A a^{2} e^{4} + 6 A a c d^{2} e^{2} + 3 A c^{2} d^{4} + 12 B a^{2} d e^{3} + 4 B a c d^{3} e\right)}{16 a^{5} c^{6}}\right)}{3 A a^{2} c e^{4} + 6 A a c^{2} d^{2} e^{2} + 3 A c^{3} d^{4} + 12 B a^{2} c d e^{3} + 4 B a c^{2} d^{3} e} \right)} + \frac{- 8 A a^{3} c d e^{3} - 8 A a^{2} c^{2} d^{3} e + 6 B a^{4} e^{4} - 12 B a^{3} c d^{2} e^{2} - 2 B a^{2} c^{2} d^{4} + x^{3} \left(- 5 A a^{2} c^{2} e^{4} + 6 A a c^{3} d^{2} e^{2} + 3 A c^{4} d^{4} - 20 B a^{2} c^{2} d e^{3} + 4 B a c^{3} d^{3} e\right) + x^{2} \left(- 16 A a^{2} c^{2} d e^{3} + 8 B a^{3} c e^{4} - 24 B a^{2} c^{2} d^{2} e^{2}\right) + x \left(- 3 A a^{3} c e^{4} - 6 A a^{2} c^{2} d^{2} e^{2} + 5 A a c^{3} d^{4} - 12 B a^{3} c d e^{3} - 4 B a^{2} c^{2} d^{3} e\right)}{8 a^{4} c^{3} + 16 a^{3} c^{4} x^{2} + 8 a^{2} c^{5} x^{4}}"," ",0,"(B*e**4/(2*c**3) - sqrt(-a**5*c**7)*(3*A*a**2*e**4 + 6*A*a*c*d**2*e**2 + 3*A*c**2*d**4 + 12*B*a**2*d*e**3 + 4*B*a*c*d**3*e)/(16*a**5*c**6))*log(x + (-8*B*a**3*e**4 + 16*a**3*c**3*(B*e**4/(2*c**3) - sqrt(-a**5*c**7)*(3*A*a**2*e**4 + 6*A*a*c*d**2*e**2 + 3*A*c**2*d**4 + 12*B*a**2*d*e**3 + 4*B*a*c*d**3*e)/(16*a**5*c**6)))/(3*A*a**2*c*e**4 + 6*A*a*c**2*d**2*e**2 + 3*A*c**3*d**4 + 12*B*a**2*c*d*e**3 + 4*B*a*c**2*d**3*e)) + (B*e**4/(2*c**3) + sqrt(-a**5*c**7)*(3*A*a**2*e**4 + 6*A*a*c*d**2*e**2 + 3*A*c**2*d**4 + 12*B*a**2*d*e**3 + 4*B*a*c*d**3*e)/(16*a**5*c**6))*log(x + (-8*B*a**3*e**4 + 16*a**3*c**3*(B*e**4/(2*c**3) + sqrt(-a**5*c**7)*(3*A*a**2*e**4 + 6*A*a*c*d**2*e**2 + 3*A*c**2*d**4 + 12*B*a**2*d*e**3 + 4*B*a*c*d**3*e)/(16*a**5*c**6)))/(3*A*a**2*c*e**4 + 6*A*a*c**2*d**2*e**2 + 3*A*c**3*d**4 + 12*B*a**2*c*d*e**3 + 4*B*a*c**2*d**3*e)) + (-8*A*a**3*c*d*e**3 - 8*A*a**2*c**2*d**3*e + 6*B*a**4*e**4 - 12*B*a**3*c*d**2*e**2 - 2*B*a**2*c**2*d**4 + x**3*(-5*A*a**2*c**2*e**4 + 6*A*a*c**3*d**2*e**2 + 3*A*c**4*d**4 - 20*B*a**2*c**2*d*e**3 + 4*B*a*c**3*d**3*e) + x**2*(-16*A*a**2*c**2*d*e**3 + 8*B*a**3*c*e**4 - 24*B*a**2*c**2*d**2*e**2) + x*(-3*A*a**3*c*e**4 - 6*A*a**2*c**2*d**2*e**2 + 5*A*a*c**3*d**4 - 12*B*a**3*c*d*e**3 - 4*B*a**2*c**2*d**3*e))/(8*a**4*c**3 + 16*a**3*c**4*x**2 + 8*a**2*c**5*x**4)","B",0
1348,1,468,0,20.046354," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(A c d + B a e\right) \log{\left(- \frac{3 a^{3} c^{2} \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(A c d + B a e\right)}{3 A a c d e^{2} + 3 A c^{2} d^{3} + 3 B a^{2} e^{3} + 3 B a c d^{2} e} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(A c d + B a e\right) \log{\left(\frac{3 a^{3} c^{2} \sqrt{- \frac{1}{a^{5} c^{5}}} \left(a e^{2} + c d^{2}\right) \left(A c d + B a e\right)}{3 A a c d e^{2} + 3 A c^{2} d^{3} + 3 B a^{2} e^{3} + 3 B a c d^{2} e} + x \right)}}{16} + \frac{- 2 A a^{3} e^{3} - 6 A a^{2} c d^{2} e - 6 B a^{3} d e^{2} - 2 B a^{2} c d^{3} + x^{3} \left(3 A a c^{2} d e^{2} + 3 A c^{3} d^{3} - 5 B a^{2} c e^{3} + 3 B a c^{2} d^{2} e\right) + x^{2} \left(- 4 A a^{2} c e^{3} - 12 B a^{2} c d e^{2}\right) + x \left(- 3 A a^{2} c d e^{2} + 5 A a c^{2} d^{3} - 3 B a^{3} e^{3} - 3 B a^{2} c d^{2} e\right)}{8 a^{4} c^{2} + 16 a^{3} c^{3} x^{2} + 8 a^{2} c^{4} x^{4}}"," ",0,"-3*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)*(A*c*d + B*a*e)*log(-3*a**3*c**2*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)*(A*c*d + B*a*e)/(3*A*a*c*d*e**2 + 3*A*c**2*d**3 + 3*B*a**2*e**3 + 3*B*a*c*d**2*e) + x)/16 + 3*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)*(A*c*d + B*a*e)*log(3*a**3*c**2*sqrt(-1/(a**5*c**5))*(a*e**2 + c*d**2)*(A*c*d + B*a*e)/(3*A*a*c*d*e**2 + 3*A*c**2*d**3 + 3*B*a**2*e**3 + 3*B*a*c*d**2*e) + x)/16 + (-2*A*a**3*e**3 - 6*A*a**2*c*d**2*e - 6*B*a**3*d*e**2 - 2*B*a**2*c*d**3 + x**3*(3*A*a*c**2*d*e**2 + 3*A*c**3*d**3 - 5*B*a**2*c*e**3 + 3*B*a*c**2*d**2*e) + x**2*(-4*A*a**2*c*e**3 - 12*B*a**2*c*d*e**2) + x*(-3*A*a**2*c*d*e**2 + 5*A*a*c**2*d**3 - 3*B*a**3*e**3 - 3*B*a**2*c*d**2*e))/(8*a**4*c**2 + 16*a**3*c**3*x**2 + 8*a**2*c**4*x**4)","B",0
1349,1,274,0,7.838097," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(A a e^{2} + 3 A c d^{2} + 2 B a d e\right) \log{\left(- a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(A a e^{2} + 3 A c d^{2} + 2 B a d e\right) \log{\left(a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{- 4 A a^{2} c d e - 2 B a^{3} e^{2} - 2 B a^{2} c d^{2} - 4 B a^{2} c e^{2} x^{2} + x^{3} \left(A a c^{2} e^{2} + 3 A c^{3} d^{2} + 2 B a c^{2} d e\right) + x \left(- A a^{2} c e^{2} + 5 A a c^{2} d^{2} - 2 B a^{2} c d e\right)}{8 a^{4} c^{2} + 16 a^{3} c^{3} x^{2} + 8 a^{2} c^{4} x^{4}}"," ",0,"-sqrt(-1/(a**5*c**3))*(A*a*e**2 + 3*A*c*d**2 + 2*B*a*d*e)*log(-a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + sqrt(-1/(a**5*c**3))*(A*a*e**2 + 3*A*c*d**2 + 2*B*a*d*e)*log(a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + (-4*A*a**2*c*d*e - 2*B*a**3*e**2 - 2*B*a**2*c*d**2 - 4*B*a**2*c*e**2*x**2 + x**3*(A*a*c**2*e**2 + 3*A*c**3*d**2 + 2*B*a*c**2*d*e) + x*(-A*a**2*c*e**2 + 5*A*a*c**2*d**2 - 2*B*a**2*c*d*e))/(8*a**4*c**2 + 16*a**3*c**3*x**2 + 8*a**2*c**4*x**4)","A",0
1350,1,180,0,1.926751," ","integrate((B*x+A)*(e*x+d)/(c*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(3 A c d + B a e\right) \log{\left(- a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(3 A c d + B a e\right) \log{\left(a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{- 2 A a^{2} e - 2 B a^{2} d + x^{3} \left(3 A c^{2} d + B a c e\right) + x \left(5 A a c d - B a^{2} e\right)}{8 a^{4} c + 16 a^{3} c^{2} x^{2} + 8 a^{2} c^{3} x^{4}}"," ",0,"-sqrt(-1/(a**5*c**3))*(3*A*c*d + B*a*e)*log(-a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + sqrt(-1/(a**5*c**3))*(3*A*c*d + B*a*e)*log(a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + (-2*A*a**2*e - 2*B*a**2*d + x**3*(3*A*c**2*d + B*a*c*e) + x*(5*A*a*c*d - B*a**2*e))/(8*a**4*c + 16*a**3*c**2*x**2 + 8*a**2*c**3*x**4)","A",0
1351,1,124,0,0.450391," ","integrate((B*x+A)/(c*x**2+a)**3,x)","A \left(- \frac{3 \sqrt{- \frac{1}{a^{5} c}} \log{\left(- a^{3} \sqrt{- \frac{1}{a^{5} c}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{5} c}} \log{\left(a^{3} \sqrt{- \frac{1}{a^{5} c}} + x \right)}}{16}\right) + \frac{5 A a c x + 3 A c^{2} x^{3} - 2 B a^{2}}{8 a^{4} c + 16 a^{3} c^{2} x^{2} + 8 a^{2} c^{3} x^{4}}"," ",0,"A*(-3*sqrt(-1/(a**5*c))*log(-a**3*sqrt(-1/(a**5*c)) + x)/16 + 3*sqrt(-1/(a**5*c))*log(a**3*sqrt(-1/(a**5*c)) + x)/16) + (5*A*a*c*x + 3*A*c**2*x**3 - 2*B*a**2)/(8*a**4*c + 16*a**3*c**2*x**2 + 8*a**2*c**3*x**4)","A",0
1352,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1353,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1354,1,26,0,0.141165," ","integrate((-11+6*x)/(-1+2*x)/(x**2-1),x)","- \frac{5 \log{\left(x - 1 \right)}}{2} + \frac{16 \log{\left(x - \frac{1}{2} \right)}}{3} - \frac{17 \log{\left(x + 1 \right)}}{6}"," ",0,"-5*log(x - 1)/2 + 16*log(x - 1/2)/3 - 17*log(x + 1)/6","A",0
1355,1,27,0,0.133759," ","integrate(x*(1+x)**2/(x**2+1)**3,x)","\frac{\operatorname{atan}{\left(x \right)}}{4} + \frac{x^{3} - 2 x^{2} - x - 2}{4 x^{4} + 8 x^{2} + 4}"," ",0,"atan(x)/4 + (x**3 - 2*x**2 - x - 2)/(4*x**4 + 8*x**2 + 4)","A",0
1356,1,131,0,3.127374," ","integrate((5-x)*(3+2*x)**4*(3*x**2+2)**(1/2),x)","- \frac{16 x^{6} \sqrt{3 x^{2} + 2}}{7} - \frac{8 x^{5} \sqrt{3 x^{2} + 2}}{3} + \frac{5512 x^{4} \sqrt{3 x^{2} + 2}}{105} + \frac{1940 x^{3} \sqrt{3 x^{2} + 2}}{9} + \frac{326029 x^{2} \sqrt{3 x^{2} + 2}}{945} + \frac{4949 x \sqrt{3 x^{2} + 2}}{18} + \frac{583994 \sqrt{3 x^{2} + 2}}{2835} + \frac{2341 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{27}"," ",0,"-16*x**6*sqrt(3*x**2 + 2)/7 - 8*x**5*sqrt(3*x**2 + 2)/3 + 5512*x**4*sqrt(3*x**2 + 2)/105 + 1940*x**3*sqrt(3*x**2 + 2)/9 + 326029*x**2*sqrt(3*x**2 + 2)/945 + 4949*x*sqrt(3*x**2 + 2)/18 + 583994*sqrt(3*x**2 + 2)/2835 + 2341*sqrt(3)*asinh(sqrt(6)*x/2)/27","A",0
1357,1,150,0,20.717673," ","integrate((5-x)*(3+2*x)**3*(3*x**2+2)**(1/2),x)","- \frac{4 x^{7}}{\sqrt{3 x^{2} + 2}} + \frac{547 x^{5}}{6 \sqrt{3 x^{2} + 2}} + \frac{1705 x^{3}}{18 \sqrt{3 x^{2} + 2}} + \frac{135 x \sqrt{3 x^{2} + 2}}{2} + \frac{193 x}{9 \sqrt{3 x^{2} + 2}} + \frac{16 \sqrt{2} \left(\frac{3 x^{2}}{2} + 1\right)^{\frac{5}{2}}}{45} - \frac{16 \sqrt{2} \left(\frac{3 x^{2}}{2} + 1\right)^{\frac{3}{2}}}{27} + 27 \left(3 x^{2} + 2\right)^{\frac{3}{2}} + \frac{1022 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{27}"," ",0,"-4*x**7/sqrt(3*x**2 + 2) + 547*x**5/(6*sqrt(3*x**2 + 2)) + 1705*x**3/(18*sqrt(3*x**2 + 2)) + 135*x*sqrt(3*x**2 + 2)/2 + 193*x/(9*sqrt(3*x**2 + 2)) + 16*sqrt(2)*(3*x**2/2 + 1)**(5/2)/45 - 16*sqrt(2)*(3*x**2/2 + 1)**(3/2)/27 + 27*(3*x**2 + 2)**(3/2) + 1022*sqrt(3)*asinh(sqrt(6)*x/2)/27","A",0
1358,1,95,0,0.931182," ","integrate((5-x)*(3+2*x)**2*(3*x**2+2)**(1/2),x)","- \frac{4 x^{4} \sqrt{3 x^{2} + 2}}{5} + 2 x^{3} \sqrt{3 x^{2} + 2} + \frac{757 x^{2} \sqrt{3 x^{2} + 2}}{45} + \frac{139 x \sqrt{3 x^{2} + 2}}{6} + \frac{1562 \sqrt{3 x^{2} + 2}}{135} + \frac{131 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"-4*x**4*sqrt(3*x**2 + 2)/5 + 2*x**3*sqrt(3*x**2 + 2) + 757*x**2*sqrt(3*x**2 + 2)/45 + 139*x*sqrt(3*x**2 + 2)/6 + 1562*sqrt(3*x**2 + 2)/135 + 131*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
1359,1,94,0,8.075581," ","integrate((5-x)*(3+2*x)*(3*x**2+2)**(1/2),x)","- \frac{3 x^{5}}{2 \sqrt{3 x^{2} + 2}} - \frac{3 x^{3}}{2 \sqrt{3 x^{2} + 2}} + \frac{15 x \sqrt{3 x^{2} + 2}}{2} - \frac{x}{3 \sqrt{3 x^{2} + 2}} + \frac{7 \left(3 x^{2} + 2\right)^{\frac{3}{2}}}{9} + \frac{46 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"-3*x**5/(2*sqrt(3*x**2 + 2)) - 3*x**3/(2*sqrt(3*x**2 + 2)) + 15*x*sqrt(3*x**2 + 2)/2 - x/(3*sqrt(3*x**2 + 2)) + 7*(3*x**2 + 2)**(3/2)/9 + 46*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
1360,1,61,0,0.263553," ","integrate((5-x)*(3*x**2+2)**(1/2),x)","- \frac{x^{2} \sqrt{3 x^{2} + 2}}{3} + \frac{5 x \sqrt{3 x^{2} + 2}}{2} - \frac{2 \sqrt{3 x^{2} + 2}}{9} + \frac{5 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{3}"," ",0,"-x**2*sqrt(3*x**2 + 2)/3 + 5*x*sqrt(3*x**2 + 2)/2 - 2*sqrt(3*x**2 + 2)/9 + 5*sqrt(3)*asinh(sqrt(6)*x/2)/3","A",0
1361,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 2}}{2 x + 3}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 2}}{2 x + 3}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 2)/(2*x + 3), x) - Integral(x*sqrt(3*x**2 + 2)/(2*x + 3), x)","F",0
1362,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x)**2,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 2}}{4 x^{2} + 12 x + 9}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 2)/(4*x**2 + 12*x + 9), x) - Integral(x*sqrt(3*x**2 + 2)/(4*x**2 + 12*x + 9), x)","F",0
1363,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x)**3,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(x*sqrt(3*x**2 + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x)","F",0
1364,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x)**4,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(x*sqrt(3*x**2 + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x)","F",0
1365,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1366,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1367,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(1/2)/(3+2*x)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1368,1,162,0,22.519219," ","integrate((5-x)*(3+2*x)**4*(3*x**2+2)**(3/2),x)","- \frac{16 x^{8} \sqrt{3 x^{2} + 2}}{3} - 6 x^{7} \sqrt{3 x^{2} + 2} + \frac{6808 x^{6} \sqrt{3 x^{2} + 2}}{63} + 426 x^{5} \sqrt{3 x^{2} + 2} + \frac{226763 x^{4} \sqrt{3 x^{2} + 2}}{315} + \frac{9689 x^{3} \sqrt{3 x^{2} + 2}}{12} + \frac{2294756 x^{2} \sqrt{3 x^{2} + 2}}{2835} + \frac{6943 x \sqrt{3 x^{2} + 2}}{12} + \frac{2149636 \sqrt{3 x^{2} + 2}}{8505} + \frac{2777 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{18}"," ",0,"-16*x**8*sqrt(3*x**2 + 2)/3 - 6*x**7*sqrt(3*x**2 + 2) + 6808*x**6*sqrt(3*x**2 + 2)/63 + 426*x**5*sqrt(3*x**2 + 2) + 226763*x**4*sqrt(3*x**2 + 2)/315 + 9689*x**3*sqrt(3*x**2 + 2)/12 + 2294756*x**2*sqrt(3*x**2 + 2)/2835 + 6943*x*sqrt(3*x**2 + 2)/12 + 2149636*sqrt(3*x**2 + 2)/8505 + 2777*sqrt(3)*asinh(sqrt(6)*x/2)/18","A",0
1369,1,144,0,14.073602," ","integrate((5-x)*(3+2*x)**3*(3*x**2+2)**(3/2),x)","- 3 x^{7} \sqrt{3 x^{2} + 2} + \frac{12 x^{6} \sqrt{3 x^{2} + 2}}{7} + 60 x^{5} \sqrt{3 x^{2} + 2} + \frac{5167 x^{4} \sqrt{3 x^{2} + 2}}{35} + \frac{2095 x^{3} \sqrt{3 x^{2} + 2}}{12} + \frac{20428 x^{2} \sqrt{3 x^{2} + 2}}{105} + \frac{2153 x \sqrt{3 x^{2} + 2}}{12} + \frac{20348 \sqrt{3 x^{2} + 2}}{315} + \frac{1087 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{18}"," ",0,"-3*x**7*sqrt(3*x**2 + 2) + 12*x**6*sqrt(3*x**2 + 2)/7 + 60*x**5*sqrt(3*x**2 + 2) + 5167*x**4*sqrt(3*x**2 + 2)/35 + 2095*x**3*sqrt(3*x**2 + 2)/12 + 20428*x**2*sqrt(3*x**2 + 2)/105 + 2153*x*sqrt(3*x**2 + 2)/12 + 20348*sqrt(3*x**2 + 2)/315 + 1087*sqrt(3)*asinh(sqrt(6)*x/2)/18","A",0
1370,1,129,0,8.155036," ","integrate((5-x)*(3+2*x)**2*(3*x**2+2)**(3/2),x)","- \frac{12 x^{6} \sqrt{3 x^{2} + 2}}{7} + 4 x^{5} \sqrt{3 x^{2} + 2} + \frac{1007 x^{4} \sqrt{3 x^{2} + 2}}{35} + \frac{461 x^{3} \sqrt{3 x^{2} + 2}}{12} + \frac{4268 x^{2} \sqrt{3 x^{2} + 2}}{105} + \frac{683 x \sqrt{3 x^{2} + 2}}{12} + \frac{4348 \sqrt{3 x^{2} + 2}}{315} + \frac{397 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{18}"," ",0,"-12*x**6*sqrt(3*x**2 + 2)/7 + 4*x**5*sqrt(3*x**2 + 2) + 1007*x**4*sqrt(3*x**2 + 2)/35 + 461*x**3*sqrt(3*x**2 + 2)/12 + 4268*x**2*sqrt(3*x**2 + 2)/105 + 683*x*sqrt(3*x**2 + 2)/12 + 4348*sqrt(3*x**2 + 2)/315 + 397*sqrt(3)*asinh(sqrt(6)*x/2)/18","A",0
1371,1,110,0,5.004232," ","integrate((5-x)*(3+2*x)*(3*x**2+2)**(3/2),x)","- x^{5} \sqrt{3 x^{2} + 2} + \frac{21 x^{4} \sqrt{3 x^{2} + 2}}{5} + \frac{121 x^{3} \sqrt{3 x^{2} + 2}}{12} + \frac{28 x^{2} \sqrt{3 x^{2} + 2}}{5} + \frac{223 x \sqrt{3 x^{2} + 2}}{12} + \frac{28 \sqrt{3 x^{2} + 2}}{15} + \frac{137 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{18}"," ",0,"-x**5*sqrt(3*x**2 + 2) + 21*x**4*sqrt(3*x**2 + 2)/5 + 121*x**3*sqrt(3*x**2 + 2)/12 + 28*x**2*sqrt(3*x**2 + 2)/5 + 223*x*sqrt(3*x**2 + 2)/12 + 28*sqrt(3*x**2 + 2)/15 + 137*sqrt(3)*asinh(sqrt(6)*x/2)/18","A",0
1372,1,97,0,2.755935," ","integrate((5-x)*(3*x**2+2)**(3/2),x)","- \frac{3 x^{4} \sqrt{3 x^{2} + 2}}{5} + \frac{15 x^{3} \sqrt{3 x^{2} + 2}}{4} - \frac{4 x^{2} \sqrt{3 x^{2} + 2}}{5} + \frac{25 x \sqrt{3 x^{2} + 2}}{4} - \frac{4 \sqrt{3 x^{2} + 2}}{15} + \frac{5 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{2}"," ",0,"-3*x**4*sqrt(3*x**2 + 2)/5 + 15*x**3*sqrt(3*x**2 + 2)/4 - 4*x**2*sqrt(3*x**2 + 2)/5 + 25*x*sqrt(3*x**2 + 2)/4 - 4*sqrt(3*x**2 + 2)/15 + 5*sqrt(3)*asinh(sqrt(6)*x/2)/2","A",0
1373,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 2}}{2 x + 3}\right)\, dx - \int \frac{2 x \sqrt{3 x^{2} + 2}}{2 x + 3}\, dx - \int \left(- \frac{15 x^{2} \sqrt{3 x^{2} + 2}}{2 x + 3}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 2}}{2 x + 3}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 2)/(2*x + 3), x) - Integral(2*x*sqrt(3*x**2 + 2)/(2*x + 3), x) - Integral(-15*x**2*sqrt(3*x**2 + 2)/(2*x + 3), x) - Integral(3*x**3*sqrt(3*x**2 + 2)/(2*x + 3), x)","F",0
1374,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**2,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{2 x \sqrt{3 x^{2} + 2}}{4 x^{2} + 12 x + 9}\, dx - \int \left(- \frac{15 x^{2} \sqrt{3 x^{2} + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 2}}{4 x^{2} + 12 x + 9}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 2)/(4*x**2 + 12*x + 9), x) - Integral(2*x*sqrt(3*x**2 + 2)/(4*x**2 + 12*x + 9), x) - Integral(-15*x**2*sqrt(3*x**2 + 2)/(4*x**2 + 12*x + 9), x) - Integral(3*x**3*sqrt(3*x**2 + 2)/(4*x**2 + 12*x + 9), x)","F",0
1375,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1376,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1377,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1378,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1379,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1380,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(3/2)/(3+2*x)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1381,1,199,0,113.005237," ","integrate((5-x)*(3+2*x)**4*(3*x**2+2)**(5/2),x)","- \frac{144 x^{10} \sqrt{3 x^{2} + 2}}{11} - \frac{72 x^{9} \sqrt{3 x^{2} + 2}}{5} + \frac{7976 x^{8} \sqrt{3 x^{2} + 2}}{33} + \frac{4734 x^{7} \sqrt{3 x^{2} + 2}}{5} + \frac{173419 x^{6} \sqrt{3 x^{2} + 2}}{99} + \frac{24311 x^{5} \sqrt{3 x^{2} + 2}}{10} + \frac{279190 x^{4} \sqrt{3 x^{2} + 2}}{99} + \frac{28535 x^{3} \sqrt{3 x^{2} + 2}}{12} + \frac{1536004 x^{2} \sqrt{3 x^{2} + 2}}{891} + \frac{14449 x \sqrt{3 x^{2} + 2}}{12} + \frac{976856 \sqrt{3 x^{2} + 2}}{2673} + \frac{4991 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{18}"," ",0,"-144*x**10*sqrt(3*x**2 + 2)/11 - 72*x**9*sqrt(3*x**2 + 2)/5 + 7976*x**8*sqrt(3*x**2 + 2)/33 + 4734*x**7*sqrt(3*x**2 + 2)/5 + 173419*x**6*sqrt(3*x**2 + 2)/99 + 24311*x**5*sqrt(3*x**2 + 2)/10 + 279190*x**4*sqrt(3*x**2 + 2)/99 + 28535*x**3*sqrt(3*x**2 + 2)/12 + 1536004*x**2*sqrt(3*x**2 + 2)/891 + 14449*x*sqrt(3*x**2 + 2)/12 + 976856*sqrt(3*x**2 + 2)/2673 + 4991*sqrt(3)*asinh(sqrt(6)*x/2)/18","A",0
1382,1,180,0,77.879588," ","integrate((5-x)*(3+2*x)**3*(3*x**2+2)**(5/2),x)","- \frac{36 x^{9} \sqrt{3 x^{2} + 2}}{5} + 4 x^{8} \sqrt{3 x^{2} + 2} + \frac{2583 x^{7} \sqrt{3 x^{2} + 2}}{20} + \frac{959 x^{6} \sqrt{3 x^{2} + 2}}{3} + \frac{9281 x^{5} \sqrt{3 x^{2} + 2}}{20} + \frac{1886 x^{4} \sqrt{3 x^{2} + 2}}{3} + \frac{14243 x^{3} \sqrt{3 x^{2} + 2}}{24} + \frac{11252 x^{2} \sqrt{3 x^{2} + 2}}{27} + \frac{9229 x \sqrt{3 x^{2} + 2}}{24} + \frac{7480 \sqrt{3 x^{2} + 2}}{81} + \frac{3731 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{36}"," ",0,"-36*x**9*sqrt(3*x**2 + 2)/5 + 4*x**8*sqrt(3*x**2 + 2) + 2583*x**7*sqrt(3*x**2 + 2)/20 + 959*x**6*sqrt(3*x**2 + 2)/3 + 9281*x**5*sqrt(3*x**2 + 2)/20 + 1886*x**4*sqrt(3*x**2 + 2)/3 + 14243*x**3*sqrt(3*x**2 + 2)/24 + 11252*x**2*sqrt(3*x**2 + 2)/27 + 9229*x*sqrt(3*x**2 + 2)/24 + 7480*sqrt(3*x**2 + 2)/81 + 3731*sqrt(3)*asinh(sqrt(6)*x/2)/36","A",0
1383,1,162,0,50.466729," ","integrate((5-x)*(3+2*x)**2*(3*x**2+2)**(5/2),x)","- 4 x^{8} \sqrt{3 x^{2} + 2} + 9 x^{7} \sqrt{3 x^{2} + 2} + \frac{175 x^{6} \sqrt{3 x^{2} + 2}}{3} + \frac{169 x^{5} \sqrt{3 x^{2} + 2}}{2} + \frac{382 x^{4} \sqrt{3 x^{2} + 2}}{3} + \frac{1873 x^{3} \sqrt{3 x^{2} + 2}}{12} + \frac{2356 x^{2} \sqrt{3 x^{2} + 2}}{27} + \frac{1495 x \sqrt{3 x^{2} + 2}}{12} + \frac{1592 \sqrt{3 x^{2} + 2}}{81} + \frac{665 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{18}"," ",0,"-4*x**8*sqrt(3*x**2 + 2) + 9*x**7*sqrt(3*x**2 + 2) + 175*x**6*sqrt(3*x**2 + 2)/3 + 169*x**5*sqrt(3*x**2 + 2)/2 + 382*x**4*sqrt(3*x**2 + 2)/3 + 1873*x**3*sqrt(3*x**2 + 2)/12 + 2356*x**2*sqrt(3*x**2 + 2)/27 + 1495*x*sqrt(3*x**2 + 2)/12 + 1592*sqrt(3*x**2 + 2)/81 + 665*sqrt(3)*asinh(sqrt(6)*x/2)/18","A",0
1384,1,143,0,34.005340," ","integrate((5-x)*(3+2*x)*(3*x**2+2)**(5/2),x)","- \frac{9 x^{7} \sqrt{3 x^{2} + 2}}{4} + 9 x^{6} \sqrt{3 x^{2} + 2} + \frac{73 x^{5} \sqrt{3 x^{2} + 2}}{4} + 18 x^{4} \sqrt{3 x^{2} + 2} + \frac{1111 x^{3} \sqrt{3 x^{2} + 2}}{24} + 12 x^{2} \sqrt{3 x^{2} + 2} + \frac{985 x \sqrt{3 x^{2} + 2}}{24} + \frac{8 \sqrt{3 x^{2} + 2}}{3} + \frac{455 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{36}"," ",0,"-9*x**7*sqrt(3*x**2 + 2)/4 + 9*x**6*sqrt(3*x**2 + 2) + 73*x**5*sqrt(3*x**2 + 2)/4 + 18*x**4*sqrt(3*x**2 + 2) + 1111*x**3*sqrt(3*x**2 + 2)/24 + 12*x**2*sqrt(3*x**2 + 2) + 985*x*sqrt(3*x**2 + 2)/24 + 8*sqrt(3*x**2 + 2)/3 + 455*sqrt(3)*asinh(sqrt(6)*x/2)/36","A",0
1385,1,131,0,20.989180," ","integrate((5-x)*(3*x**2+2)**(5/2),x)","- \frac{9 x^{6} \sqrt{3 x^{2} + 2}}{7} + \frac{15 x^{5} \sqrt{3 x^{2} + 2}}{2} - \frac{18 x^{4} \sqrt{3 x^{2} + 2}}{7} + \frac{65 x^{3} \sqrt{3 x^{2} + 2}}{4} - \frac{12 x^{2} \sqrt{3 x^{2} + 2}}{7} + \frac{55 x \sqrt{3 x^{2} + 2}}{4} - \frac{8 \sqrt{3 x^{2} + 2}}{21} + \frac{25 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{6}"," ",0,"-9*x**6*sqrt(3*x**2 + 2)/7 + 15*x**5*sqrt(3*x**2 + 2)/2 - 18*x**4*sqrt(3*x**2 + 2)/7 + 65*x**3*sqrt(3*x**2 + 2)/4 - 12*x**2*sqrt(3*x**2 + 2)/7 + 55*x*sqrt(3*x**2 + 2)/4 - 8*sqrt(3*x**2 + 2)/21 + 25*sqrt(3)*asinh(sqrt(6)*x/2)/6","A",0
1386,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1387,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1388,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1389,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1390,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1391,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1392,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1393,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1394,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1395,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1396,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1397,1,97,0,1.933709," ","integrate((5-x)*(3+2*x)**4/(3*x**2+2)**(1/2),x)","- \frac{16 x^{4} \sqrt{3 x^{2} + 2}}{15} - \frac{4 x^{3} \sqrt{3 x^{2} + 2}}{3} + \frac{4088 x^{2} \sqrt{3 x^{2} + 2}}{135} + \frac{436 x \sqrt{3 x^{2} + 2}}{3} + \frac{118513 \sqrt{3 x^{2} + 2}}{405} + \frac{343 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"-16*x**4*sqrt(3*x**2 + 2)/15 - 4*x**3*sqrt(3*x**2 + 2)/3 + 4088*x**2*sqrt(3*x**2 + 2)/135 + 436*x*sqrt(3*x**2 + 2)/3 + 118513*sqrt(3*x**2 + 2)/405 + 343*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
1398,1,80,0,1.078149," ","integrate((5-x)*(3+2*x)**3/(3*x**2+2)**(1/2),x)","- \frac{2 x^{3} \sqrt{3 x^{2} + 2}}{3} + \frac{4 x^{2} \sqrt{3 x^{2} + 2}}{9} + \frac{65 x \sqrt{3 x^{2} + 2}}{3} + \frac{2171 \sqrt{3 x^{2} + 2}}{27} + \frac{275 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"-2*x**3*sqrt(3*x**2 + 2)/3 + 4*x**2*sqrt(3*x**2 + 2)/9 + 65*x*sqrt(3*x**2 + 2)/3 + 2171*sqrt(3*x**2 + 2)/27 + 275*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
1399,1,63,0,0.541632," ","integrate((5-x)*(3+2*x)**2/(3*x**2+2)**(1/2),x)","- \frac{4 x^{2} \sqrt{3 x^{2} + 2}}{9} + \frac{4 x \sqrt{3 x^{2} + 2}}{3} + \frac{475 \sqrt{3 x^{2} + 2}}{27} + \frac{127 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"-4*x**2*sqrt(3*x**2 + 2)/9 + 4*x*sqrt(3*x**2 + 2)/3 + 475*sqrt(3*x**2 + 2)/27 + 127*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
1400,1,44,0,0.299044," ","integrate((5-x)*(3+2*x)/(3*x**2+2)**(1/2),x)","- \frac{x \sqrt{3 x^{2} + 2}}{3} + \frac{7 \sqrt{3 x^{2} + 2}}{3} + \frac{47 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"-x*sqrt(3*x**2 + 2)/3 + 7*sqrt(3*x**2 + 2)/3 + 47*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
1401,1,29,0,0.184139," ","integrate((5-x)/(3*x**2+2)**(1/2),x)","- \frac{\sqrt{3 x^{2} + 2}}{3} + \frac{5 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{3}"," ",0,"-sqrt(3*x**2 + 2)/3 + 5*sqrt(3)*asinh(sqrt(6)*x/2)/3","A",0
1402,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)/(3*x**2+2)**(1/2),x)","- \int \frac{x}{2 x \sqrt{3 x^{2} + 2} + 3 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{5}{2 x \sqrt{3 x^{2} + 2} + 3 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(x/(2*x*sqrt(3*x**2 + 2) + 3*sqrt(3*x**2 + 2)), x) - Integral(-5/(2*x*sqrt(3*x**2 + 2) + 3*sqrt(3*x**2 + 2)), x)","F",0
1403,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**2/(3*x**2+2)**(1/2),x)","- \int \frac{x}{4 x^{2} \sqrt{3 x^{2} + 2} + 12 x \sqrt{3 x^{2} + 2} + 9 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{5}{4 x^{2} \sqrt{3 x^{2} + 2} + 12 x \sqrt{3 x^{2} + 2} + 9 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(x/(4*x**2*sqrt(3*x**2 + 2) + 12*x*sqrt(3*x**2 + 2) + 9*sqrt(3*x**2 + 2)), x) - Integral(-5/(4*x**2*sqrt(3*x**2 + 2) + 12*x*sqrt(3*x**2 + 2) + 9*sqrt(3*x**2 + 2)), x)","F",0
1404,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**3/(3*x**2+2)**(1/2),x)","- \int \frac{x}{8 x^{3} \sqrt{3 x^{2} + 2} + 36 x^{2} \sqrt{3 x^{2} + 2} + 54 x \sqrt{3 x^{2} + 2} + 27 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{5}{8 x^{3} \sqrt{3 x^{2} + 2} + 36 x^{2} \sqrt{3 x^{2} + 2} + 54 x \sqrt{3 x^{2} + 2} + 27 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(x/(8*x**3*sqrt(3*x**2 + 2) + 36*x**2*sqrt(3*x**2 + 2) + 54*x*sqrt(3*x**2 + 2) + 27*sqrt(3*x**2 + 2)), x) - Integral(-5/(8*x**3*sqrt(3*x**2 + 2) + 36*x**2*sqrt(3*x**2 + 2) + 54*x*sqrt(3*x**2 + 2) + 27*sqrt(3*x**2 + 2)), x)","F",0
1405,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**4/(3*x**2+2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1406,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**5/(3*x**2+2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1407,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**6/(3*x**2+2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1408,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4/(3*x**2+2)**(3/2),x)","- \int \left(- \frac{999 x}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{864 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{264 x^{3}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{16 x^{4}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\, dx - \int \frac{16 x^{5}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{405}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-999*x/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-864*x**2/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-264*x**3/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(16*x**4/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(16*x**5/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-405/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x)","F",0
1409,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3/(3*x**2+2)**(3/2),x)","- \int \left(- \frac{243 x}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{126 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{4 x^{3}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{8 x^{4}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{135}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-243*x/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-126*x**2/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-4*x**3/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(8*x**4/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-135/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x)","F",0
1410,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2/(3*x**2+2)**(3/2),x)","- \int \left(- \frac{51 x}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{8 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{4 x^{3}}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{45}{3 x^{2} \sqrt{3 x^{2} + 2} + 2 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-51*x/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-8*x**2/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(4*x**3/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x) - Integral(-45/(3*x**2*sqrt(3*x**2 + 2) + 2*sqrt(3*x**2 + 2)), x)","F",0
1411,1,99,0,14.977674," ","integrate((5-x)*(3+2*x)/(3*x**2+2)**(3/2),x)","- \frac{6 \sqrt{3} x^{2} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{27 x^{2} + 18} + \frac{6 x \sqrt{3 x^{2} + 2}}{27 x^{2} + 18} + \frac{15 x}{2 \sqrt{3 x^{2} + 2}} - \frac{4 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{27 x^{2} + 18} - \frac{7}{3 \sqrt{3 x^{2} + 2}}"," ",0,"-6*sqrt(3)*x**2*asinh(sqrt(6)*x/2)/(27*x**2 + 18) + 6*x*sqrt(3*x**2 + 2)/(27*x**2 + 18) + 15*x/(2*sqrt(3*x**2 + 2)) - 4*sqrt(3)*asinh(sqrt(6)*x/2)/(27*x**2 + 18) - 7/(3*sqrt(3*x**2 + 2))","B",0
1412,1,27,0,14.368915," ","integrate((5-x)/(3*x**2+2)**(3/2),x)","\frac{5 x}{2 \sqrt{3 x^{2} + 2}} + \frac{1}{3 \sqrt{3 x^{2} + 2}}"," ",0,"5*x/(2*sqrt(3*x**2 + 2)) + 1/(3*sqrt(3*x**2 + 2))","A",0
1413,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)/(3*x**2+2)**(3/2),x)","- \int \frac{x}{6 x^{3} \sqrt{3 x^{2} + 2} + 9 x^{2} \sqrt{3 x^{2} + 2} + 4 x \sqrt{3 x^{2} + 2} + 6 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{5}{6 x^{3} \sqrt{3 x^{2} + 2} + 9 x^{2} \sqrt{3 x^{2} + 2} + 4 x \sqrt{3 x^{2} + 2} + 6 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(x/(6*x**3*sqrt(3*x**2 + 2) + 9*x**2*sqrt(3*x**2 + 2) + 4*x*sqrt(3*x**2 + 2) + 6*sqrt(3*x**2 + 2)), x) - Integral(-5/(6*x**3*sqrt(3*x**2 + 2) + 9*x**2*sqrt(3*x**2 + 2) + 4*x*sqrt(3*x**2 + 2) + 6*sqrt(3*x**2 + 2)), x)","F",0
1414,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**2/(3*x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1415,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**3/(3*x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1416,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**4/(3*x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1417,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**5/(3*x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1418,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**6/(3*x**2+2)**(5/2),x)","- \int \left(- \frac{13851 x}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{21384 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{16740 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{6480 x^{4}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{720 x^{5}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{256 x^{6}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \frac{64 x^{7}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{3645}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-13851*x/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-21384*x**2/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-16740*x**3/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-6480*x**4/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-720*x**5/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(256*x**6/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(64*x**7/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-3645/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x)","F",0
1419,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**5/(3*x**2+2)**(5/2),x)","- \int \left(- \frac{3807 x}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{4590 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{2520 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{480 x^{4}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{80 x^{5}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \frac{32 x^{6}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{1215}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-3807*x/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-4590*x**2/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-2520*x**3/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-480*x**4/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(80*x**5/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(32*x**6/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-1215/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x)","F",0
1420,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4/(3*x**2+2)**(5/2),x)","- \int \left(- \frac{999 x}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{864 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{264 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{16 x^{4}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \frac{16 x^{5}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{405}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-999*x/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-864*x**2/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-264*x**3/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(16*x**4/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(16*x**5/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-405/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x)","F",0
1421,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3/(3*x**2+2)**(5/2),x)","- \int \left(- \frac{243 x}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{126 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{4 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{8 x^{4}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{135}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-243*x/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-126*x**2/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-4*x**3/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(8*x**4/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-135/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x)","F",0
1422,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2/(3*x**2+2)**(5/2),x)","- \int \left(- \frac{51 x}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \left(- \frac{8 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx - \int \frac{4 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\, dx - \int \left(- \frac{45}{9 x^{4} \sqrt{3 x^{2} + 2} + 12 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}}\right)\, dx"," ",0,"-Integral(-51*x/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-8*x**2/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(4*x**3/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x) - Integral(-45/(9*x**4*sqrt(3*x**2 + 2) + 12*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)), x)","F",0
1423,1,122,0,58.398879," ","integrate((5-x)*(3+2*x)/(3*x**2+2)**(5/2),x)","- \frac{2 x^{3}}{18 x^{2} \sqrt{3 x^{2} + 2} + 12 \sqrt{3 x^{2} + 2}} + \frac{15 x^{3}}{6 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}} + \frac{15 x}{6 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}} - \frac{7}{27 x^{2} \sqrt{3 x^{2} + 2} + 18 \sqrt{3 x^{2} + 2}}"," ",0,"-2*x**3/(18*x**2*sqrt(3*x**2 + 2) + 12*sqrt(3*x**2 + 2)) + 15*x**3/(6*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)) + 15*x/(6*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)) - 7/(27*x**2*sqrt(3*x**2 + 2) + 18*sqrt(3*x**2 + 2))","B",0
1424,1,90,0,43.078417," ","integrate((5-x)/(3*x**2+2)**(5/2),x)","\frac{5 x^{3}}{6 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}} + \frac{5 x}{6 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}} + \frac{1}{27 x^{2} \sqrt{3 x^{2} + 2} + 18 \sqrt{3 x^{2} + 2}}"," ",0,"5*x**3/(6*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)) + 5*x/(6*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)) + 1/(27*x**2*sqrt(3*x**2 + 2) + 18*sqrt(3*x**2 + 2))","B",0
1425,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1426,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**2/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1427,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**3/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1428,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**4/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1429,1,379,0,15.780086," ","integrate((B*x+A)*(e*x+d)**(3/2)*(c*x**2+a),x)","A a d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 A a \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 A c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 A c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 B a d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 B a \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 B c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 B c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}}"," ",0,"A*a*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*A*a*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*A*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*A*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*B*a*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*B*a*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*B*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*B*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4","A",0
1430,1,131,0,3.738450," ","integrate((B*x+A)*(c*x**2+a)*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{B c \left(d + e x\right)^{\frac{9}{2}}}{9 e^{3}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(A c e - 3 B c d\right)}{7 e^{3}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 2 A c d e + B a e^{2} + 3 B c d^{2}\right)}{5 e^{3}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A a e^{3} + A c d^{2} e - B a d e^{2} - B c d^{3}\right)}{3 e^{3}}\right)}{e}"," ",0,"2*(B*c*(d + e*x)**(9/2)/(9*e**3) + (d + e*x)**(7/2)*(A*c*e - 3*B*c*d)/(7*e**3) + (d + e*x)**(5/2)*(-2*A*c*d*e + B*a*e**2 + 3*B*c*d**2)/(5*e**3) + (d + e*x)**(3/2)*(A*a*e**3 + A*c*d**2*e - B*a*d*e**2 - B*c*d**3)/(3*e**3))/e","A",0
1431,1,374,0,36.488204," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a d}{\sqrt{d + e x}} - 2 A a \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{2 A c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 A c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 B a d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 B a \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 B c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 B c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a*d/sqrt(d + e*x) - 2*A*a*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*A*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*A*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*B*a*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*B*a*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*B*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*B*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3)/e, Ne(e, 0)), ((A*a*x + A*c*x**3/3 + B*a*x**2/2 + B*c*x**4/4)/sqrt(d), True))","A",0
1432,1,112,0,21.209597," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**(3/2),x)","\frac{2 B c \left(d + e x\right)^{\frac{5}{2}}}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 A c e - 6 B c d\right)}{3 e^{4}} + \frac{\sqrt{d + e x} \left(- 4 A c d e + 2 B a e^{2} + 6 B c d^{2}\right)}{e^{4}} + \frac{2 \left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)}{e^{4} \sqrt{d + e x}}"," ",0,"2*B*c*(d + e*x)**(5/2)/(5*e**4) + (d + e*x)**(3/2)*(2*A*c*e - 6*B*c*d)/(3*e**4) + sqrt(d + e*x)*(-4*A*c*d*e + 2*B*a*e**2 + 6*B*c*d**2)/e**4 + 2*(-A*e + B*d)*(a*e**2 + c*d**2)/(e**4*sqrt(d + e*x))","A",0
1433,1,449,0,1.438531," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 A a e^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{16 A c d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{24 A c d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{6 A c e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{4 B a d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{6 B a e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{32 B c d^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{48 B c d^{2} e x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 B c d e^{2} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{2 B c e^{3} x^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a*e**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 16*A*c*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 24*A*c*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 6*A*c*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 4*B*a*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 6*B*a*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 32*B*c*d**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 48*B*c*d**2*e*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*B*c*d*e**2*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 2*B*c*e**3*x**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)), Ne(e, 0)), ((A*a*x + A*c*x**3/3 + B*a*x**2/2 + B*c*x**4/4)/d**(5/2), True))","A",0
1434,1,653,0,3.221446," ","integrate((B*x+A)*(c*x**2+a)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 A a e^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{16 A c d^{2} e}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{40 A c d e^{2} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{30 A c e^{3} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{4 B a d e^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{10 B a e^{3} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{96 B c d^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{240 B c d^{2} e x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{180 B c d e^{2} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{30 B c e^{3} x^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*a*e**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 16*A*c*d**2*e/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 40*A*c*d*e**2*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 30*A*c*e**3*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 4*B*a*d*e**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 10*B*a*e**3*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 96*B*c*d**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 240*B*c*d**2*e*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 180*B*c*d*e**2*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 30*B*c*e**3*x**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)), Ne(e, 0)), ((A*a*x + A*c*x**3/3 + B*a*x**2/2 + B*c*x**4/4)/d**(7/2), True))","A",0
1435,1,308,0,5.557477," ","integrate((B*x+A)*(c*x**2+a)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{B c^{2} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{5}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(A c^{2} e - 5 B c^{2} d\right)}{11 e^{5}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(- 4 A c^{2} d e + 2 B a c e^{2} + 10 B c^{2} d^{2}\right)}{9 e^{5}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(2 A a c e^{3} + 6 A c^{2} d^{2} e - 6 B a c d e^{2} - 10 B c^{2} d^{3}\right)}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 4 A a c d e^{3} - 4 A c^{2} d^{3} e + B a^{2} e^{4} + 6 B a c d^{2} e^{2} + 5 B c^{2} d^{4}\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A a^{2} e^{5} + 2 A a c d^{2} e^{3} + A c^{2} d^{4} e - B a^{2} d e^{4} - 2 B a c d^{3} e^{2} - B c^{2} d^{5}\right)}{3 e^{5}}\right)}{e}"," ",0,"2*(B*c**2*(d + e*x)**(13/2)/(13*e**5) + (d + e*x)**(11/2)*(A*c**2*e - 5*B*c**2*d)/(11*e**5) + (d + e*x)**(9/2)*(-4*A*c**2*d*e + 2*B*a*c*e**2 + 10*B*c**2*d**2)/(9*e**5) + (d + e*x)**(7/2)*(2*A*a*c*e**3 + 6*A*c**2*d**2*e - 6*B*a*c*d*e**2 - 10*B*c**2*d**3)/(7*e**5) + (d + e*x)**(5/2)*(-4*A*a*c*d*e**3 - 4*A*c**2*d**3*e + B*a**2*e**4 + 6*B*a*c*d**2*e**2 + 5*B*c**2*d**4)/(5*e**5) + (d + e*x)**(3/2)*(A*a**2*e**5 + 2*A*a*c*d**2*e**3 + A*c**2*d**4*e - B*a**2*d*e**4 - 2*B*a*c*d**3*e**2 - B*c**2*d**5)/(3*e**5))/e","A",0
1436,1,772,0,79.704347," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a^{2} d}{\sqrt{d + e x}} - 2 A a^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 A a c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{4 A a c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 A c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 A c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 B a^{2} d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 B a^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{4 B a c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{4 B a c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 B c^{2} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{2 B c^{2} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}}}{e} & \text{for}\: e \neq 0 \\\frac{A a^{2} x + \frac{2 A a c x^{3}}{3} + \frac{A c^{2} x^{5}}{5} + \frac{B a^{2} x^{2}}{2} + \frac{B a c x^{4}}{2} + \frac{B c^{2} x^{6}}{6}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a**2*d/sqrt(d + e*x) - 2*A*a**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*A*a*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 4*A*a*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*A*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*A*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*B*a**2*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*B*a**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 4*B*a*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 4*B*a*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*B*c**2*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 2*B*c**2*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5)/e, Ne(e, 0)), ((A*a**2*x + 2*A*a*c*x**3/3 + A*c**2*x**5/5 + B*a**2*x**2/2 + B*a*c*x**4/2 + B*c**2*x**6/6)/sqrt(d), True))","A",0
1437,1,253,0,48.985154," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**(3/2),x)","\frac{2 B c^{2} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(2 A c^{2} e - 10 B c^{2} d\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 8 A c^{2} d e + 4 B a c e^{2} + 20 B c^{2} d^{2}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(4 A a c e^{3} + 12 A c^{2} d^{2} e - 12 B a c d e^{2} - 20 B c^{2} d^{3}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(- 8 A a c d e^{3} - 8 A c^{2} d^{3} e + 2 B a^{2} e^{4} + 12 B a c d^{2} e^{2} + 10 B c^{2} d^{4}\right)}{e^{6}} + \frac{2 \left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)^{2}}{e^{6} \sqrt{d + e x}}"," ",0,"2*B*c**2*(d + e*x)**(9/2)/(9*e**6) + (d + e*x)**(7/2)*(2*A*c**2*e - 10*B*c**2*d)/(7*e**6) + (d + e*x)**(5/2)*(-8*A*c**2*d*e + 4*B*a*c*e**2 + 20*B*c**2*d**2)/(5*e**6) + (d + e*x)**(3/2)*(4*A*a*c*e**3 + 12*A*c**2*d**2*e - 12*B*a*c*d*e**2 - 20*B*c**2*d**3)/(3*e**6) + sqrt(d + e*x)*(-8*A*a*c*d*e**3 - 8*A*c**2*d**3*e + 2*B*a**2*e**4 + 12*B*a*c*d**2*e**2 + 10*B*c**2*d**4)/e**6 + 2*(-A*e + B*d)*(a*e**2 + c*d**2)**2/(e**6*sqrt(d + e*x))","A",0
1438,1,231,0,61.952134," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**(5/2),x)","\frac{2 B c^{2} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 A c^{2} e - 10 B c^{2} d\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- 8 A c^{2} d e + 4 B a c e^{2} + 20 B c^{2} d^{2}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(4 A a c e^{3} + 12 A c^{2} d^{2} e - 12 B a c d e^{2} - 20 B c^{2} d^{3}\right)}{e^{6}} - \frac{2 \left(a e^{2} + c d^{2}\right) \left(- 4 A c d e + B a e^{2} + 5 B c d^{2}\right)}{e^{6} \sqrt{d + e x}} + \frac{2 \left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)^{2}}{3 e^{6} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*B*c**2*(d + e*x)**(7/2)/(7*e**6) + (d + e*x)**(5/2)*(2*A*c**2*e - 10*B*c**2*d)/(5*e**6) + (d + e*x)**(3/2)*(-8*A*c**2*d*e + 4*B*a*c*e**2 + 20*B*c**2*d**2)/(3*e**6) + sqrt(d + e*x)*(4*A*a*c*e**3 + 12*A*c**2*d**2*e - 12*B*a*c*d*e**2 - 20*B*c**2*d**3)/e**6 - 2*(a*e**2 + c*d**2)*(-4*A*c*d*e + B*a*e**2 + 5*B*c*d**2)/(e**6*sqrt(d + e*x)) + 2*(-A*e + B*d)*(a*e**2 + c*d**2)**2/(3*e**6*(d + e*x)**(3/2))","A",0
1439,1,1426,0,4.402846," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 A a^{2} e^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{32 A a c d^{2} e^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{80 A a c d e^{4} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{60 A a c e^{5} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{256 A c^{2} d^{4} e}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{640 A c^{2} d^{3} e^{2} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{480 A c^{2} d^{2} e^{3} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{80 A c^{2} d e^{4} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{10 A c^{2} e^{5} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{4 B a^{2} d e^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{10 B a^{2} e^{5} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{192 B a c d^{3} e^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{480 B a c d^{2} e^{3} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{360 B a c d e^{4} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{60 B a c e^{5} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{512 B c^{2} d^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1280 B c^{2} d^{4} e x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{960 B c^{2} d^{3} e^{2} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{160 B c^{2} d^{2} e^{3} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{20 B c^{2} d e^{4} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{6 B c^{2} e^{5} x^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{2} x + \frac{2 A a c x^{3}}{3} + \frac{A c^{2} x^{5}}{5} + \frac{B a^{2} x^{2}}{2} + \frac{B a c x^{4}}{2} + \frac{B c^{2} x^{6}}{6}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*a**2*e**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 32*A*a*c*d**2*e**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 80*A*a*c*d*e**4*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 60*A*a*c*e**5*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 256*A*c**2*d**4*e/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 640*A*c**2*d**3*e**2*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 480*A*c**2*d**2*e**3*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 80*A*c**2*d*e**4*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 10*A*c**2*e**5*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 4*B*a**2*d*e**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 10*B*a**2*e**5*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 192*B*a*c*d**3*e**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 480*B*a*c*d**2*e**3*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 360*B*a*c*d*e**4*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 60*B*a*c*e**5*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 512*B*c**2*d**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1280*B*c**2*d**4*e*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 960*B*c**2*d**3*e**2*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 160*B*c**2*d**2*e**3*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 20*B*c**2*d*e**4*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 6*B*c**2*e**5*x**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)), Ne(e, 0)), ((A*a**2*x + 2*A*a*c*x**3/3 + A*c**2*x**5/5 + B*a**2*x**2/2 + B*a*c*x**4/2 + B*c**2*x**6/6)/d**(7/2), True))","A",0
1440,1,1855,0,8.149729," ","integrate((B*x+A)*(c*x**2+a)**2/(e*x+d)**(9/2),x)","\begin{cases} - \frac{30 A a^{2} e^{5}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{32 A a c d^{2} e^{3}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{112 A a c d e^{4} x}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{140 A a c e^{5} x^{2}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} + \frac{768 A c^{2} d^{4} e}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} + \frac{2688 A c^{2} d^{3} e^{2} x}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} + \frac{3360 A c^{2} d^{2} e^{3} x^{2}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} + \frac{1680 A c^{2} d e^{4} x^{3}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} + \frac{210 A c^{2} e^{5} x^{4}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{12 B a^{2} d e^{4}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{42 B a^{2} e^{5} x}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{192 B a c d^{3} e^{2}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{672 B a c d^{2} e^{3} x}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{840 B a c d e^{4} x^{2}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{420 B a c e^{5} x^{3}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{2560 B c^{2} d^{5}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{8960 B c^{2} d^{4} e x}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{11200 B c^{2} d^{3} e^{2} x^{2}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{5600 B c^{2} d^{2} e^{3} x^{3}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} - \frac{700 B c^{2} d e^{4} x^{4}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} + \frac{70 B c^{2} e^{5} x^{5}}{105 d^{3} e^{6} \sqrt{d + e x} + 315 d^{2} e^{7} x \sqrt{d + e x} + 315 d e^{8} x^{2} \sqrt{d + e x} + 105 e^{9} x^{3} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{2} x + \frac{2 A a c x^{3}}{3} + \frac{A c^{2} x^{5}}{5} + \frac{B a^{2} x^{2}}{2} + \frac{B a c x^{4}}{2} + \frac{B c^{2} x^{6}}{6}}{d^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*a**2*e**5/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 32*A*a*c*d**2*e**3/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 112*A*a*c*d*e**4*x/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 140*A*a*c*e**5*x**2/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) + 768*A*c**2*d**4*e/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) + 2688*A*c**2*d**3*e**2*x/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) + 3360*A*c**2*d**2*e**3*x**2/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) + 1680*A*c**2*d*e**4*x**3/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) + 210*A*c**2*e**5*x**4/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 12*B*a**2*d*e**4/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 42*B*a**2*e**5*x/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 192*B*a*c*d**3*e**2/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 672*B*a*c*d**2*e**3*x/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 840*B*a*c*d*e**4*x**2/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 420*B*a*c*e**5*x**3/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 2560*B*c**2*d**5/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 8960*B*c**2*d**4*e*x/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 11200*B*c**2*d**3*e**2*x**2/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 5600*B*c**2*d**2*e**3*x**3/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) - 700*B*c**2*d*e**4*x**4/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)) + 70*B*c**2*e**5*x**5/(105*d**3*e**6*sqrt(d + e*x) + 315*d**2*e**7*x*sqrt(d + e*x) + 315*d*e**8*x**2*sqrt(d + e*x) + 105*e**9*x**3*sqrt(d + e*x)), Ne(e, 0)), ((A*a**2*x + 2*A*a*c*x**3/3 + A*c**2*x**5/5 + B*a**2*x**2/2 + B*a*c*x**4/2 + B*c**2*x**6/6)/d**(9/2), True))","A",0
1441,1,1284,0,139.186822," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a^{3} d}{\sqrt{d + e x}} - 2 A a^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{6 A a^{2} c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 A a^{2} c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{6 A a c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{6 A a c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 A c^{3} d \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{6}} - \frac{2 A c^{3} \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} - \frac{2 B a^{3} d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 B a^{3} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{6 B a^{2} c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{6 B a^{2} c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{6 B a c^{2} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{6 B a c^{2} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} - \frac{2 B c^{3} d \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{7}} - \frac{2 B c^{3} \left(\frac{d^{8}}{\sqrt{d + e x}} + 8 d^{7} \sqrt{d + e x} - \frac{28 d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{56 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} - 10 d^{4} \left(d + e x\right)^{\frac{7}{2}} + \frac{56 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{28 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{8 d \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}}}{e} & \text{for}\: e \neq 0 \\\frac{A a^{3} x + A a^{2} c x^{3} + \frac{3 A a c^{2} x^{5}}{5} + \frac{A c^{3} x^{7}}{7} + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} c x^{4}}{4} + \frac{B a c^{2} x^{6}}{2} + \frac{B c^{3} x^{8}}{8}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a**3*d/sqrt(d + e*x) - 2*A*a**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 6*A*a**2*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*A*a**2*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 6*A*a*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 6*A*a*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*A*c**3*d*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**6 - 2*A*c**3*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**6 - 2*B*a**3*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*B*a**3*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 6*B*a**2*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 6*B*a**2*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 6*B*a*c**2*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 6*B*a*c**2*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5 - 2*B*c**3*d*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**7 - 2*B*c**3*(d**8/sqrt(d + e*x) + 8*d**7*sqrt(d + e*x) - 28*d**6*(d + e*x)**(3/2)/3 + 56*d**5*(d + e*x)**(5/2)/5 - 10*d**4*(d + e*x)**(7/2) + 56*d**3*(d + e*x)**(9/2)/9 - 28*d**2*(d + e*x)**(11/2)/11 + 8*d*(d + e*x)**(13/2)/13 - (d + e*x)**(15/2)/15)/e**7)/e, Ne(e, 0)), ((A*a**3*x + A*a**2*c*x**3 + 3*A*a*c**2*x**5/5 + A*c**3*x**7/7 + B*a**3*x**2/2 + 3*B*a**2*c*x**4/4 + B*a*c**2*x**6/2 + B*c**3*x**8/8)/sqrt(d), True))","A",0
1442,1,461,0,101.300676," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**(3/2),x)","\frac{2 B c^{3} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{8}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(2 A c^{3} e - 14 B c^{3} d\right)}{11 e^{8}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(- 12 A c^{3} d e + 6 B a c^{2} e^{2} + 42 B c^{3} d^{2}\right)}{9 e^{8}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 A a c^{2} e^{3} + 30 A c^{3} d^{2} e - 30 B a c^{2} d e^{2} - 70 B c^{3} d^{3}\right)}{7 e^{8}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(- 24 A a c^{2} d e^{3} - 40 A c^{3} d^{3} e + 6 B a^{2} c e^{4} + 60 B a c^{2} d^{2} e^{2} + 70 B c^{3} d^{4}\right)}{5 e^{8}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 A a^{2} c e^{5} + 36 A a c^{2} d^{2} e^{3} + 30 A c^{3} d^{4} e - 18 B a^{2} c d e^{4} - 60 B a c^{2} d^{3} e^{2} - 42 B c^{3} d^{5}\right)}{3 e^{8}} + \frac{\sqrt{d + e x} \left(- 12 A a^{2} c d e^{5} - 24 A a c^{2} d^{3} e^{3} - 12 A c^{3} d^{5} e + 2 B a^{3} e^{6} + 18 B a^{2} c d^{2} e^{4} + 30 B a c^{2} d^{4} e^{2} + 14 B c^{3} d^{6}\right)}{e^{8}} + \frac{2 \left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)^{3}}{e^{8} \sqrt{d + e x}}"," ",0,"2*B*c**3*(d + e*x)**(13/2)/(13*e**8) + (d + e*x)**(11/2)*(2*A*c**3*e - 14*B*c**3*d)/(11*e**8) + (d + e*x)**(9/2)*(-12*A*c**3*d*e + 6*B*a*c**2*e**2 + 42*B*c**3*d**2)/(9*e**8) + (d + e*x)**(7/2)*(6*A*a*c**2*e**3 + 30*A*c**3*d**2*e - 30*B*a*c**2*d*e**2 - 70*B*c**3*d**3)/(7*e**8) + (d + e*x)**(5/2)*(-24*A*a*c**2*d*e**3 - 40*A*c**3*d**3*e + 6*B*a**2*c*e**4 + 60*B*a*c**2*d**2*e**2 + 70*B*c**3*d**4)/(5*e**8) + (d + e*x)**(3/2)*(6*A*a**2*c*e**5 + 36*A*a*c**2*d**2*e**3 + 30*A*c**3*d**4*e - 18*B*a**2*c*d*e**4 - 60*B*a*c**2*d**3*e**2 - 42*B*c**3*d**5)/(3*e**8) + sqrt(d + e*x)*(-12*A*a**2*c*d*e**5 - 24*A*a*c**2*d**3*e**3 - 12*A*c**3*d**5*e + 2*B*a**3*e**6 + 18*B*a**2*c*d**2*e**4 + 30*B*a*c**2*d**4*e**2 + 14*B*c**3*d**6)/e**8 + 2*(-A*e + B*d)*(a*e**2 + c*d**2)**3/(e**8*sqrt(d + e*x))","A",0
1443,1,406,0,113.121813," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**(5/2),x)","\frac{2 B c^{3} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{8}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(2 A c^{3} e - 14 B c^{3} d\right)}{9 e^{8}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(- 12 A c^{3} d e + 6 B a c^{2} e^{2} + 42 B c^{3} d^{2}\right)}{7 e^{8}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 A a c^{2} e^{3} + 30 A c^{3} d^{2} e - 30 B a c^{2} d e^{2} - 70 B c^{3} d^{3}\right)}{5 e^{8}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(- 24 A a c^{2} d e^{3} - 40 A c^{3} d^{3} e + 6 B a^{2} c e^{4} + 60 B a c^{2} d^{2} e^{2} + 70 B c^{3} d^{4}\right)}{3 e^{8}} + \frac{\sqrt{d + e x} \left(6 A a^{2} c e^{5} + 36 A a c^{2} d^{2} e^{3} + 30 A c^{3} d^{4} e - 18 B a^{2} c d e^{4} - 60 B a c^{2} d^{3} e^{2} - 42 B c^{3} d^{5}\right)}{e^{8}} - \frac{2 \left(a e^{2} + c d^{2}\right)^{2} \left(- 6 A c d e + B a e^{2} + 7 B c d^{2}\right)}{e^{8} \sqrt{d + e x}} + \frac{2 \left(- A e + B d\right) \left(a e^{2} + c d^{2}\right)^{3}}{3 e^{8} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*B*c**3*(d + e*x)**(11/2)/(11*e**8) + (d + e*x)**(9/2)*(2*A*c**3*e - 14*B*c**3*d)/(9*e**8) + (d + e*x)**(7/2)*(-12*A*c**3*d*e + 6*B*a*c**2*e**2 + 42*B*c**3*d**2)/(7*e**8) + (d + e*x)**(5/2)*(6*A*a*c**2*e**3 + 30*A*c**3*d**2*e - 30*B*a*c**2*d*e**2 - 70*B*c**3*d**3)/(5*e**8) + (d + e*x)**(3/2)*(-24*A*a*c**2*d*e**3 - 40*A*c**3*d**3*e + 6*B*a**2*c*e**4 + 60*B*a*c**2*d**2*e**2 + 70*B*c**3*d**4)/(3*e**8) + sqrt(d + e*x)*(6*A*a**2*c*e**5 + 36*A*a*c**2*d**2*e**3 + 30*A*c**3*d**4*e - 18*B*a**2*c*d*e**4 - 60*B*a*c**2*d**3*e**2 - 42*B*c**3*d**5)/e**8 - 2*(a*e**2 + c*d**2)**2*(-6*A*c*d*e + B*a*e**2 + 7*B*c*d**2)/(e**8*sqrt(d + e*x)) + 2*(-A*e + B*d)*(a*e**2 + c*d**2)**3/(3*e**8*(d + e*x)**(3/2))","A",0
1444,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1445,1,3218,0,9.860058," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**(9/2),x)","\begin{cases} - \frac{10 A a^{3} e^{7}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{16 A a^{2} c d^{2} e^{5}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{56 A a^{2} c d e^{6} x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{70 A a^{2} c e^{7} x^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{768 A a c^{2} d^{4} e^{3}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{2688 A a c^{2} d^{3} e^{4} x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{3360 A a c^{2} d^{2} e^{5} x^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{1680 A a c^{2} d e^{6} x^{3}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{210 A a c^{2} e^{7} x^{4}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{2048 A c^{3} d^{6} e}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{7168 A c^{3} d^{5} e^{2} x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{8960 A c^{3} d^{4} e^{3} x^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{4480 A c^{3} d^{3} e^{4} x^{3}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{560 A c^{3} d^{2} e^{5} x^{4}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{56 A c^{3} d e^{6} x^{5}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{14 A c^{3} e^{7} x^{6}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{4 B a^{3} d e^{6}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{14 B a^{3} e^{7} x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{96 B a^{2} c d^{3} e^{4}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{336 B a^{2} c d^{2} e^{5} x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{420 B a^{2} c d e^{6} x^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{210 B a^{2} c e^{7} x^{3}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{2560 B a c^{2} d^{5} e^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{8960 B a c^{2} d^{4} e^{3} x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{11200 B a c^{2} d^{3} e^{4} x^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{5600 B a c^{2} d^{2} e^{5} x^{3}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{700 B a c^{2} d e^{6} x^{4}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{70 B a c^{2} e^{7} x^{5}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{4096 B c^{3} d^{7}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{14336 B c^{3} d^{6} e x}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{17920 B c^{3} d^{5} e^{2} x^{2}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{8960 B c^{3} d^{4} e^{3} x^{3}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{1120 B c^{3} d^{3} e^{4} x^{4}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{112 B c^{3} d^{2} e^{5} x^{5}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} - \frac{28 B c^{3} d e^{6} x^{6}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} + \frac{10 B c^{3} e^{7} x^{7}}{35 d^{3} e^{8} \sqrt{d + e x} + 105 d^{2} e^{9} x \sqrt{d + e x} + 105 d e^{10} x^{2} \sqrt{d + e x} + 35 e^{11} x^{3} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{3} x + A a^{2} c x^{3} + \frac{3 A a c^{2} x^{5}}{5} + \frac{A c^{3} x^{7}}{7} + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} c x^{4}}{4} + \frac{B a c^{2} x^{6}}{2} + \frac{B c^{3} x^{8}}{8}}{d^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-10*A*a**3*e**7/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 16*A*a**2*c*d**2*e**5/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 56*A*a**2*c*d*e**6*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 70*A*a**2*c*e**7*x**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 768*A*a*c**2*d**4*e**3/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 2688*A*a*c**2*d**3*e**4*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 3360*A*a*c**2*d**2*e**5*x**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 1680*A*a*c**2*d*e**6*x**3/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 210*A*a*c**2*e**7*x**4/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 2048*A*c**3*d**6*e/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 7168*A*c**3*d**5*e**2*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 8960*A*c**3*d**4*e**3*x**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 4480*A*c**3*d**3*e**4*x**3/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 560*A*c**3*d**2*e**5*x**4/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 56*A*c**3*d*e**6*x**5/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 14*A*c**3*e**7*x**6/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 4*B*a**3*d*e**6/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 14*B*a**3*e**7*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 96*B*a**2*c*d**3*e**4/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 336*B*a**2*c*d**2*e**5*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 420*B*a**2*c*d*e**6*x**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 210*B*a**2*c*e**7*x**3/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 2560*B*a*c**2*d**5*e**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 8960*B*a*c**2*d**4*e**3*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 11200*B*a*c**2*d**3*e**4*x**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 5600*B*a*c**2*d**2*e**5*x**3/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 700*B*a*c**2*d*e**6*x**4/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 70*B*a*c**2*e**7*x**5/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 4096*B*c**3*d**7/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 14336*B*c**3*d**6*e*x/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 17920*B*c**3*d**5*e**2*x**2/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 8960*B*c**3*d**4*e**3*x**3/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 1120*B*c**3*d**3*e**4*x**4/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 112*B*c**3*d**2*e**5*x**5/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) - 28*B*c**3*d*e**6*x**6/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)) + 10*B*c**3*e**7*x**7/(35*d**3*e**8*sqrt(d + e*x) + 105*d**2*e**9*x*sqrt(d + e*x) + 105*d*e**10*x**2*sqrt(d + e*x) + 35*e**11*x**3*sqrt(d + e*x)), Ne(e, 0)), ((A*a**3*x + A*a**2*c*x**3 + 3*A*a*c**2*x**5/5 + A*c**3*x**7/7 + B*a**3*x**2/2 + 3*B*a**2*c*x**4/4 + B*a*c**2*x**6/2 + B*c**3*x**8/8)/d**(9/2), True))","A",0
1446,1,3952,0,16.440146," ","integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**(11/2),x)","\begin{cases} - \frac{70 A a^{3} e^{7}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{48 A a^{2} c d^{2} e^{5}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{216 A a^{2} c d e^{6} x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{378 A a^{2} c e^{7} x^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{768 A a c^{2} d^{4} e^{3}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{3456 A a c^{2} d^{3} e^{4} x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{6048 A a c^{2} d^{2} e^{5} x^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{5040 A a c^{2} d e^{6} x^{3}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{1890 A a c^{2} e^{7} x^{4}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{10240 A c^{3} d^{6} e}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{46080 A c^{3} d^{5} e^{2} x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{80640 A c^{3} d^{4} e^{3} x^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{67200 A c^{3} d^{3} e^{4} x^{3}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{25200 A c^{3} d^{2} e^{5} x^{4}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{2520 A c^{3} d e^{6} x^{5}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{210 A c^{3} e^{7} x^{6}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{20 B a^{3} d e^{6}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{90 B a^{3} e^{7} x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{96 B a^{2} c d^{3} e^{4}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{432 B a^{2} c d^{2} e^{5} x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{756 B a^{2} c d e^{6} x^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{630 B a^{2} c e^{7} x^{3}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{7680 B a c^{2} d^{5} e^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{34560 B a c^{2} d^{4} e^{3} x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{60480 B a c^{2} d^{3} e^{4} x^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{50400 B a c^{2} d^{2} e^{5} x^{3}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{18900 B a c^{2} d e^{6} x^{4}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{1890 B a c^{2} e^{7} x^{5}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{28672 B c^{3} d^{7}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{129024 B c^{3} d^{6} e x}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{225792 B c^{3} d^{5} e^{2} x^{2}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{188160 B c^{3} d^{4} e^{3} x^{3}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{70560 B c^{3} d^{3} e^{4} x^{4}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{7056 B c^{3} d^{2} e^{5} x^{5}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} - \frac{588 B c^{3} d e^{6} x^{6}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} + \frac{126 B c^{3} e^{7} x^{7}}{315 d^{4} e^{8} \sqrt{d + e x} + 1260 d^{3} e^{9} x \sqrt{d + e x} + 1890 d^{2} e^{10} x^{2} \sqrt{d + e x} + 1260 d e^{11} x^{3} \sqrt{d + e x} + 315 e^{12} x^{4} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{3} x + A a^{2} c x^{3} + \frac{3 A a c^{2} x^{5}}{5} + \frac{A c^{3} x^{7}}{7} + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} c x^{4}}{4} + \frac{B a c^{2} x^{6}}{2} + \frac{B c^{3} x^{8}}{8}}{d^{\frac{11}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-70*A*a**3*e**7/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 48*A*a**2*c*d**2*e**5/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 216*A*a**2*c*d*e**6*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 378*A*a**2*c*e**7*x**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 768*A*a*c**2*d**4*e**3/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 3456*A*a*c**2*d**3*e**4*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 6048*A*a*c**2*d**2*e**5*x**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 5040*A*a*c**2*d*e**6*x**3/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 1890*A*a*c**2*e**7*x**4/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 10240*A*c**3*d**6*e/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 46080*A*c**3*d**5*e**2*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 80640*A*c**3*d**4*e**3*x**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 67200*A*c**3*d**3*e**4*x**3/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 25200*A*c**3*d**2*e**5*x**4/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 2520*A*c**3*d*e**6*x**5/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 210*A*c**3*e**7*x**6/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 20*B*a**3*d*e**6/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 90*B*a**3*e**7*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 96*B*a**2*c*d**3*e**4/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 432*B*a**2*c*d**2*e**5*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 756*B*a**2*c*d*e**6*x**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 630*B*a**2*c*e**7*x**3/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 7680*B*a*c**2*d**5*e**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 34560*B*a*c**2*d**4*e**3*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 60480*B*a*c**2*d**3*e**4*x**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 50400*B*a*c**2*d**2*e**5*x**3/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 18900*B*a*c**2*d*e**6*x**4/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 1890*B*a*c**2*e**7*x**5/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 28672*B*c**3*d**7/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 129024*B*c**3*d**6*e*x/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 225792*B*c**3*d**5*e**2*x**2/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 188160*B*c**3*d**4*e**3*x**3/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 70560*B*c**3*d**3*e**4*x**4/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 7056*B*c**3*d**2*e**5*x**5/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) - 588*B*c**3*d*e**6*x**6/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)) + 126*B*c**3*e**7*x**7/(315*d**4*e**8*sqrt(d + e*x) + 1260*d**3*e**9*x*sqrt(d + e*x) + 1890*d**2*e**10*x**2*sqrt(d + e*x) + 1260*d*e**11*x**3*sqrt(d + e*x) + 315*e**12*x**4*sqrt(d + e*x)), Ne(e, 0)), ((A*a**3*x + A*a**2*c*x**3 + 3*A*a*c**2*x**5/5 + A*c**3*x**7/7 + B*a**3*x**2/2 + 3*B*a**2*c*x**4/4 + B*a*c**2*x**6/2 + B*c**3*x**8/8)/d**(11/2), True))","A",0
1447,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(-c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1448,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(-c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1449,1,396,0,38.486238," ","integrate((B*x+A)*(e*x+d)**(1/2)/(-c*x**2+a),x)","- 2 A e \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} - \frac{2 B a e^{2} \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} - 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} - 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} + 64 t^{3} a c^{2} d^{3} e^{2} - 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)}}{c} + 2 B d^{2} \operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c e^{6} - 256 a^{2} c^{2} d^{2} e^{4}\right) + 32 t^{2} a c d e^{2} - 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} c d e^{4} + 64 t^{3} a c^{2} d^{3} e^{2} - 4 t a e^{2} - 4 t c d^{2} + \sqrt{d + e x} \right)} \right)\right)} - 2 B d \operatorname{RootSum} {\left(256 t^{4} a^{2} c^{3} e^{4} - 32 t^{2} a c^{2} d e^{2} - a e^{2} + c d^{2}, \left( t \mapsto t \log{\left(- 64 t^{3} a c^{2} e^{2} + 4 t c d + \sqrt{d + e x} \right)} \right)\right)} - \frac{2 B \sqrt{d + e x}}{c}"," ",0,"-2*A*e*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) - 2*B*a*e**2*RootSum(_t**4*(256*a**3*c*e**6 - 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 - 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 + 64*_t**3*a*c**2*d**3*e**2 - 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x))))/c + 2*B*d**2*RootSum(_t**4*(256*a**3*c*e**6 - 256*a**2*c**2*d**2*e**4) + 32*_t**2*a*c*d*e**2 - 1, Lambda(_t, _t*log(-64*_t**3*a**2*c*d*e**4 + 64*_t**3*a*c**2*d**3*e**2 - 4*_t*a*e**2 - 4*_t*c*d**2 + sqrt(d + e*x)))) - 2*B*d*RootSum(256*_t**4*a**2*c**3*e**4 - 32*_t**2*a*c**2*d*e**2 - a*e**2 + c*d**2, Lambda(_t, _t*log(-64*_t**3*a*c**2*e**2 + 4*_t*c*d + sqrt(d + e*x)))) - 2*B*sqrt(d + e*x)/c","B",0
1450,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(-c*x**2+a),x)","- \int \frac{A}{- a \sqrt{d + e x} + c x^{2} \sqrt{d + e x}}\, dx - \int \frac{B x}{- a \sqrt{d + e x} + c x^{2} \sqrt{d + e x}}\, dx"," ",0,"-Integral(A/(-a*sqrt(d + e*x) + c*x**2*sqrt(d + e*x)), x) - Integral(B*x/(-a*sqrt(d + e*x) + c*x**2*sqrt(d + e*x)), x)","F",0
1451,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(-c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1452,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(-c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1453,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1454,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1455,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1456,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1457,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(-c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1458,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1459,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1460,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1461,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1462,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(-c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1463,0,0,0,0.000000," ","integrate((B*x+A)/(-B**2*e*x**2-A**2*e+2*A*B*d)/(e*x+d)**(1/2),x)","- \int \frac{A}{A^{2} e \sqrt{d + e x} - 2 A B d \sqrt{d + e x} + B^{2} e x^{2} \sqrt{d + e x}}\, dx - \int \frac{B x}{A^{2} e \sqrt{d + e x} - 2 A B d \sqrt{d + e x} + B^{2} e x^{2} \sqrt{d + e x}}\, dx"," ",0,"-Integral(A/(A**2*e*sqrt(d + e*x) - 2*A*B*d*sqrt(d + e*x) + B**2*e*x**2*sqrt(d + e*x)), x) - Integral(B*x/(A**2*e*sqrt(d + e*x) - 2*A*B*d*sqrt(d + e*x) + B**2*e*x**2*sqrt(d + e*x)), x)","F",0
1464,-1,0,0,0.000000," ","integrate(2*(B*x+A)/(x**2+1)/(2*(A**2*e-B**2*e)/A/B+4*e*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1465,1,78,0,57.363842," ","integrate((B*x+A)/(-x**2+1)/(e*x+d)**(1/2),x)","\frac{\left(- A - B\right) \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d + e}} \sqrt{d + e x}} \right)}}{\sqrt{- \frac{1}{d + e}} \left(d + e\right)} + \frac{\left(A - B\right) \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d - e}} \sqrt{d + e x}} \right)}}{\sqrt{- \frac{1}{d - e}} \left(d - e\right)}"," ",0,"(-A - B)*atan(1/(sqrt(-1/(d + e))*sqrt(d + e*x)))/(sqrt(-1/(d + e))*(d + e)) + (A - B)*atan(1/(sqrt(-1/(d - e))*sqrt(d + e*x)))/(sqrt(-1/(d - e))*(d - e))","A",0
1466,0,0,0,0.000000," ","integrate((B*x+A)/(x**2+1)/(e*x+d)**(1/2),x)","\int \frac{A + B x}{\sqrt{d + e x} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral((A + B*x)/(sqrt(d + e*x)*(x**2 + 1)), x)","F",0
1467,1,36,0,10.716605," ","integrate((1-x)*(1+x)**(1/2)/(x**2+1),x)","- 2 \sqrt{x + 1} + 4 \operatorname{RootSum} {\left(512 t^{4} + 32 t^{2} + 1, \left( t \mapsto t \log{\left(- 128 t^{3} + \sqrt{x + 1} \right)} \right)\right)}"," ",0,"-2*sqrt(x + 1) + 4*RootSum(512*_t**4 + 32*_t**2 + 1, Lambda(_t, _t*log(-128*_t**3 + sqrt(x + 1))))","A",0
1468,0,0,0,0.000000," ","integrate((3+x)/(x**2+1)/(4+3*x)**(1/2),x)","\int \frac{x + 3}{\sqrt{3 x + 4} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral((x + 3)/(sqrt(3*x + 4)*(x**2 + 1)), x)","F",0
1469,0,0,0,0.000000," ","integrate((1-3*x)/(x**2+1)/(4+3*x)**(1/2),x)","- \int \frac{3 x}{x^{2} \sqrt{3 x + 4} + \sqrt{3 x + 4}}\, dx - \int \left(- \frac{1}{x^{2} \sqrt{3 x + 4} + \sqrt{3 x + 4}}\right)\, dx"," ",0,"-Integral(3*x/(x**2*sqrt(3*x + 4) + sqrt(3*x + 4)), x) - Integral(-1/(x**2*sqrt(3*x + 4) + sqrt(3*x + 4)), x)","F",0
1470,1,26,0,99.082676," ","integrate((2+x)/(x**2+1)/(3+4*x)**(1/2),x)","\operatorname{atan}{\left(2 - \frac{5}{\sqrt{4 x + 3}} \right)} - \operatorname{atan}{\left(2 + \frac{5}{\sqrt{4 x + 3}} \right)}"," ",0,"atan(2 - 5/sqrt(4*x + 3)) - atan(2 + 5/sqrt(4*x + 3))","A",0
1471,0,0,0,0.000000," ","integrate((-2+x)/(x**2-8)/(-3+x)**(1/2),x)","\int \frac{x - 2}{\sqrt{x - 3} \left(x^{2} - 8\right)}\, dx"," ",0,"Integral((x - 2)/(sqrt(x - 3)*(x**2 - 8)), x)","F",0
1472,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)*(c*x**2+a)**(1/2),x)","\int \left(A + B x\right) \sqrt{a + c x^{2}} \sqrt{d + e x}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + c*x**2)*sqrt(d + e*x), x)","F",0
1473,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + c x^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + c*x**2)/sqrt(d + e*x), x)","F",0
1474,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + c x^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + c*x**2)/(d + e*x)**(3/2), x)","F",0
1475,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\left(A + B x\right) \sqrt{a + c x^{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(a + c*x**2)/(d + e*x)**(5/2), x)","F",0
1476,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{\left(A + B x\right) \left(a + c x^{2}\right)^{\frac{3}{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)*(a + c*x**2)**(3/2)/sqrt(d + e*x), x)","F",0
1477,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(A + B x\right) \left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(a + c*x**2)**(3/2)/(d + e*x)**(3/2), x)","F",0
1478,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(A + B x\right) \left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(a + c*x**2)**(3/2)/(d + e*x)**(5/2), x)","F",0
1479,0,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(A + B x\right) \left(a + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((A + B*x)*(a + c*x**2)**(3/2)/(d + e*x)**(7/2), x)","F",0
1480,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{\frac{3}{2}}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**(3/2)/sqrt(a + c*x**2), x)","F",0
1481,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/sqrt(a + c*x**2), x)","F",0
1482,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{A + B x}{\sqrt{a + c x^{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(a + c*x**2)*sqrt(d + e*x)), x)","F",0
1483,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+a)**(1/2),x)","\int \frac{A + B x}{\sqrt{a + c x^{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(a + c*x**2)*(d + e*x)**(3/2)), x)","F",0
1484,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1485,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+a)**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/(a + c*x**2)**(3/2), x)","F",0
1486,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+a)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{A + B x}{\left(a + c x^{2}\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)/((a + c*x**2)**(3/2)*sqrt(d + e*x)), x)","F",0
1487,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1488,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1489,1,3958,0,4.753275," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+a),x)","\begin{cases} d^{m} \left(A a x + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{2 A a e^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 A c d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A c d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A c e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{B a d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 B a e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 B c d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 B c d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B c e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{A a e^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 A c d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A c d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A c e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{B a d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 B a e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 B c d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B c d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B c e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\- \frac{2 A a e^{3}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A c e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 B c d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{B c e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\\frac{A a \log{\left(\frac{d}{e} + x \right)}}{e} + \frac{A c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{A c d x}{e^{2}} + \frac{A c x^{2}}{2 e} - \frac{B a d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{B a x}{e} - \frac{B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{B c d^{2} x}{e^{3}} - \frac{B c d x^{2}}{2 e^{2}} + \frac{B c x^{3}}{3 e} & \text{for}\: m = -1 \\\frac{A a d e^{3} m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 A a d e^{3} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 A a d e^{3} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a d e^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A a e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 A a e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 A a e^{4} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a e^{4} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 A c d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A c d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 A c d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 A c d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A c d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 A c d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 A c d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A c e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 A c e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 A c e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A c e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{B a d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 B a d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 B a d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B a d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 B a d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 B a d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B a e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B a e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 B a e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 B a e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 B c d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B c d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B c d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B c d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 B c d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B c d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B c e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 B c e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(A*a*x + A*c*x**3/3 + B*a*x**2/2 + B*c*x**4/4), Eq(e, 0)), (-2*A*a*e**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*A*c*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*c*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*c*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - B*a*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*B*a*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*c*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*B*c*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*B*c*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*c*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-A*a*e**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*c*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*A*c*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*c*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*c*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*c*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - B*a*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*B*a*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*c*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*B*c*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*c*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*c*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*c*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*c*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (-2*A*a*e**3/(2*d*e**4 + 2*e**5*x) - 4*A*c*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*c*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*A*c*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*A*c*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 2*B*a*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*B*a*d*e**2/(2*d*e**4 + 2*e**5*x) + 2*B*a*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**3/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*B*c*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + B*c*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (A*a*log(d/e + x)/e + A*c*d**2*log(d/e + x)/e**3 - A*c*d*x/e**2 + A*c*x**2/(2*e) - B*a*d*log(d/e + x)/e**2 + B*a*x/e - B*c*d**3*log(d/e + x)/e**4 + B*c*d**2*x/e**3 - B*c*d*x**2/(2*e**2) + B*c*x**3/(3*e), Eq(m, -1)), (A*a*d*e**3*m**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*A*a*d*e**3*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*A*a*d*e**3*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a*d*e**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*a*e**4*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*A*a*e**4*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*A*a*e**4*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a*e**4*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*A*c*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*c*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*A*c*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*A*c*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*c*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*A*c*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*A*c*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*c*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*A*c*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*A*c*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*c*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - B*a*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*B*a*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*B*a*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*a*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*B*a*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*B*a*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*a*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*a*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*B*a*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*B*a*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*B*c*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*c*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*c*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*c*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*B*c*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*c*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*c*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*B*c*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
1490,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(c*x**2+a),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{m}}{a + c x^{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m/(a + c*x**2), x)","F",0
1491,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1492,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1+m)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1493,-1,0,0,0.000000," ","integrate((c*d*x-a*e)*(e*x+d)**(-3-2*p)*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1494,1,279,0,0.114751," ","integrate((2*c*x+b)*(e*x+d)**4*(c*x**2+b*x+a),x)","a b d^{4} x + \frac{c^{2} e^{4} x^{8}}{4} + x^{7} \left(\frac{3 b c e^{4}}{7} + \frac{8 c^{2} d e^{3}}{7}\right) + x^{6} \left(\frac{a c e^{4}}{3} + \frac{b^{2} e^{4}}{6} + 2 b c d e^{3} + 2 c^{2} d^{2} e^{2}\right) + x^{5} \left(\frac{a b e^{4}}{5} + \frac{8 a c d e^{3}}{5} + \frac{4 b^{2} d e^{3}}{5} + \frac{18 b c d^{2} e^{2}}{5} + \frac{8 c^{2} d^{3} e}{5}\right) + x^{4} \left(a b d e^{3} + 3 a c d^{2} e^{2} + \frac{3 b^{2} d^{2} e^{2}}{2} + 3 b c d^{3} e + \frac{c^{2} d^{4}}{2}\right) + x^{3} \left(2 a b d^{2} e^{2} + \frac{8 a c d^{3} e}{3} + \frac{4 b^{2} d^{3} e}{3} + b c d^{4}\right) + x^{2} \left(2 a b d^{3} e + a c d^{4} + \frac{b^{2} d^{4}}{2}\right)"," ",0,"a*b*d**4*x + c**2*e**4*x**8/4 + x**7*(3*b*c*e**4/7 + 8*c**2*d*e**3/7) + x**6*(a*c*e**4/3 + b**2*e**4/6 + 2*b*c*d*e**3 + 2*c**2*d**2*e**2) + x**5*(a*b*e**4/5 + 8*a*c*d*e**3/5 + 4*b**2*d*e**3/5 + 18*b*c*d**2*e**2/5 + 8*c**2*d**3*e/5) + x**4*(a*b*d*e**3 + 3*a*c*d**2*e**2 + 3*b**2*d**2*e**2/2 + 3*b*c*d**3*e + c**2*d**4/2) + x**3*(2*a*b*d**2*e**2 + 8*a*c*d**3*e/3 + 4*b**2*d**3*e/3 + b*c*d**4) + x**2*(2*a*b*d**3*e + a*c*d**4 + b**2*d**4/2)","B",0
1495,1,211,0,0.101886," ","integrate((2*c*x+b)*(e*x+d)**3*(c*x**2+b*x+a),x)","a b d^{3} x + \frac{2 c^{2} e^{3} x^{7}}{7} + x^{6} \left(\frac{b c e^{3}}{2} + c^{2} d e^{2}\right) + x^{5} \left(\frac{2 a c e^{3}}{5} + \frac{b^{2} e^{3}}{5} + \frac{9 b c d e^{2}}{5} + \frac{6 c^{2} d^{2} e}{5}\right) + x^{4} \left(\frac{a b e^{3}}{4} + \frac{3 a c d e^{2}}{2} + \frac{3 b^{2} d e^{2}}{4} + \frac{9 b c d^{2} e}{4} + \frac{c^{2} d^{3}}{2}\right) + x^{3} \left(a b d e^{2} + 2 a c d^{2} e + b^{2} d^{2} e + b c d^{3}\right) + x^{2} \left(\frac{3 a b d^{2} e}{2} + a c d^{3} + \frac{b^{2} d^{3}}{2}\right)"," ",0,"a*b*d**3*x + 2*c**2*e**3*x**7/7 + x**6*(b*c*e**3/2 + c**2*d*e**2) + x**5*(2*a*c*e**3/5 + b**2*e**3/5 + 9*b*c*d*e**2/5 + 6*c**2*d**2*e/5) + x**4*(a*b*e**3/4 + 3*a*c*d*e**2/2 + 3*b**2*d*e**2/4 + 9*b*c*d**2*e/4 + c**2*d**3/2) + x**3*(a*b*d*e**2 + 2*a*c*d**2*e + b**2*d**2*e + b*c*d**3) + x**2*(3*a*b*d**2*e/2 + a*c*d**3 + b**2*d**3/2)","A",0
1496,1,146,0,0.089845," ","integrate((2*c*x+b)*(e*x+d)**2*(c*x**2+b*x+a),x)","a b d^{2} x + \frac{c^{2} e^{2} x^{6}}{3} + x^{5} \left(\frac{3 b c e^{2}}{5} + \frac{4 c^{2} d e}{5}\right) + x^{4} \left(\frac{a c e^{2}}{2} + \frac{b^{2} e^{2}}{4} + \frac{3 b c d e}{2} + \frac{c^{2} d^{2}}{2}\right) + x^{3} \left(\frac{a b e^{2}}{3} + \frac{4 a c d e}{3} + \frac{2 b^{2} d e}{3} + b c d^{2}\right) + x^{2} \left(a b d e + a c d^{2} + \frac{b^{2} d^{2}}{2}\right)"," ",0,"a*b*d**2*x + c**2*e**2*x**6/3 + x**5*(3*b*c*e**2/5 + 4*c**2*d*e/5) + x**4*(a*c*e**2/2 + b**2*e**2/4 + 3*b*c*d*e/2 + c**2*d**2/2) + x**3*(a*b*e**2/3 + 4*a*c*d*e/3 + 2*b**2*d*e/3 + b*c*d**2) + x**2*(a*b*d*e + a*c*d**2 + b**2*d**2/2)","A",0
1497,1,82,0,0.076674," ","integrate((2*c*x+b)*(e*x+d)*(c*x**2+b*x+a),x)","a b d x + \frac{2 c^{2} e x^{5}}{5} + x^{4} \left(\frac{3 b c e}{4} + \frac{c^{2} d}{2}\right) + x^{3} \left(\frac{2 a c e}{3} + \frac{b^{2} e}{3} + b c d\right) + x^{2} \left(\frac{a b e}{2} + a c d + \frac{b^{2} d}{2}\right)"," ",0,"a*b*d*x + 2*c**2*e*x**5/5 + x**4*(3*b*c*e/4 + c**2*d/2) + x**3*(2*a*c*e/3 + b**2*e/3 + b*c*d) + x**2*(a*b*e/2 + a*c*d + b**2*d/2)","A",0
1498,1,31,0,0.066422," ","integrate((2*c*x+b)*(c*x**2+b*x+a),x)","a b x + b c x^{3} + \frac{c^{2} x^{4}}{2} + x^{2} \left(a c + \frac{b^{2}}{2}\right)"," ",0,"a*b*x + b*c*x**3 + c**2*x**4/2 + x**2*(a*c + b**2/2)","B",0
1499,1,100,0,0.346025," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d),x)","\frac{2 c^{2} x^{3}}{3 e} + x^{2} \left(\frac{3 b c}{2 e} - \frac{c^{2} d}{e^{2}}\right) + x \left(\frac{2 a c}{e} + \frac{b^{2}}{e} - \frac{3 b c d}{e^{2}} + \frac{2 c^{2} d^{2}}{e^{3}}\right) + \frac{\left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"2*c**2*x**3/(3*e) + x**2*(3*b*c/(2*e) - c**2*d/e**2) + x*(2*a*c/e + b**2/e - 3*b*c*d/e**2 + 2*c**2*d**2/e**3) + (b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)*log(d + e*x)/e**4","A",0
1500,1,126,0,0.666045," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**2,x)","\frac{c^{2} x^{2}}{e^{2}} + x \left(\frac{3 b c}{e^{2}} - \frac{4 c^{2} d}{e^{3}}\right) + \frac{- a b e^{3} + 2 a c d e^{2} + b^{2} d e^{2} - 3 b c d^{2} e + 2 c^{2} d^{3}}{d e^{4} + e^{5} x} + \frac{\left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"c**2*x**2/e**2 + x*(3*b*c/e**2 - 4*c**2*d/e**3) + (-a*b*e**3 + 2*a*c*d*e**2 + b**2*d*e**2 - 3*b*c*d**2*e + 2*c**2*d**3)/(d*e**4 + e**5*x) + (2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)*log(d + e*x)/e**4","A",0
1501,1,139,0,1.710499," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**3,x)","\frac{2 c^{2} x}{e^{3}} + \frac{3 c \left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{4}} + \frac{- a b e^{3} - 2 a c d e^{2} - b^{2} d e^{2} + 9 b c d^{2} e - 10 c^{2} d^{3} + x \left(- 4 a c e^{3} - 2 b^{2} e^{3} + 12 b c d e^{2} - 12 c^{2} d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}}"," ",0,"2*c**2*x/e**3 + 3*c*(b*e - 2*c*d)*log(d + e*x)/e**4 + (-a*b*e**3 - 2*a*c*d*e**2 - b**2*d*e**2 + 9*b*c*d**2*e - 10*c**2*d**3 + x*(-4*a*c*e**3 - 2*b**2*e**3 + 12*b*c*d*e**2 - 12*c**2*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2)","A",0
1502,1,158,0,3.820453," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**4,x)","\frac{2 c^{2} \log{\left(d + e x \right)}}{e^{4}} + \frac{- 2 a b e^{3} - 2 a c d e^{2} - b^{2} d e^{2} - 6 b c d^{2} e + 22 c^{2} d^{3} + x^{2} \left(- 18 b c e^{3} + 36 c^{2} d e^{2}\right) + x \left(- 6 a c e^{3} - 3 b^{2} e^{3} - 18 b c d e^{2} + 54 c^{2} d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"2*c**2*log(d + e*x)/e**4 + (-2*a*b*e**3 - 2*a*c*d*e**2 - b**2*d*e**2 - 6*b*c*d**2*e + 22*c**2*d**3 + x**2*(-18*b*c*e**3 + 36*c**2*d*e**2) + x*(-6*a*c*e**3 - 3*b**2*e**3 - 18*b*c*d*e**2 + 54*c**2*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
1503,1,170,0,7.371955," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**5,x)","\frac{- 3 a b e^{3} - 2 a c d e^{2} - b^{2} d e^{2} - 3 b c d^{2} e - 6 c^{2} d^{3} - 24 c^{2} e^{3} x^{3} + x^{2} \left(- 18 b c e^{3} - 36 c^{2} d e^{2}\right) + x \left(- 8 a c e^{3} - 4 b^{2} e^{3} - 12 b c d e^{2} - 24 c^{2} d^{2} e\right)}{12 d^{4} e^{4} + 48 d^{3} e^{5} x + 72 d^{2} e^{6} x^{2} + 48 d e^{7} x^{3} + 12 e^{8} x^{4}}"," ",0,"(-3*a*b*e**3 - 2*a*c*d*e**2 - b**2*d*e**2 - 3*b*c*d**2*e - 6*c**2*d**3 - 24*c**2*e**3*x**3 + x**2*(-18*b*c*e**3 - 36*c**2*d*e**2) + x*(-8*a*c*e**3 - 4*b**2*e**3 - 12*b*c*d*e**2 - 24*c**2*d**2*e))/(12*d**4*e**4 + 48*d**3*e**5*x + 72*d**2*e**6*x**2 + 48*d*e**7*x**3 + 12*e**8*x**4)","A",0
1504,1,552,0,0.160336," ","integrate((2*c*x+b)*(e*x+d)**4*(c*x**2+b*x+a)**2,x)","a^{2} b d^{4} x + \frac{c^{3} e^{4} x^{10}}{5} + x^{9} \left(\frac{5 b c^{2} e^{4}}{9} + \frac{8 c^{3} d e^{3}}{9}\right) + x^{8} \left(\frac{a c^{2} e^{4}}{2} + \frac{b^{2} c e^{4}}{2} + \frac{5 b c^{2} d e^{3}}{2} + \frac{3 c^{3} d^{2} e^{2}}{2}\right) + x^{7} \left(\frac{6 a b c e^{4}}{7} + \frac{16 a c^{2} d e^{3}}{7} + \frac{b^{3} e^{4}}{7} + \frac{16 b^{2} c d e^{3}}{7} + \frac{30 b c^{2} d^{2} e^{2}}{7} + \frac{8 c^{3} d^{3} e}{7}\right) + x^{6} \left(\frac{a^{2} c e^{4}}{3} + \frac{a b^{2} e^{4}}{3} + 4 a b c d e^{3} + 4 a c^{2} d^{2} e^{2} + \frac{2 b^{3} d e^{3}}{3} + 4 b^{2} c d^{2} e^{2} + \frac{10 b c^{2} d^{3} e}{3} + \frac{c^{3} d^{4}}{3}\right) + x^{5} \left(\frac{a^{2} b e^{4}}{5} + \frac{8 a^{2} c d e^{3}}{5} + \frac{8 a b^{2} d e^{3}}{5} + \frac{36 a b c d^{2} e^{2}}{5} + \frac{16 a c^{2} d^{3} e}{5} + \frac{6 b^{3} d^{2} e^{2}}{5} + \frac{16 b^{2} c d^{3} e}{5} + b c^{2} d^{4}\right) + x^{4} \left(a^{2} b d e^{3} + 3 a^{2} c d^{2} e^{2} + 3 a b^{2} d^{2} e^{2} + 6 a b c d^{3} e + a c^{2} d^{4} + b^{3} d^{3} e + b^{2} c d^{4}\right) + x^{3} \left(2 a^{2} b d^{2} e^{2} + \frac{8 a^{2} c d^{3} e}{3} + \frac{8 a b^{2} d^{3} e}{3} + 2 a b c d^{4} + \frac{b^{3} d^{4}}{3}\right) + x^{2} \left(2 a^{2} b d^{3} e + a^{2} c d^{4} + a b^{2} d^{4}\right)"," ",0,"a**2*b*d**4*x + c**3*e**4*x**10/5 + x**9*(5*b*c**2*e**4/9 + 8*c**3*d*e**3/9) + x**8*(a*c**2*e**4/2 + b**2*c*e**4/2 + 5*b*c**2*d*e**3/2 + 3*c**3*d**2*e**2/2) + x**7*(6*a*b*c*e**4/7 + 16*a*c**2*d*e**3/7 + b**3*e**4/7 + 16*b**2*c*d*e**3/7 + 30*b*c**2*d**2*e**2/7 + 8*c**3*d**3*e/7) + x**6*(a**2*c*e**4/3 + a*b**2*e**4/3 + 4*a*b*c*d*e**3 + 4*a*c**2*d**2*e**2 + 2*b**3*d*e**3/3 + 4*b**2*c*d**2*e**2 + 10*b*c**2*d**3*e/3 + c**3*d**4/3) + x**5*(a**2*b*e**4/5 + 8*a**2*c*d*e**3/5 + 8*a*b**2*d*e**3/5 + 36*a*b*c*d**2*e**2/5 + 16*a*c**2*d**3*e/5 + 6*b**3*d**2*e**2/5 + 16*b**2*c*d**3*e/5 + b*c**2*d**4) + x**4*(a**2*b*d*e**3 + 3*a**2*c*d**2*e**2 + 3*a*b**2*d**2*e**2 + 6*a*b*c*d**3*e + a*c**2*d**4 + b**3*d**3*e + b**2*c*d**4) + x**3*(2*a**2*b*d**2*e**2 + 8*a**2*c*d**3*e/3 + 8*a*b**2*d**3*e/3 + 2*a*b*c*d**4 + b**3*d**4/3) + x**2*(2*a**2*b*d**3*e + a**2*c*d**4 + a*b**2*d**4)","B",0
1505,1,430,0,0.142222," ","integrate((2*c*x+b)*(e*x+d)**3*(c*x**2+b*x+a)**2,x)","a^{2} b d^{3} x + \frac{2 c^{3} e^{3} x^{9}}{9} + x^{8} \left(\frac{5 b c^{2} e^{3}}{8} + \frac{3 c^{3} d e^{2}}{4}\right) + x^{7} \left(\frac{4 a c^{2} e^{3}}{7} + \frac{4 b^{2} c e^{3}}{7} + \frac{15 b c^{2} d e^{2}}{7} + \frac{6 c^{3} d^{2} e}{7}\right) + x^{6} \left(a b c e^{3} + 2 a c^{2} d e^{2} + \frac{b^{3} e^{3}}{6} + 2 b^{2} c d e^{2} + \frac{5 b c^{2} d^{2} e}{2} + \frac{c^{3} d^{3}}{3}\right) + x^{5} \left(\frac{2 a^{2} c e^{3}}{5} + \frac{2 a b^{2} e^{3}}{5} + \frac{18 a b c d e^{2}}{5} + \frac{12 a c^{2} d^{2} e}{5} + \frac{3 b^{3} d e^{2}}{5} + \frac{12 b^{2} c d^{2} e}{5} + b c^{2} d^{3}\right) + x^{4} \left(\frac{a^{2} b e^{3}}{4} + \frac{3 a^{2} c d e^{2}}{2} + \frac{3 a b^{2} d e^{2}}{2} + \frac{9 a b c d^{2} e}{2} + a c^{2} d^{3} + \frac{3 b^{3} d^{2} e}{4} + b^{2} c d^{3}\right) + x^{3} \left(a^{2} b d e^{2} + 2 a^{2} c d^{2} e + 2 a b^{2} d^{2} e + 2 a b c d^{3} + \frac{b^{3} d^{3}}{3}\right) + x^{2} \left(\frac{3 a^{2} b d^{2} e}{2} + a^{2} c d^{3} + a b^{2} d^{3}\right)"," ",0,"a**2*b*d**3*x + 2*c**3*e**3*x**9/9 + x**8*(5*b*c**2*e**3/8 + 3*c**3*d*e**2/4) + x**7*(4*a*c**2*e**3/7 + 4*b**2*c*e**3/7 + 15*b*c**2*d*e**2/7 + 6*c**3*d**2*e/7) + x**6*(a*b*c*e**3 + 2*a*c**2*d*e**2 + b**3*e**3/6 + 2*b**2*c*d*e**2 + 5*b*c**2*d**2*e/2 + c**3*d**3/3) + x**5*(2*a**2*c*e**3/5 + 2*a*b**2*e**3/5 + 18*a*b*c*d*e**2/5 + 12*a*c**2*d**2*e/5 + 3*b**3*d*e**2/5 + 12*b**2*c*d**2*e/5 + b*c**2*d**3) + x**4*(a**2*b*e**3/4 + 3*a**2*c*d*e**2/2 + 3*a*b**2*d*e**2/2 + 9*a*b*c*d**2*e/2 + a*c**2*d**3 + 3*b**3*d**2*e/4 + b**2*c*d**3) + x**3*(a**2*b*d*e**2 + 2*a**2*c*d**2*e + 2*a*b**2*d**2*e + 2*a*b*c*d**3 + b**3*d**3/3) + x**2*(3*a**2*b*d**2*e/2 + a**2*c*d**3 + a*b**2*d**3)","A",0
1506,1,294,0,0.120594," ","integrate((2*c*x+b)*(e*x+d)**2*(c*x**2+b*x+a)**2,x)","a^{2} b d^{2} x + \frac{c^{3} e^{2} x^{8}}{4} + x^{7} \left(\frac{5 b c^{2} e^{2}}{7} + \frac{4 c^{3} d e}{7}\right) + x^{6} \left(\frac{2 a c^{2} e^{2}}{3} + \frac{2 b^{2} c e^{2}}{3} + \frac{5 b c^{2} d e}{3} + \frac{c^{3} d^{2}}{3}\right) + x^{5} \left(\frac{6 a b c e^{2}}{5} + \frac{8 a c^{2} d e}{5} + \frac{b^{3} e^{2}}{5} + \frac{8 b^{2} c d e}{5} + b c^{2} d^{2}\right) + x^{4} \left(\frac{a^{2} c e^{2}}{2} + \frac{a b^{2} e^{2}}{2} + 3 a b c d e + a c^{2} d^{2} + \frac{b^{3} d e}{2} + b^{2} c d^{2}\right) + x^{3} \left(\frac{a^{2} b e^{2}}{3} + \frac{4 a^{2} c d e}{3} + \frac{4 a b^{2} d e}{3} + 2 a b c d^{2} + \frac{b^{3} d^{2}}{3}\right) + x^{2} \left(a^{2} b d e + a^{2} c d^{2} + a b^{2} d^{2}\right)"," ",0,"a**2*b*d**2*x + c**3*e**2*x**8/4 + x**7*(5*b*c**2*e**2/7 + 4*c**3*d*e/7) + x**6*(2*a*c**2*e**2/3 + 2*b**2*c*e**2/3 + 5*b*c**2*d*e/3 + c**3*d**2/3) + x**5*(6*a*b*c*e**2/5 + 8*a*c**2*d*e/5 + b**3*e**2/5 + 8*b**2*c*d*e/5 + b*c**2*d**2) + x**4*(a**2*c*e**2/2 + a*b**2*e**2/2 + 3*a*b*c*d*e + a*c**2*d**2 + b**3*d*e/2 + b**2*c*d**2) + x**3*(a**2*b*e**2/3 + 4*a**2*c*d*e/3 + 4*a*b**2*d*e/3 + 2*a*b*c*d**2 + b**3*d**2/3) + x**2*(a**2*b*d*e + a**2*c*d**2 + a*b**2*d**2)","A",0
1507,1,168,0,0.101703," ","integrate((2*c*x+b)*(e*x+d)*(c*x**2+b*x+a)**2,x)","a^{2} b d x + \frac{2 c^{3} e x^{7}}{7} + x^{6} \left(\frac{5 b c^{2} e}{6} + \frac{c^{3} d}{3}\right) + x^{5} \left(\frac{4 a c^{2} e}{5} + \frac{4 b^{2} c e}{5} + b c^{2} d\right) + x^{4} \left(\frac{3 a b c e}{2} + a c^{2} d + \frac{b^{3} e}{4} + b^{2} c d\right) + x^{3} \left(\frac{2 a^{2} c e}{3} + \frac{2 a b^{2} e}{3} + 2 a b c d + \frac{b^{3} d}{3}\right) + x^{2} \left(\frac{a^{2} b e}{2} + a^{2} c d + a b^{2} d\right)"," ",0,"a**2*b*d*x + 2*c**3*e*x**7/7 + x**6*(5*b*c**2*e/6 + c**3*d/3) + x**5*(4*a*c**2*e/5 + 4*b**2*c*e/5 + b*c**2*d) + x**4*(3*a*b*c*e/2 + a*c**2*d + b**3*e/4 + b**2*c*d) + x**3*(2*a**2*c*e/3 + 2*a*b**2*e/3 + 2*a*b*c*d + b**3*d/3) + x**2*(a**2*b*e/2 + a**2*c*d + a*b**2*d)","A",0
1508,1,65,0,0.093895," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2,x)","a^{2} b x + b c^{2} x^{5} + \frac{c^{3} x^{6}}{3} + x^{4} \left(a c^{2} + b^{2} c\right) + x^{3} \left(2 a b c + \frac{b^{3}}{3}\right) + x^{2} \left(a^{2} c + a b^{2}\right)"," ",0,"a**2*b*x + b*c**2*x**5 + c**3*x**6/3 + x**4*(a*c**2 + b**2*c) + x**3*(2*a*b*c + b**3/3) + x**2*(a**2*c + a*b**2)","B",0
1509,1,280,0,0.749087," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d),x)","\frac{2 c^{3} x^{5}}{5 e} + x^{4} \left(\frac{5 b c^{2}}{4 e} - \frac{c^{3} d}{2 e^{2}}\right) + x^{3} \left(\frac{4 a c^{2}}{3 e} + \frac{4 b^{2} c}{3 e} - \frac{5 b c^{2} d}{3 e^{2}} + \frac{2 c^{3} d^{2}}{3 e^{3}}\right) + x^{2} \left(\frac{3 a b c}{e} - \frac{2 a c^{2} d}{e^{2}} + \frac{b^{3}}{2 e} - \frac{2 b^{2} c d}{e^{2}} + \frac{5 b c^{2} d^{2}}{2 e^{3}} - \frac{c^{3} d^{3}}{e^{4}}\right) + x \left(\frac{2 a^{2} c}{e} + \frac{2 a b^{2}}{e} - \frac{6 a b c d}{e^{2}} + \frac{4 a c^{2} d^{2}}{e^{3}} - \frac{b^{3} d}{e^{2}} + \frac{4 b^{2} c d^{2}}{e^{3}} - \frac{5 b c^{2} d^{3}}{e^{4}} + \frac{2 c^{3} d^{4}}{e^{5}}\right) + \frac{\left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{6}}"," ",0,"2*c**3*x**5/(5*e) + x**4*(5*b*c**2/(4*e) - c**3*d/(2*e**2)) + x**3*(4*a*c**2/(3*e) + 4*b**2*c/(3*e) - 5*b*c**2*d/(3*e**2) + 2*c**3*d**2/(3*e**3)) + x**2*(3*a*b*c/e - 2*a*c**2*d/e**2 + b**3/(2*e) - 2*b**2*c*d/e**2 + 5*b*c**2*d**2/(2*e**3) - c**3*d**3/e**4) + x*(2*a**2*c/e + 2*a*b**2/e - 6*a*b*c*d/e**2 + 4*a*c**2*d**2/e**3 - b**3*d/e**2 + 4*b**2*c*d**2/e**3 - 5*b*c**2*d**3/e**4 + 2*c**3*d**4/e**5) + (b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**2*log(d + e*x)/e**6","A",0
1510,1,325,0,1.824199," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**2,x)","\frac{c^{3} x^{4}}{2 e^{2}} + x^{3} \left(\frac{5 b c^{2}}{3 e^{2}} - \frac{4 c^{3} d}{3 e^{3}}\right) + x^{2} \left(\frac{2 a c^{2}}{e^{2}} + \frac{2 b^{2} c}{e^{2}} - \frac{5 b c^{2} d}{e^{3}} + \frac{3 c^{3} d^{2}}{e^{4}}\right) + x \left(\frac{6 a b c}{e^{2}} - \frac{8 a c^{2} d}{e^{3}} + \frac{b^{3}}{e^{2}} - \frac{8 b^{2} c d}{e^{3}} + \frac{15 b c^{2} d^{2}}{e^{4}} - \frac{8 c^{3} d^{3}}{e^{5}}\right) + \frac{- a^{2} b e^{5} + 2 a^{2} c d e^{4} + 2 a b^{2} d e^{4} - 6 a b c d^{2} e^{3} + 4 a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} + 4 b^{2} c d^{3} e^{2} - 5 b c^{2} d^{4} e + 2 c^{3} d^{5}}{d e^{6} + e^{7} x} + \frac{2 \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"c**3*x**4/(2*e**2) + x**3*(5*b*c**2/(3*e**2) - 4*c**3*d/(3*e**3)) + x**2*(2*a*c**2/e**2 + 2*b**2*c/e**2 - 5*b*c**2*d/e**3 + 3*c**3*d**2/e**4) + x*(6*a*b*c/e**2 - 8*a*c**2*d/e**3 + b**3/e**2 - 8*b**2*c*d/e**3 + 15*b*c**2*d**2/e**4 - 8*c**3*d**3/e**5) + (-a**2*b*e**5 + 2*a**2*c*d*e**4 + 2*a*b**2*d*e**4 - 6*a*b*c*d**2*e**3 + 4*a*c**2*d**3*e**2 - b**3*d**2*e**3 + 4*b**2*c*d**3*e**2 - 5*b*c**2*d**4*e + 2*c**3*d**5)/(d*e**6 + e**7*x) + 2*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(d + e*x)/e**6","A",0
1511,1,360,0,6.706472," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**3,x)","\frac{2 c^{3} x^{3}}{3 e^{3}} + x^{2} \left(\frac{5 b c^{2}}{2 e^{3}} - \frac{3 c^{3} d}{e^{4}}\right) + x \left(\frac{4 a c^{2}}{e^{3}} + \frac{4 b^{2} c}{e^{3}} - \frac{15 b c^{2} d}{e^{4}} + \frac{12 c^{3} d^{2}}{e^{5}}\right) + \frac{- a^{2} b e^{5} - 2 a^{2} c d e^{4} - 2 a b^{2} d e^{4} + 18 a b c d^{2} e^{3} - 20 a c^{2} d^{3} e^{2} + 3 b^{3} d^{2} e^{3} - 20 b^{2} c d^{3} e^{2} + 35 b c^{2} d^{4} e - 18 c^{3} d^{5} + x \left(- 4 a^{2} c e^{5} - 4 a b^{2} e^{5} + 24 a b c d e^{4} - 24 a c^{2} d^{2} e^{3} + 4 b^{3} d e^{4} - 24 b^{2} c d^{2} e^{3} + 40 b c^{2} d^{3} e^{2} - 20 c^{3} d^{4} e\right)}{2 d^{2} e^{6} + 4 d e^{7} x + 2 e^{8} x^{2}} + \frac{\left(b e - 2 c d\right) \left(6 a c e^{2} + b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"2*c**3*x**3/(3*e**3) + x**2*(5*b*c**2/(2*e**3) - 3*c**3*d/e**4) + x*(4*a*c**2/e**3 + 4*b**2*c/e**3 - 15*b*c**2*d/e**4 + 12*c**3*d**2/e**5) + (-a**2*b*e**5 - 2*a**2*c*d*e**4 - 2*a*b**2*d*e**4 + 18*a*b*c*d**2*e**3 - 20*a*c**2*d**3*e**2 + 3*b**3*d**2*e**3 - 20*b**2*c*d**3*e**2 + 35*b*c**2*d**4*e - 18*c**3*d**5 + x*(-4*a**2*c*e**5 - 4*a*b**2*e**5 + 24*a*b*c*d*e**4 - 24*a*c**2*d**2*e**3 + 4*b**3*d*e**4 - 24*b**2*c*d**2*e**3 + 40*b*c**2*d**3*e**2 - 20*c**3*d**4*e))/(2*d**2*e**6 + 4*d*e**7*x + 2*e**8*x**2) + (b*e - 2*c*d)*(6*a*c*e**2 + b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2)*log(d + e*x)/e**6","A",0
1512,1,379,0,21.025105," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**4,x)","\frac{c^{3} x^{2}}{e^{4}} + \frac{4 c \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{6}} + x \left(\frac{5 b c^{2}}{e^{4}} - \frac{8 c^{3} d}{e^{5}}\right) + \frac{- a^{2} b e^{5} - a^{2} c d e^{4} - a b^{2} d e^{4} - 6 a b c d^{2} e^{3} + 22 a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} + 22 b^{2} c d^{3} e^{2} - 65 b c^{2} d^{4} e + 47 c^{3} d^{5} + x^{2} \left(- 18 a b c e^{5} + 36 a c^{2} d e^{4} - 3 b^{3} e^{5} + 36 b^{2} c d e^{4} - 90 b c^{2} d^{2} e^{3} + 60 c^{3} d^{3} e^{2}\right) + x \left(- 3 a^{2} c e^{5} - 3 a b^{2} e^{5} - 18 a b c d e^{4} + 54 a c^{2} d^{2} e^{3} - 3 b^{3} d e^{4} + 54 b^{2} c d^{2} e^{3} - 150 b c^{2} d^{3} e^{2} + 105 c^{3} d^{4} e\right)}{3 d^{3} e^{6} + 9 d^{2} e^{7} x + 9 d e^{8} x^{2} + 3 e^{9} x^{3}}"," ",0,"c**3*x**2/e**4 + 4*c*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)*log(d + e*x)/e**6 + x*(5*b*c**2/e**4 - 8*c**3*d/e**5) + (-a**2*b*e**5 - a**2*c*d*e**4 - a*b**2*d*e**4 - 6*a*b*c*d**2*e**3 + 22*a*c**2*d**3*e**2 - b**3*d**2*e**3 + 22*b**2*c*d**3*e**2 - 65*b*c**2*d**4*e + 47*c**3*d**5 + x**2*(-18*a*b*c*e**5 + 36*a*c**2*d*e**4 - 3*b**3*e**5 + 36*b**2*c*d*e**4 - 90*b*c**2*d**2*e**3 + 60*c**3*d**3*e**2) + x*(-3*a**2*c*e**5 - 3*a*b**2*e**5 - 18*a*b*c*d*e**4 + 54*a*c**2*d**2*e**3 - 3*b**3*d*e**4 + 54*b**2*c*d**2*e**3 - 150*b*c**2*d**3*e**2 + 105*c**3*d**4*e))/(3*d**3*e**6 + 9*d**2*e**7*x + 9*d*e**8*x**2 + 3*e**9*x**3)","A",0
1513,1,401,0,58.011399," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**5,x)","\frac{2 c^{3} x}{e^{5}} + \frac{5 c^{2} \left(b e - 2 c d\right) \log{\left(d + e x \right)}}{e^{6}} + \frac{- 3 a^{2} b e^{5} - 2 a^{2} c d e^{4} - 2 a b^{2} d e^{4} - 6 a b c d^{2} e^{3} - 12 a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 12 b^{2} c d^{3} e^{2} + 125 b c^{2} d^{4} e - 154 c^{3} d^{5} + x^{3} \left(- 48 a c^{2} e^{5} - 48 b^{2} c e^{5} + 240 b c^{2} d e^{4} - 240 c^{3} d^{2} e^{3}\right) + x^{2} \left(- 36 a b c e^{5} - 72 a c^{2} d e^{4} - 6 b^{3} e^{5} - 72 b^{2} c d e^{4} + 540 b c^{2} d^{2} e^{3} - 600 c^{3} d^{3} e^{2}\right) + x \left(- 8 a^{2} c e^{5} - 8 a b^{2} e^{5} - 24 a b c d e^{4} - 48 a c^{2} d^{2} e^{3} - 4 b^{3} d e^{4} - 48 b^{2} c d^{2} e^{3} + 440 b c^{2} d^{3} e^{2} - 520 c^{3} d^{4} e\right)}{12 d^{4} e^{6} + 48 d^{3} e^{7} x + 72 d^{2} e^{8} x^{2} + 48 d e^{9} x^{3} + 12 e^{10} x^{4}}"," ",0,"2*c**3*x/e**5 + 5*c**2*(b*e - 2*c*d)*log(d + e*x)/e**6 + (-3*a**2*b*e**5 - 2*a**2*c*d*e**4 - 2*a*b**2*d*e**4 - 6*a*b*c*d**2*e**3 - 12*a*c**2*d**3*e**2 - b**3*d**2*e**3 - 12*b**2*c*d**3*e**2 + 125*b*c**2*d**4*e - 154*c**3*d**5 + x**3*(-48*a*c**2*e**5 - 48*b**2*c*e**5 + 240*b*c**2*d*e**4 - 240*c**3*d**2*e**3) + x**2*(-36*a*b*c*e**5 - 72*a*c**2*d*e**4 - 6*b**3*e**5 - 72*b**2*c*d*e**4 + 540*b*c**2*d**2*e**3 - 600*c**3*d**3*e**2) + x*(-8*a**2*c*e**5 - 8*a*b**2*e**5 - 24*a*b*c*d*e**4 - 48*a*c**2*d**2*e**3 - 4*b**3*d*e**4 - 48*b**2*c*d**2*e**3 + 440*b*c**2*d**3*e**2 - 520*c**3*d**4*e))/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4)","A",0
1514,1,935,0,0.206739," ","integrate((2*c*x+b)*(e*x+d)**4*(c*x**2+b*x+a)**3,x)","a^{3} b d^{4} x + \frac{c^{4} e^{4} x^{12}}{6} + x^{11} \left(\frac{7 b c^{3} e^{4}}{11} + \frac{8 c^{4} d e^{3}}{11}\right) + x^{10} \left(\frac{3 a c^{3} e^{4}}{5} + \frac{9 b^{2} c^{2} e^{4}}{10} + \frac{14 b c^{3} d e^{3}}{5} + \frac{6 c^{4} d^{2} e^{2}}{5}\right) + x^{9} \left(\frac{5 a b c^{2} e^{4}}{3} + \frac{8 a c^{3} d e^{3}}{3} + \frac{5 b^{3} c e^{4}}{9} + 4 b^{2} c^{2} d e^{3} + \frac{14 b c^{3} d^{2} e^{2}}{3} + \frac{8 c^{4} d^{3} e}{9}\right) + x^{8} \left(\frac{3 a^{2} c^{2} e^{4}}{4} + \frac{3 a b^{2} c e^{4}}{2} + \frac{15 a b c^{2} d e^{3}}{2} + \frac{9 a c^{3} d^{2} e^{2}}{2} + \frac{b^{4} e^{4}}{8} + \frac{5 b^{3} c d e^{3}}{2} + \frac{27 b^{2} c^{2} d^{2} e^{2}}{4} + \frac{7 b c^{3} d^{3} e}{2} + \frac{c^{4} d^{4}}{4}\right) + x^{7} \left(\frac{9 a^{2} b c e^{4}}{7} + \frac{24 a^{2} c^{2} d e^{3}}{7} + \frac{3 a b^{3} e^{4}}{7} + \frac{48 a b^{2} c d e^{3}}{7} + \frac{90 a b c^{2} d^{2} e^{2}}{7} + \frac{24 a c^{3} d^{3} e}{7} + \frac{4 b^{4} d e^{3}}{7} + \frac{30 b^{3} c d^{2} e^{2}}{7} + \frac{36 b^{2} c^{2} d^{3} e}{7} + b c^{3} d^{4}\right) + x^{6} \left(\frac{a^{3} c e^{4}}{3} + \frac{a^{2} b^{2} e^{4}}{2} + 6 a^{2} b c d e^{3} + 6 a^{2} c^{2} d^{2} e^{2} + 2 a b^{3} d e^{3} + 12 a b^{2} c d^{2} e^{2} + 10 a b c^{2} d^{3} e + a c^{3} d^{4} + b^{4} d^{2} e^{2} + \frac{10 b^{3} c d^{3} e}{3} + \frac{3 b^{2} c^{2} d^{4}}{2}\right) + x^{5} \left(\frac{a^{3} b e^{4}}{5} + \frac{8 a^{3} c d e^{3}}{5} + \frac{12 a^{2} b^{2} d e^{3}}{5} + \frac{54 a^{2} b c d^{2} e^{2}}{5} + \frac{24 a^{2} c^{2} d^{3} e}{5} + \frac{18 a b^{3} d^{2} e^{2}}{5} + \frac{48 a b^{2} c d^{3} e}{5} + 3 a b c^{2} d^{4} + \frac{4 b^{4} d^{3} e}{5} + b^{3} c d^{4}\right) + x^{4} \left(a^{3} b d e^{3} + 3 a^{3} c d^{2} e^{2} + \frac{9 a^{2} b^{2} d^{2} e^{2}}{2} + 9 a^{2} b c d^{3} e + \frac{3 a^{2} c^{2} d^{4}}{2} + 3 a b^{3} d^{3} e + 3 a b^{2} c d^{4} + \frac{b^{4} d^{4}}{4}\right) + x^{3} \left(2 a^{3} b d^{2} e^{2} + \frac{8 a^{3} c d^{3} e}{3} + 4 a^{2} b^{2} d^{3} e + 3 a^{2} b c d^{4} + a b^{3} d^{4}\right) + x^{2} \left(2 a^{3} b d^{3} e + a^{3} c d^{4} + \frac{3 a^{2} b^{2} d^{4}}{2}\right)"," ",0,"a**3*b*d**4*x + c**4*e**4*x**12/6 + x**11*(7*b*c**3*e**4/11 + 8*c**4*d*e**3/11) + x**10*(3*a*c**3*e**4/5 + 9*b**2*c**2*e**4/10 + 14*b*c**3*d*e**3/5 + 6*c**4*d**2*e**2/5) + x**9*(5*a*b*c**2*e**4/3 + 8*a*c**3*d*e**3/3 + 5*b**3*c*e**4/9 + 4*b**2*c**2*d*e**3 + 14*b*c**3*d**2*e**2/3 + 8*c**4*d**3*e/9) + x**8*(3*a**2*c**2*e**4/4 + 3*a*b**2*c*e**4/2 + 15*a*b*c**2*d*e**3/2 + 9*a*c**3*d**2*e**2/2 + b**4*e**4/8 + 5*b**3*c*d*e**3/2 + 27*b**2*c**2*d**2*e**2/4 + 7*b*c**3*d**3*e/2 + c**4*d**4/4) + x**7*(9*a**2*b*c*e**4/7 + 24*a**2*c**2*d*e**3/7 + 3*a*b**3*e**4/7 + 48*a*b**2*c*d*e**3/7 + 90*a*b*c**2*d**2*e**2/7 + 24*a*c**3*d**3*e/7 + 4*b**4*d*e**3/7 + 30*b**3*c*d**2*e**2/7 + 36*b**2*c**2*d**3*e/7 + b*c**3*d**4) + x**6*(a**3*c*e**4/3 + a**2*b**2*e**4/2 + 6*a**2*b*c*d*e**3 + 6*a**2*c**2*d**2*e**2 + 2*a*b**3*d*e**3 + 12*a*b**2*c*d**2*e**2 + 10*a*b*c**2*d**3*e + a*c**3*d**4 + b**4*d**2*e**2 + 10*b**3*c*d**3*e/3 + 3*b**2*c**2*d**4/2) + x**5*(a**3*b*e**4/5 + 8*a**3*c*d*e**3/5 + 12*a**2*b**2*d*e**3/5 + 54*a**2*b*c*d**2*e**2/5 + 24*a**2*c**2*d**3*e/5 + 18*a*b**3*d**2*e**2/5 + 48*a*b**2*c*d**3*e/5 + 3*a*b*c**2*d**4 + 4*b**4*d**3*e/5 + b**3*c*d**4) + x**4*(a**3*b*d*e**3 + 3*a**3*c*d**2*e**2 + 9*a**2*b**2*d**2*e**2/2 + 9*a**2*b*c*d**3*e + 3*a**2*c**2*d**4/2 + 3*a*b**3*d**3*e + 3*a*b**2*c*d**4 + b**4*d**4/4) + x**3*(2*a**3*b*d**2*e**2 + 8*a**3*c*d**3*e/3 + 4*a**2*b**2*d**3*e + 3*a**2*b*c*d**4 + a*b**3*d**4) + x**2*(2*a**3*b*d**3*e + a**3*c*d**4 + 3*a**2*b**2*d**4/2)","B",0
1515,1,726,0,0.177812," ","integrate((2*c*x+b)*(e*x+d)**3*(c*x**2+b*x+a)**3,x)","a^{3} b d^{3} x + \frac{2 c^{4} e^{3} x^{11}}{11} + x^{10} \left(\frac{7 b c^{3} e^{3}}{10} + \frac{3 c^{4} d e^{2}}{5}\right) + x^{9} \left(\frac{2 a c^{3} e^{3}}{3} + b^{2} c^{2} e^{3} + \frac{7 b c^{3} d e^{2}}{3} + \frac{2 c^{4} d^{2} e}{3}\right) + x^{8} \left(\frac{15 a b c^{2} e^{3}}{8} + \frac{9 a c^{3} d e^{2}}{4} + \frac{5 b^{3} c e^{3}}{8} + \frac{27 b^{2} c^{2} d e^{2}}{8} + \frac{21 b c^{3} d^{2} e}{8} + \frac{c^{4} d^{3}}{4}\right) + x^{7} \left(\frac{6 a^{2} c^{2} e^{3}}{7} + \frac{12 a b^{2} c e^{3}}{7} + \frac{45 a b c^{2} d e^{2}}{7} + \frac{18 a c^{3} d^{2} e}{7} + \frac{b^{4} e^{3}}{7} + \frac{15 b^{3} c d e^{2}}{7} + \frac{27 b^{2} c^{2} d^{2} e}{7} + b c^{3} d^{3}\right) + x^{6} \left(\frac{3 a^{2} b c e^{3}}{2} + 3 a^{2} c^{2} d e^{2} + \frac{a b^{3} e^{3}}{2} + 6 a b^{2} c d e^{2} + \frac{15 a b c^{2} d^{2} e}{2} + a c^{3} d^{3} + \frac{b^{4} d e^{2}}{2} + \frac{5 b^{3} c d^{2} e}{2} + \frac{3 b^{2} c^{2} d^{3}}{2}\right) + x^{5} \left(\frac{2 a^{3} c e^{3}}{5} + \frac{3 a^{2} b^{2} e^{3}}{5} + \frac{27 a^{2} b c d e^{2}}{5} + \frac{18 a^{2} c^{2} d^{2} e}{5} + \frac{9 a b^{3} d e^{2}}{5} + \frac{36 a b^{2} c d^{2} e}{5} + 3 a b c^{2} d^{3} + \frac{3 b^{4} d^{2} e}{5} + b^{3} c d^{3}\right) + x^{4} \left(\frac{a^{3} b e^{3}}{4} + \frac{3 a^{3} c d e^{2}}{2} + \frac{9 a^{2} b^{2} d e^{2}}{4} + \frac{27 a^{2} b c d^{2} e}{4} + \frac{3 a^{2} c^{2} d^{3}}{2} + \frac{9 a b^{3} d^{2} e}{4} + 3 a b^{2} c d^{3} + \frac{b^{4} d^{3}}{4}\right) + x^{3} \left(a^{3} b d e^{2} + 2 a^{3} c d^{2} e + 3 a^{2} b^{2} d^{2} e + 3 a^{2} b c d^{3} + a b^{3} d^{3}\right) + x^{2} \left(\frac{3 a^{3} b d^{2} e}{2} + a^{3} c d^{3} + \frac{3 a^{2} b^{2} d^{3}}{2}\right)"," ",0,"a**3*b*d**3*x + 2*c**4*e**3*x**11/11 + x**10*(7*b*c**3*e**3/10 + 3*c**4*d*e**2/5) + x**9*(2*a*c**3*e**3/3 + b**2*c**2*e**3 + 7*b*c**3*d*e**2/3 + 2*c**4*d**2*e/3) + x**8*(15*a*b*c**2*e**3/8 + 9*a*c**3*d*e**2/4 + 5*b**3*c*e**3/8 + 27*b**2*c**2*d*e**2/8 + 21*b*c**3*d**2*e/8 + c**4*d**3/4) + x**7*(6*a**2*c**2*e**3/7 + 12*a*b**2*c*e**3/7 + 45*a*b*c**2*d*e**2/7 + 18*a*c**3*d**2*e/7 + b**4*e**3/7 + 15*b**3*c*d*e**2/7 + 27*b**2*c**2*d**2*e/7 + b*c**3*d**3) + x**6*(3*a**2*b*c*e**3/2 + 3*a**2*c**2*d*e**2 + a*b**3*e**3/2 + 6*a*b**2*c*d*e**2 + 15*a*b*c**2*d**2*e/2 + a*c**3*d**3 + b**4*d*e**2/2 + 5*b**3*c*d**2*e/2 + 3*b**2*c**2*d**3/2) + x**5*(2*a**3*c*e**3/5 + 3*a**2*b**2*e**3/5 + 27*a**2*b*c*d*e**2/5 + 18*a**2*c**2*d**2*e/5 + 9*a*b**3*d*e**2/5 + 36*a*b**2*c*d**2*e/5 + 3*a*b*c**2*d**3 + 3*b**4*d**2*e/5 + b**3*c*d**3) + x**4*(a**3*b*e**3/4 + 3*a**3*c*d*e**2/2 + 9*a**2*b**2*d*e**2/4 + 27*a**2*b*c*d**2*e/4 + 3*a**2*c**2*d**3/2 + 9*a*b**3*d**2*e/4 + 3*a*b**2*c*d**3 + b**4*d**3/4) + x**3*(a**3*b*d*e**2 + 2*a**3*c*d**2*e + 3*a**2*b**2*d**2*e + 3*a**2*b*c*d**3 + a*b**3*d**3) + x**2*(3*a**3*b*d**2*e/2 + a**3*c*d**3 + 3*a**2*b**2*d**3/2)","A",0
1516,1,503,0,0.153441," ","integrate((2*c*x+b)*(e*x+d)**2*(c*x**2+b*x+a)**3,x)","a^{3} b d^{2} x + \frac{c^{4} e^{2} x^{10}}{5} + x^{9} \left(\frac{7 b c^{3} e^{2}}{9} + \frac{4 c^{4} d e}{9}\right) + x^{8} \left(\frac{3 a c^{3} e^{2}}{4} + \frac{9 b^{2} c^{2} e^{2}}{8} + \frac{7 b c^{3} d e}{4} + \frac{c^{4} d^{2}}{4}\right) + x^{7} \left(\frac{15 a b c^{2} e^{2}}{7} + \frac{12 a c^{3} d e}{7} + \frac{5 b^{3} c e^{2}}{7} + \frac{18 b^{2} c^{2} d e}{7} + b c^{3} d^{2}\right) + x^{6} \left(a^{2} c^{2} e^{2} + 2 a b^{2} c e^{2} + 5 a b c^{2} d e + a c^{3} d^{2} + \frac{b^{4} e^{2}}{6} + \frac{5 b^{3} c d e}{3} + \frac{3 b^{2} c^{2} d^{2}}{2}\right) + x^{5} \left(\frac{9 a^{2} b c e^{2}}{5} + \frac{12 a^{2} c^{2} d e}{5} + \frac{3 a b^{3} e^{2}}{5} + \frac{24 a b^{2} c d e}{5} + 3 a b c^{2} d^{2} + \frac{2 b^{4} d e}{5} + b^{3} c d^{2}\right) + x^{4} \left(\frac{a^{3} c e^{2}}{2} + \frac{3 a^{2} b^{2} e^{2}}{4} + \frac{9 a^{2} b c d e}{2} + \frac{3 a^{2} c^{2} d^{2}}{2} + \frac{3 a b^{3} d e}{2} + 3 a b^{2} c d^{2} + \frac{b^{4} d^{2}}{4}\right) + x^{3} \left(\frac{a^{3} b e^{2}}{3} + \frac{4 a^{3} c d e}{3} + 2 a^{2} b^{2} d e + 3 a^{2} b c d^{2} + a b^{3} d^{2}\right) + x^{2} \left(a^{3} b d e + a^{3} c d^{2} + \frac{3 a^{2} b^{2} d^{2}}{2}\right)"," ",0,"a**3*b*d**2*x + c**4*e**2*x**10/5 + x**9*(7*b*c**3*e**2/9 + 4*c**4*d*e/9) + x**8*(3*a*c**3*e**2/4 + 9*b**2*c**2*e**2/8 + 7*b*c**3*d*e/4 + c**4*d**2/4) + x**7*(15*a*b*c**2*e**2/7 + 12*a*c**3*d*e/7 + 5*b**3*c*e**2/7 + 18*b**2*c**2*d*e/7 + b*c**3*d**2) + x**6*(a**2*c**2*e**2 + 2*a*b**2*c*e**2 + 5*a*b*c**2*d*e + a*c**3*d**2 + b**4*e**2/6 + 5*b**3*c*d*e/3 + 3*b**2*c**2*d**2/2) + x**5*(9*a**2*b*c*e**2/5 + 12*a**2*c**2*d*e/5 + 3*a*b**3*e**2/5 + 24*a*b**2*c*d*e/5 + 3*a*b*c**2*d**2 + 2*b**4*d*e/5 + b**3*c*d**2) + x**4*(a**3*c*e**2/2 + 3*a**2*b**2*e**2/4 + 9*a**2*b*c*d*e/2 + 3*a**2*c**2*d**2/2 + 3*a*b**3*d*e/2 + 3*a*b**2*c*d**2 + b**4*d**2/4) + x**3*(a**3*b*e**2/3 + 4*a**3*c*d*e/3 + 2*a**2*b**2*d*e + 3*a**2*b*c*d**2 + a*b**3*d**2) + x**2*(a**3*b*d*e + a**3*c*d**2 + 3*a**2*b**2*d**2/2)","A",0
1517,1,291,0,0.119193," ","integrate((2*c*x+b)*(e*x+d)*(c*x**2+b*x+a)**3,x)","a^{3} b d x + \frac{2 c^{4} e x^{9}}{9} + x^{8} \left(\frac{7 b c^{3} e}{8} + \frac{c^{4} d}{4}\right) + x^{7} \left(\frac{6 a c^{3} e}{7} + \frac{9 b^{2} c^{2} e}{7} + b c^{3} d\right) + x^{6} \left(\frac{5 a b c^{2} e}{2} + a c^{3} d + \frac{5 b^{3} c e}{6} + \frac{3 b^{2} c^{2} d}{2}\right) + x^{5} \left(\frac{6 a^{2} c^{2} e}{5} + \frac{12 a b^{2} c e}{5} + 3 a b c^{2} d + \frac{b^{4} e}{5} + b^{3} c d\right) + x^{4} \left(\frac{9 a^{2} b c e}{4} + \frac{3 a^{2} c^{2} d}{2} + \frac{3 a b^{3} e}{4} + 3 a b^{2} c d + \frac{b^{4} d}{4}\right) + x^{3} \left(\frac{2 a^{3} c e}{3} + a^{2} b^{2} e + 3 a^{2} b c d + a b^{3} d\right) + x^{2} \left(\frac{a^{3} b e}{2} + a^{3} c d + \frac{3 a^{2} b^{2} d}{2}\right)"," ",0,"a**3*b*d*x + 2*c**4*e*x**9/9 + x**8*(7*b*c**3*e/8 + c**4*d/4) + x**7*(6*a*c**3*e/7 + 9*b**2*c**2*e/7 + b*c**3*d) + x**6*(5*a*b*c**2*e/2 + a*c**3*d + 5*b**3*c*e/6 + 3*b**2*c**2*d/2) + x**5*(6*a**2*c**2*e/5 + 12*a*b**2*c*e/5 + 3*a*b*c**2*d + b**4*e/5 + b**3*c*d) + x**4*(9*a**2*b*c*e/4 + 3*a**2*c**2*d/2 + 3*a*b**3*e/4 + 3*a*b**2*c*d + b**4*d/4) + x**3*(2*a**3*c*e/3 + a**2*b**2*e + 3*a**2*b*c*d + a*b**3*d) + x**2*(a**3*b*e/2 + a**3*c*d + 3*a**2*b**2*d/2)","A",0
1518,1,121,0,0.097380," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3,x)","a^{3} b x + b c^{3} x^{7} + \frac{c^{4} x^{8}}{4} + x^{6} \left(a c^{3} + \frac{3 b^{2} c^{2}}{2}\right) + x^{5} \left(3 a b c^{2} + b^{3} c\right) + x^{4} \left(\frac{3 a^{2} c^{2}}{2} + 3 a b^{2} c + \frac{b^{4}}{4}\right) + x^{3} \left(3 a^{2} b c + a b^{3}\right) + x^{2} \left(a^{3} c + \frac{3 a^{2} b^{2}}{2}\right)"," ",0,"a**3*b*x + b*c**3*x**7 + c**4*x**8/4 + x**6*(a*c**3 + 3*b**2*c**2/2) + x**5*(3*a*b*c**2 + b**3*c) + x**4*(3*a**2*c**2/2 + 3*a*b**2*c + b**4/4) + x**3*(3*a**2*b*c + a*b**3) + x**2*(a**3*c + 3*a**2*b**2/2)","B",0
1519,1,641,0,1.361235," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d),x)","\frac{2 c^{4} x^{7}}{7 e} + x^{6} \left(\frac{7 b c^{3}}{6 e} - \frac{c^{4} d}{3 e^{2}}\right) + x^{5} \left(\frac{6 a c^{3}}{5 e} + \frac{9 b^{2} c^{2}}{5 e} - \frac{7 b c^{3} d}{5 e^{2}} + \frac{2 c^{4} d^{2}}{5 e^{3}}\right) + x^{4} \left(\frac{15 a b c^{2}}{4 e} - \frac{3 a c^{3} d}{2 e^{2}} + \frac{5 b^{3} c}{4 e} - \frac{9 b^{2} c^{2} d}{4 e^{2}} + \frac{7 b c^{3} d^{2}}{4 e^{3}} - \frac{c^{4} d^{3}}{2 e^{4}}\right) + x^{3} \left(\frac{2 a^{2} c^{2}}{e} + \frac{4 a b^{2} c}{e} - \frac{5 a b c^{2} d}{e^{2}} + \frac{2 a c^{3} d^{2}}{e^{3}} + \frac{b^{4}}{3 e} - \frac{5 b^{3} c d}{3 e^{2}} + \frac{3 b^{2} c^{2} d^{2}}{e^{3}} - \frac{7 b c^{3} d^{3}}{3 e^{4}} + \frac{2 c^{4} d^{4}}{3 e^{5}}\right) + x^{2} \left(\frac{9 a^{2} b c}{2 e} - \frac{3 a^{2} c^{2} d}{e^{2}} + \frac{3 a b^{3}}{2 e} - \frac{6 a b^{2} c d}{e^{2}} + \frac{15 a b c^{2} d^{2}}{2 e^{3}} - \frac{3 a c^{3} d^{3}}{e^{4}} - \frac{b^{4} d}{2 e^{2}} + \frac{5 b^{3} c d^{2}}{2 e^{3}} - \frac{9 b^{2} c^{2} d^{3}}{2 e^{4}} + \frac{7 b c^{3} d^{4}}{2 e^{5}} - \frac{c^{4} d^{5}}{e^{6}}\right) + x \left(\frac{2 a^{3} c}{e} + \frac{3 a^{2} b^{2}}{e} - \frac{9 a^{2} b c d}{e^{2}} + \frac{6 a^{2} c^{2} d^{2}}{e^{3}} - \frac{3 a b^{3} d}{e^{2}} + \frac{12 a b^{2} c d^{2}}{e^{3}} - \frac{15 a b c^{2} d^{3}}{e^{4}} + \frac{6 a c^{3} d^{4}}{e^{5}} + \frac{b^{4} d^{2}}{e^{3}} - \frac{5 b^{3} c d^{3}}{e^{4}} + \frac{9 b^{2} c^{2} d^{4}}{e^{5}} - \frac{7 b c^{3} d^{5}}{e^{6}} + \frac{2 c^{4} d^{6}}{e^{7}}\right) + \frac{\left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{8}}"," ",0,"2*c**4*x**7/(7*e) + x**6*(7*b*c**3/(6*e) - c**4*d/(3*e**2)) + x**5*(6*a*c**3/(5*e) + 9*b**2*c**2/(5*e) - 7*b*c**3*d/(5*e**2) + 2*c**4*d**2/(5*e**3)) + x**4*(15*a*b*c**2/(4*e) - 3*a*c**3*d/(2*e**2) + 5*b**3*c/(4*e) - 9*b**2*c**2*d/(4*e**2) + 7*b*c**3*d**2/(4*e**3) - c**4*d**3/(2*e**4)) + x**3*(2*a**2*c**2/e + 4*a*b**2*c/e - 5*a*b*c**2*d/e**2 + 2*a*c**3*d**2/e**3 + b**4/(3*e) - 5*b**3*c*d/(3*e**2) + 3*b**2*c**2*d**2/e**3 - 7*b*c**3*d**3/(3*e**4) + 2*c**4*d**4/(3*e**5)) + x**2*(9*a**2*b*c/(2*e) - 3*a**2*c**2*d/e**2 + 3*a*b**3/(2*e) - 6*a*b**2*c*d/e**2 + 15*a*b*c**2*d**2/(2*e**3) - 3*a*c**3*d**3/e**4 - b**4*d/(2*e**2) + 5*b**3*c*d**2/(2*e**3) - 9*b**2*c**2*d**3/(2*e**4) + 7*b*c**3*d**4/(2*e**5) - c**4*d**5/e**6) + x*(2*a**3*c/e + 3*a**2*b**2/e - 9*a**2*b*c*d/e**2 + 6*a**2*c**2*d**2/e**3 - 3*a*b**3*d/e**2 + 12*a*b**2*c*d**2/e**3 - 15*a*b*c**2*d**3/e**4 + 6*a*c**3*d**4/e**5 + b**4*d**2/e**3 - 5*b**3*c*d**3/e**4 + 9*b**2*c**2*d**4/e**5 - 7*b*c**3*d**5/e**6 + 2*c**4*d**6/e**7) + (b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**3*log(d + e*x)/e**8","A",0
1520,1,688,0,4.109100," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**2,x)","\frac{c^{4} x^{6}}{3 e^{2}} + x^{5} \left(\frac{7 b c^{3}}{5 e^{2}} - \frac{4 c^{4} d}{5 e^{3}}\right) + x^{4} \left(\frac{3 a c^{3}}{2 e^{2}} + \frac{9 b^{2} c^{2}}{4 e^{2}} - \frac{7 b c^{3} d}{2 e^{3}} + \frac{3 c^{4} d^{2}}{2 e^{4}}\right) + x^{3} \left(\frac{5 a b c^{2}}{e^{2}} - \frac{4 a c^{3} d}{e^{3}} + \frac{5 b^{3} c}{3 e^{2}} - \frac{6 b^{2} c^{2} d}{e^{3}} + \frac{7 b c^{3} d^{2}}{e^{4}} - \frac{8 c^{4} d^{3}}{3 e^{5}}\right) + x^{2} \left(\frac{3 a^{2} c^{2}}{e^{2}} + \frac{6 a b^{2} c}{e^{2}} - \frac{15 a b c^{2} d}{e^{3}} + \frac{9 a c^{3} d^{2}}{e^{4}} + \frac{b^{4}}{2 e^{2}} - \frac{5 b^{3} c d}{e^{3}} + \frac{27 b^{2} c^{2} d^{2}}{2 e^{4}} - \frac{14 b c^{3} d^{3}}{e^{5}} + \frac{5 c^{4} d^{4}}{e^{6}}\right) + x \left(\frac{9 a^{2} b c}{e^{2}} - \frac{12 a^{2} c^{2} d}{e^{3}} + \frac{3 a b^{3}}{e^{2}} - \frac{24 a b^{2} c d}{e^{3}} + \frac{45 a b c^{2} d^{2}}{e^{4}} - \frac{24 a c^{3} d^{3}}{e^{5}} - \frac{2 b^{4} d}{e^{3}} + \frac{15 b^{3} c d^{2}}{e^{4}} - \frac{36 b^{2} c^{2} d^{3}}{e^{5}} + \frac{35 b c^{3} d^{4}}{e^{6}} - \frac{12 c^{4} d^{5}}{e^{7}}\right) + \frac{- a^{3} b e^{7} + 2 a^{3} c d e^{6} + 3 a^{2} b^{2} d e^{6} - 9 a^{2} b c d^{2} e^{5} + 6 a^{2} c^{2} d^{3} e^{4} - 3 a b^{3} d^{2} e^{5} + 12 a b^{2} c d^{3} e^{4} - 15 a b c^{2} d^{4} e^{3} + 6 a c^{3} d^{5} e^{2} + b^{4} d^{3} e^{4} - 5 b^{3} c d^{4} e^{3} + 9 b^{2} c^{2} d^{5} e^{2} - 7 b c^{3} d^{6} e + 2 c^{4} d^{7}}{d e^{8} + e^{9} x} + \frac{\left(a e^{2} - b d e + c d^{2}\right)^{2} \left(2 a c e^{2} + 3 b^{2} e^{2} - 14 b c d e + 14 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"c**4*x**6/(3*e**2) + x**5*(7*b*c**3/(5*e**2) - 4*c**4*d/(5*e**3)) + x**4*(3*a*c**3/(2*e**2) + 9*b**2*c**2/(4*e**2) - 7*b*c**3*d/(2*e**3) + 3*c**4*d**2/(2*e**4)) + x**3*(5*a*b*c**2/e**2 - 4*a*c**3*d/e**3 + 5*b**3*c/(3*e**2) - 6*b**2*c**2*d/e**3 + 7*b*c**3*d**2/e**4 - 8*c**4*d**3/(3*e**5)) + x**2*(3*a**2*c**2/e**2 + 6*a*b**2*c/e**2 - 15*a*b*c**2*d/e**3 + 9*a*c**3*d**2/e**4 + b**4/(2*e**2) - 5*b**3*c*d/e**3 + 27*b**2*c**2*d**2/(2*e**4) - 14*b*c**3*d**3/e**5 + 5*c**4*d**4/e**6) + x*(9*a**2*b*c/e**2 - 12*a**2*c**2*d/e**3 + 3*a*b**3/e**2 - 24*a*b**2*c*d/e**3 + 45*a*b*c**2*d**2/e**4 - 24*a*c**3*d**3/e**5 - 2*b**4*d/e**3 + 15*b**3*c*d**2/e**4 - 36*b**2*c**2*d**3/e**5 + 35*b*c**3*d**4/e**6 - 12*c**4*d**5/e**7) + (-a**3*b*e**7 + 2*a**3*c*d*e**6 + 3*a**2*b**2*d*e**6 - 9*a**2*b*c*d**2*e**5 + 6*a**2*c**2*d**3*e**4 - 3*a*b**3*d**2*e**5 + 12*a*b**2*c*d**3*e**4 - 15*a*b*c**2*d**4*e**3 + 6*a*c**3*d**5*e**2 + b**4*d**3*e**4 - 5*b**3*c*d**4*e**3 + 9*b**2*c**2*d**5*e**2 - 7*b*c**3*d**6*e + 2*c**4*d**7)/(d*e**8 + e**9*x) + (a*e**2 - b*d*e + c*d**2)**2*(2*a*c*e**2 + 3*b**2*e**2 - 14*b*c*d*e + 14*c**2*d**2)*log(d + e*x)/e**8","A",0
1521,1,733,0,17.281335," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**3,x)","\frac{2 c^{4} x^{5}}{5 e^{3}} + x^{4} \left(\frac{7 b c^{3}}{4 e^{3}} - \frac{3 c^{4} d}{2 e^{4}}\right) + x^{3} \left(\frac{2 a c^{3}}{e^{3}} + \frac{3 b^{2} c^{2}}{e^{3}} - \frac{7 b c^{3} d}{e^{4}} + \frac{4 c^{4} d^{2}}{e^{5}}\right) + x^{2} \left(\frac{15 a b c^{2}}{2 e^{3}} - \frac{9 a c^{3} d}{e^{4}} + \frac{5 b^{3} c}{2 e^{3}} - \frac{27 b^{2} c^{2} d}{2 e^{4}} + \frac{21 b c^{3} d^{2}}{e^{5}} - \frac{10 c^{4} d^{3}}{e^{6}}\right) + x \left(\frac{6 a^{2} c^{2}}{e^{3}} + \frac{12 a b^{2} c}{e^{3}} - \frac{45 a b c^{2} d}{e^{4}} + \frac{36 a c^{3} d^{2}}{e^{5}} + \frac{b^{4}}{e^{3}} - \frac{15 b^{3} c d}{e^{4}} + \frac{54 b^{2} c^{2} d^{2}}{e^{5}} - \frac{70 b c^{3} d^{3}}{e^{6}} + \frac{30 c^{4} d^{4}}{e^{7}}\right) + \frac{- a^{3} b e^{7} - 2 a^{3} c d e^{6} - 3 a^{2} b^{2} d e^{6} + 27 a^{2} b c d^{2} e^{5} - 30 a^{2} c^{2} d^{3} e^{4} + 9 a b^{3} d^{2} e^{5} - 60 a b^{2} c d^{3} e^{4} + 105 a b c^{2} d^{4} e^{3} - 54 a c^{3} d^{5} e^{2} - 5 b^{4} d^{3} e^{4} + 35 b^{3} c d^{4} e^{3} - 81 b^{2} c^{2} d^{5} e^{2} + 77 b c^{3} d^{6} e - 26 c^{4} d^{7} + x \left(- 4 a^{3} c e^{7} - 6 a^{2} b^{2} e^{7} + 36 a^{2} b c d e^{6} - 36 a^{2} c^{2} d^{2} e^{5} + 12 a b^{3} d e^{6} - 72 a b^{2} c d^{2} e^{5} + 120 a b c^{2} d^{3} e^{4} - 60 a c^{3} d^{4} e^{3} - 6 b^{4} d^{2} e^{5} + 40 b^{3} c d^{3} e^{4} - 90 b^{2} c^{2} d^{4} e^{3} + 84 b c^{3} d^{5} e^{2} - 28 c^{4} d^{6} e\right)}{2 d^{2} e^{8} + 4 d e^{9} x + 2 e^{10} x^{2}} + \frac{3 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right) \left(3 a c e^{2} + b^{2} e^{2} - 7 b c d e + 7 c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"2*c**4*x**5/(5*e**3) + x**4*(7*b*c**3/(4*e**3) - 3*c**4*d/(2*e**4)) + x**3*(2*a*c**3/e**3 + 3*b**2*c**2/e**3 - 7*b*c**3*d/e**4 + 4*c**4*d**2/e**5) + x**2*(15*a*b*c**2/(2*e**3) - 9*a*c**3*d/e**4 + 5*b**3*c/(2*e**3) - 27*b**2*c**2*d/(2*e**4) + 21*b*c**3*d**2/e**5 - 10*c**4*d**3/e**6) + x*(6*a**2*c**2/e**3 + 12*a*b**2*c/e**3 - 45*a*b*c**2*d/e**4 + 36*a*c**3*d**2/e**5 + b**4/e**3 - 15*b**3*c*d/e**4 + 54*b**2*c**2*d**2/e**5 - 70*b*c**3*d**3/e**6 + 30*c**4*d**4/e**7) + (-a**3*b*e**7 - 2*a**3*c*d*e**6 - 3*a**2*b**2*d*e**6 + 27*a**2*b*c*d**2*e**5 - 30*a**2*c**2*d**3*e**4 + 9*a*b**3*d**2*e**5 - 60*a*b**2*c*d**3*e**4 + 105*a*b*c**2*d**4*e**3 - 54*a*c**3*d**5*e**2 - 5*b**4*d**3*e**4 + 35*b**3*c*d**4*e**3 - 81*b**2*c**2*d**5*e**2 + 77*b*c**3*d**6*e - 26*c**4*d**7 + x*(-4*a**3*c*e**7 - 6*a**2*b**2*e**7 + 36*a**2*b*c*d*e**6 - 36*a**2*c**2*d**2*e**5 + 12*a*b**3*d*e**6 - 72*a*b**2*c*d**2*e**5 + 120*a*b*c**2*d**3*e**4 - 60*a*c**3*d**4*e**3 - 6*b**4*d**2*e**5 + 40*b**3*c*d**3*e**4 - 90*b**2*c**2*d**4*e**3 + 84*b*c**3*d**5*e**2 - 28*c**4*d**6*e))/(2*d**2*e**8 + 4*d*e**9*x + 2*e**10*x**2) + 3*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)*(3*a*c*e**2 + b**2*e**2 - 7*b*c*d*e + 7*c**2*d**2)*log(d + e*x)/e**8","A",0
1522,1,821,0,71.721978," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**4,x)","\frac{c^{4} x^{4}}{2 e^{4}} + x^{3} \left(\frac{7 b c^{3}}{3 e^{4}} - \frac{8 c^{4} d}{3 e^{5}}\right) + x^{2} \left(\frac{3 a c^{3}}{e^{4}} + \frac{9 b^{2} c^{2}}{2 e^{4}} - \frac{14 b c^{3} d}{e^{5}} + \frac{10 c^{4} d^{2}}{e^{6}}\right) + x \left(\frac{15 a b c^{2}}{e^{4}} - \frac{24 a c^{3} d}{e^{5}} + \frac{5 b^{3} c}{e^{4}} - \frac{36 b^{2} c^{2} d}{e^{5}} + \frac{70 b c^{3} d^{2}}{e^{6}} - \frac{40 c^{4} d^{3}}{e^{7}}\right) + \frac{- 2 a^{3} b e^{7} - 2 a^{3} c d e^{6} - 3 a^{2} b^{2} d e^{6} - 18 a^{2} b c d^{2} e^{5} + 66 a^{2} c^{2} d^{3} e^{4} - 6 a b^{3} d^{2} e^{5} + 132 a b^{2} c d^{3} e^{4} - 390 a b c^{2} d^{4} e^{3} + 282 a c^{3} d^{5} e^{2} + 11 b^{4} d^{3} e^{4} - 130 b^{3} c d^{4} e^{3} + 423 b^{2} c^{2} d^{5} e^{2} - 518 b c^{3} d^{6} e + 214 c^{4} d^{7} + x^{2} \left(- 54 a^{2} b c e^{7} + 108 a^{2} c^{2} d e^{6} - 18 a b^{3} e^{7} + 216 a b^{2} c d e^{6} - 540 a b c^{2} d^{2} e^{5} + 360 a c^{3} d^{3} e^{4} + 18 b^{4} d e^{6} - 180 b^{3} c d^{2} e^{5} + 540 b^{2} c^{2} d^{3} e^{4} - 630 b c^{3} d^{4} e^{3} + 252 c^{4} d^{5} e^{2}\right) + x \left(- 6 a^{3} c e^{7} - 9 a^{2} b^{2} e^{7} - 54 a^{2} b c d e^{6} + 162 a^{2} c^{2} d^{2} e^{5} - 18 a b^{3} d e^{6} + 324 a b^{2} c d^{2} e^{5} - 900 a b c^{2} d^{3} e^{4} + 630 a c^{3} d^{4} e^{3} + 27 b^{4} d^{2} e^{5} - 300 b^{3} c d^{3} e^{4} + 945 b^{2} c^{2} d^{4} e^{3} - 1134 b c^{3} d^{5} e^{2} + 462 c^{4} d^{6} e\right)}{6 d^{3} e^{8} + 18 d^{2} e^{9} x + 18 d e^{10} x^{2} + 6 e^{11} x^{3}} + \frac{\left(6 a^{2} c^{2} e^{4} + 12 a b^{2} c e^{4} - 60 a b c^{2} d e^{3} + 60 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 20 b^{3} c d e^{3} + 90 b^{2} c^{2} d^{2} e^{2} - 140 b c^{3} d^{3} e + 70 c^{4} d^{4}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"c**4*x**4/(2*e**4) + x**3*(7*b*c**3/(3*e**4) - 8*c**4*d/(3*e**5)) + x**2*(3*a*c**3/e**4 + 9*b**2*c**2/(2*e**4) - 14*b*c**3*d/e**5 + 10*c**4*d**2/e**6) + x*(15*a*b*c**2/e**4 - 24*a*c**3*d/e**5 + 5*b**3*c/e**4 - 36*b**2*c**2*d/e**5 + 70*b*c**3*d**2/e**6 - 40*c**4*d**3/e**7) + (-2*a**3*b*e**7 - 2*a**3*c*d*e**6 - 3*a**2*b**2*d*e**6 - 18*a**2*b*c*d**2*e**5 + 66*a**2*c**2*d**3*e**4 - 6*a*b**3*d**2*e**5 + 132*a*b**2*c*d**3*e**4 - 390*a*b*c**2*d**4*e**3 + 282*a*c**3*d**5*e**2 + 11*b**4*d**3*e**4 - 130*b**3*c*d**4*e**3 + 423*b**2*c**2*d**5*e**2 - 518*b*c**3*d**6*e + 214*c**4*d**7 + x**2*(-54*a**2*b*c*e**7 + 108*a**2*c**2*d*e**6 - 18*a*b**3*e**7 + 216*a*b**2*c*d*e**6 - 540*a*b*c**2*d**2*e**5 + 360*a*c**3*d**3*e**4 + 18*b**4*d*e**6 - 180*b**3*c*d**2*e**5 + 540*b**2*c**2*d**3*e**4 - 630*b*c**3*d**4*e**3 + 252*c**4*d**5*e**2) + x*(-6*a**3*c*e**7 - 9*a**2*b**2*e**7 - 54*a**2*b*c*d*e**6 + 162*a**2*c**2*d**2*e**5 - 18*a*b**3*d*e**6 + 324*a*b**2*c*d**2*e**5 - 900*a*b*c**2*d**3*e**4 + 630*a*c**3*d**4*e**3 + 27*b**4*d**2*e**5 - 300*b**3*c*d**3*e**4 + 945*b**2*c**2*d**4*e**3 - 1134*b*c**3*d**5*e**2 + 462*c**4*d**6*e))/(6*d**3*e**8 + 18*d**2*e**9*x + 18*d*e**10*x**2 + 6*e**11*x**3) + (6*a**2*c**2*e**4 + 12*a*b**2*c*e**4 - 60*a*b*c**2*d*e**3 + 60*a*c**3*d**2*e**2 + b**4*e**4 - 20*b**3*c*d*e**3 + 90*b**2*c**2*d**2*e**2 - 140*b*c**3*d**3*e + 70*c**4*d**4)*log(d + e*x)/e**8","B",0
1523,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1524,1,1056,0,12.738807," ","integrate((2*c*x+b)*(e*x+d)**4/(c*x**2+b*x+a),x)","\frac{e^{4} x^{4}}{2} + x^{3} \left(- \frac{b e^{4}}{3 c} + \frac{8 d e^{3}}{3}\right) + x^{2} \left(- \frac{a e^{4}}{c} + \frac{b^{2} e^{4}}{2 c^{2}} - \frac{2 b d e^{3}}{c} + 6 d^{2} e^{2}\right) + x \left(\frac{3 a b e^{4}}{c^{2}} - \frac{8 a d e^{3}}{c} - \frac{b^{3} e^{4}}{c^{3}} + \frac{4 b^{2} d e^{3}}{c^{2}} - \frac{6 b d^{2} e^{2}}{c} + 8 d^{3} e\right) + \left(- \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}}{2 c^{4}}\right) \log{\left(x + \frac{a^{2} c e^{4} - a b^{2} e^{4} + 4 a b c d e^{3} - 6 a c^{2} d^{2} e^{2} + c^{3} d^{4} - c^{3} \left(- \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}}{2 c^{4}}\right)}{2 a b c e^{4} - 4 a c^{2} d e^{3} - b^{3} e^{4} + 4 b^{2} c d e^{3} - 6 b c^{2} d^{2} e^{2} + 4 c^{3} d^{3} e} \right)} + \left(\frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}}{2 c^{4}}\right) \log{\left(x + \frac{a^{2} c e^{4} - a b^{2} e^{4} + 4 a b c d e^{3} - 6 a c^{2} d^{2} e^{2} + c^{3} d^{4} - c^{3} \left(\frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{4}} + \frac{2 a^{2} c^{2} e^{4} - 4 a b^{2} c e^{4} + 12 a b c^{2} d e^{3} - 12 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 4 b^{3} c d e^{3} + 6 b^{2} c^{2} d^{2} e^{2} - 4 b c^{3} d^{3} e + 2 c^{4} d^{4}}{2 c^{4}}\right)}{2 a b c e^{4} - 4 a c^{2} d e^{3} - b^{3} e^{4} + 4 b^{2} c d e^{3} - 6 b c^{2} d^{2} e^{2} + 4 c^{3} d^{3} e} \right)}"," ",0,"e**4*x**4/2 + x**3*(-b*e**4/(3*c) + 8*d*e**3/3) + x**2*(-a*e**4/c + b**2*e**4/(2*c**2) - 2*b*d*e**3/c + 6*d**2*e**2) + x*(3*a*b*e**4/c**2 - 8*a*d*e**3/c - b**3*e**4/c**3 + 4*b**2*d*e**3/c**2 - 6*b*d**2*e**2/c + 8*d**3*e) + (-e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + (2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4))*log(x + (a**2*c*e**4 - a*b**2*e**4 + 4*a*b*c*d*e**3 - 6*a*c**2*d**2*e**2 + c**3*d**4 - c**3*(-e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + (2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4)))/(2*a*b*c*e**4 - 4*a*c**2*d*e**3 - b**3*e**4 + 4*b**2*c*d*e**3 - 6*b*c**2*d**2*e**2 + 4*c**3*d**3*e)) + (e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + (2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4))*log(x + (a**2*c*e**4 - a*b**2*e**4 + 4*a*b*c*d*e**3 - 6*a*c**2*d**2*e**2 + c**3*d**4 - c**3*(e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**4) + (2*a**2*c**2*e**4 - 4*a*b**2*c*e**4 + 12*a*b*c**2*d*e**3 - 12*a*c**3*d**2*e**2 + b**4*e**4 - 4*b**3*c*d*e**3 + 6*b**2*c**2*d**2*e**2 - 4*b*c**3*d**3*e + 2*c**4*d**4)/(2*c**4)))/(2*a*b*c*e**4 - 4*a*c**2*d*e**3 - b**3*e**4 + 4*b**2*c*d*e**3 - 6*b*c**2*d**2*e**2 + 4*c**3*d**3*e))","B",0
1525,1,561,0,4.805377," ","integrate((2*c*x+b)*(e*x+d)**3/(c*x**2+b*x+a),x)","\frac{2 e^{3} x^{3}}{3} + x^{2} \left(- \frac{b e^{3}}{2 c} + 3 d e^{2}\right) + x \left(- \frac{2 a e^{3}}{c} + \frac{b^{2} e^{3}}{c^{2}} - \frac{3 b d e^{2}}{c} + 6 d^{2} e\right) + \left(- \frac{e \sqrt{- 4 a c + b^{2}} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3}}\right) \log{\left(x + \frac{- a b e^{3} + 3 a c d e^{2} - c^{2} d^{3} + c^{2} \left(- \frac{e \sqrt{- 4 a c + b^{2}} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3}}\right)}{a c e^{3} - b^{2} e^{3} + 3 b c d e^{2} - 3 c^{2} d^{2} e} \right)} + \left(\frac{e \sqrt{- 4 a c + b^{2}} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3}}\right) \log{\left(x + \frac{- a b e^{3} + 3 a c d e^{2} - c^{2} d^{3} + c^{2} \left(\frac{e \sqrt{- 4 a c + b^{2}} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{2 c^{3}} + \frac{\left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{2 c^{3}}\right)}{a c e^{3} - b^{2} e^{3} + 3 b c d e^{2} - 3 c^{2} d^{2} e} \right)}"," ",0,"2*e**3*x**3/3 + x**2*(-b*e**3/(2*c) + 3*d*e**2) + x*(-2*a*e**3/c + b**2*e**3/c**2 - 3*b*d*e**2/c + 6*d**2*e) + (-e*sqrt(-4*a*c + b**2)*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + (b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3))*log(x + (-a*b*e**3 + 3*a*c*d*e**2 - c**2*d**3 + c**2*(-e*sqrt(-4*a*c + b**2)*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + (b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3)))/(a*c*e**3 - b**2*e**3 + 3*b*c*d*e**2 - 3*c**2*d**2*e)) + (e*sqrt(-4*a*c + b**2)*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + (b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3))*log(x + (-a*b*e**3 + 3*a*c*d*e**2 - c**2*d**3 + c**2*(e*sqrt(-4*a*c + b**2)*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/(2*c**3) + (b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(2*c**3)))/(a*c*e**3 - b**2*e**3 + 3*b*c*d*e**2 - 3*c**2*d**2*e))","B",0
1526,1,335,0,1.799482," ","integrate((2*c*x+b)*(e*x+d)**2/(c*x**2+b*x+a),x)","e^{2} x^{2} + x \left(- \frac{b e^{2}}{c} + 4 d e\right) + \left(- \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}}{2 c^{2}}\right) \log{\left(x + \frac{a e^{2} - c d^{2} + c \left(- \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}}{2 c^{2}}\right)}{b e^{2} - 2 c d e} \right)} + \left(\frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}}{2 c^{2}}\right) \log{\left(x + \frac{a e^{2} - c d^{2} + c \left(\frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}}{2 c^{2}}\right)}{b e^{2} - 2 c d e} \right)}"," ",0,"e**2*x**2 + x*(-b*e**2/c + 4*d*e) + (-e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c**2) - (2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2))*log(x + (a*e**2 - c*d**2 + c*(-e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c**2) - (2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2)))/(b*e**2 - 2*c*d*e)) + (e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c**2) - (2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2))*log(x + (a*e**2 - c*d**2 + c*(e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(2*c**2) - (2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2)))/(b*e**2 - 2*c*d*e))","B",0
1527,1,134,0,0.705756," ","integrate((2*c*x+b)*(e*x+d)/(c*x**2+b*x+a),x)","2 e x + \left(- \frac{e \sqrt{- 4 a c + b^{2}}}{2 c} - \frac{b e - 2 c d}{2 c}\right) \log{\left(x + \frac{d + \frac{e \sqrt{- 4 a c + b^{2}}}{2 c} + \frac{b e - 2 c d}{2 c}}{e} \right)} + \left(\frac{e \sqrt{- 4 a c + b^{2}}}{2 c} - \frac{b e - 2 c d}{2 c}\right) \log{\left(x + \frac{d - \frac{e \sqrt{- 4 a c + b^{2}}}{2 c} + \frac{b e - 2 c d}{2 c}}{e} \right)}"," ",0,"2*e*x + (-e*sqrt(-4*a*c + b**2)/(2*c) - (b*e - 2*c*d)/(2*c))*log(x + (d + e*sqrt(-4*a*c + b**2)/(2*c) + (b*e - 2*c*d)/(2*c))/e) + (e*sqrt(-4*a*c + b**2)/(2*c) - (b*e - 2*c*d)/(2*c))*log(x + (d - e*sqrt(-4*a*c + b**2)/(2*c) + (b*e - 2*c*d)/(2*c))/e)","B",0
1528,1,10,0,0.154170," ","integrate((2*c*x+b)/(c*x**2+b*x+a),x)","\log{\left(a + b x + c x^{2} \right)}"," ",0,"log(a + b*x + c*x**2)","A",0
1529,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1530,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1531,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1532,1,1071,0,25.123606," ","integrate((2*c*x+b)*(e*x+d)**4/(c*x**2+b*x+a)**2,x)","x \left(- \frac{3 b e^{4}}{c^{2}} + \frac{8 d e^{3}}{c}\right) + \left(- \frac{2 e^{2} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{c^{3}} - \frac{2 e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{c^{3} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{8 a^{2} c e^{4} - 4 a b^{2} e^{4} + 12 a b c d e^{3} + 4 a c^{3} \left(- \frac{2 e^{2} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{c^{3}} - \frac{2 e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{c^{3} \left(4 a c - b^{2}\right)}\right) - 24 a c^{2} d^{2} e^{2} - b^{2} c^{2} \left(- \frac{2 e^{2} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{c^{3}} - \frac{2 e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{c^{3} \left(4 a c - b^{2}\right)}\right) + 4 b c^{2} d^{3} e}{12 a b c e^{4} - 24 a c^{2} d e^{3} - 4 b^{3} e^{4} + 12 b^{2} c d e^{3} - 12 b c^{2} d^{2} e^{2} + 8 c^{3} d^{3} e} \right)} + \left(- \frac{2 e^{2} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{c^{3}} + \frac{2 e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{c^{3} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{8 a^{2} c e^{4} - 4 a b^{2} e^{4} + 12 a b c d e^{3} + 4 a c^{3} \left(- \frac{2 e^{2} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{c^{3}} + \frac{2 e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{c^{3} \left(4 a c - b^{2}\right)}\right) - 24 a c^{2} d^{2} e^{2} - b^{2} c^{2} \left(- \frac{2 e^{2} \left(a c e^{2} - b^{2} e^{2} + 3 b c d e - 3 c^{2} d^{2}\right)}{c^{3}} + \frac{2 e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right) \left(3 a c e^{2} - b^{2} e^{2} + b c d e - c^{2} d^{2}\right)}{c^{3} \left(4 a c - b^{2}\right)}\right) + 4 b c^{2} d^{3} e}{12 a b c e^{4} - 24 a c^{2} d e^{3} - 4 b^{3} e^{4} + 12 b^{2} c d e^{3} - 12 b c^{2} d^{2} e^{2} + 8 c^{3} d^{3} e} \right)} + \frac{- a^{2} c e^{4} + a b^{2} e^{4} - 4 a b c d e^{3} + 6 a c^{2} d^{2} e^{2} - c^{3} d^{4} + x \left(- 2 a b c e^{4} + 4 a c^{2} d e^{3} + b^{3} e^{4} - 4 b^{2} c d e^{3} + 6 b c^{2} d^{2} e^{2} - 4 c^{3} d^{3} e\right)}{a c^{3} + b c^{3} x + c^{4} x^{2}} + \frac{e^{4} x^{2}}{c}"," ",0,"x*(-3*b*e**4/c**2 + 8*d*e**3/c) + (-2*e**2*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/c**3 - 2*e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(c**3*(4*a*c - b**2)))*log(x + (8*a**2*c*e**4 - 4*a*b**2*e**4 + 12*a*b*c*d*e**3 + 4*a*c**3*(-2*e**2*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/c**3 - 2*e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(c**3*(4*a*c - b**2))) - 24*a*c**2*d**2*e**2 - b**2*c**2*(-2*e**2*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/c**3 - 2*e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(c**3*(4*a*c - b**2))) + 4*b*c**2*d**3*e)/(12*a*b*c*e**4 - 24*a*c**2*d*e**3 - 4*b**3*e**4 + 12*b**2*c*d*e**3 - 12*b*c**2*d**2*e**2 + 8*c**3*d**3*e)) + (-2*e**2*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/c**3 + 2*e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(c**3*(4*a*c - b**2)))*log(x + (8*a**2*c*e**4 - 4*a*b**2*e**4 + 12*a*b*c*d*e**3 + 4*a*c**3*(-2*e**2*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/c**3 + 2*e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(c**3*(4*a*c - b**2))) - 24*a*c**2*d**2*e**2 - b**2*c**2*(-2*e**2*(a*c*e**2 - b**2*e**2 + 3*b*c*d*e - 3*c**2*d**2)/c**3 + 2*e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)*(3*a*c*e**2 - b**2*e**2 + b*c*d*e - c**2*d**2)/(c**3*(4*a*c - b**2))) + 4*b*c**2*d**3*e)/(12*a*b*c*e**4 - 24*a*c**2*d*e**3 - 4*b**3*e**4 + 12*b**2*c*d*e**3 - 12*b*c**2*d**2*e**2 + 8*c**3*d**3*e)) + (-a**2*c*e**4 + a*b**2*e**4 - 4*a*b*c*d*e**3 + 6*a*c**2*d**2*e**2 - c**3*d**4 + x*(-2*a*b*c*e**4 + 4*a*c**2*d*e**3 + b**3*e**4 - 4*b**2*c*d*e**3 + 6*b*c**2*d**2*e**2 - 4*c**3*d**3*e))/(a*c**3 + b*c**3*x + c**4*x**2) + e**4*x**2/c","B",0
1533,1,733,0,11.140429," ","integrate((2*c*x+b)*(e*x+d)**3/(c*x**2+b*x+a)**2,x)","\left(- \frac{3 e^{2} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{3 e \sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 3 a b e^{3} - 4 a c^{2} \left(- \frac{3 e^{2} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{3 e \sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + 12 a c d e^{2} + b^{2} c \left(- \frac{3 e^{2} \left(b e - 2 c d\right)}{2 c^{2}} - \frac{3 e \sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) - 3 b c d^{2} e}{6 a c e^{3} - 3 b^{2} e^{3} + 6 b c d e^{2} - 6 c^{2} d^{2} e} \right)} + \left(- \frac{3 e^{2} \left(b e - 2 c d\right)}{2 c^{2}} + \frac{3 e \sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 3 a b e^{3} - 4 a c^{2} \left(- \frac{3 e^{2} \left(b e - 2 c d\right)}{2 c^{2}} + \frac{3 e \sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + 12 a c d e^{2} + b^{2} c \left(- \frac{3 e^{2} \left(b e - 2 c d\right)}{2 c^{2}} + \frac{3 e \sqrt{- 4 a c + b^{2}} \left(2 a c e^{2} - b^{2} e^{2} + 2 b c d e - 2 c^{2} d^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) - 3 b c d^{2} e}{6 a c e^{3} - 3 b^{2} e^{3} + 6 b c d e^{2} - 6 c^{2} d^{2} e} \right)} + \frac{- a b e^{3} + 3 a c d e^{2} - c^{2} d^{3} + x \left(a c e^{3} - b^{2} e^{3} + 3 b c d e^{2} - 3 c^{2} d^{2} e\right)}{a c^{2} + b c^{2} x + c^{3} x^{2}} + \frac{2 e^{3} x}{c}"," ",0,"(-3*e**2*(b*e - 2*c*d)/(2*c**2) - 3*e*sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-3*a*b*e**3 - 4*a*c**2*(-3*e**2*(b*e - 2*c*d)/(2*c**2) - 3*e*sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) + 12*a*c*d*e**2 + b**2*c*(-3*e**2*(b*e - 2*c*d)/(2*c**2) - 3*e*sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) - 3*b*c*d**2*e)/(6*a*c*e**3 - 3*b**2*e**3 + 6*b*c*d*e**2 - 6*c**2*d**2*e)) + (-3*e**2*(b*e - 2*c*d)/(2*c**2) + 3*e*sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-3*a*b*e**3 - 4*a*c**2*(-3*e**2*(b*e - 2*c*d)/(2*c**2) + 3*e*sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) + 12*a*c*d*e**2 + b**2*c*(-3*e**2*(b*e - 2*c*d)/(2*c**2) + 3*e*sqrt(-4*a*c + b**2)*(2*a*c*e**2 - b**2*e**2 + 2*b*c*d*e - 2*c**2*d**2)/(2*c**2*(4*a*c - b**2))) - 3*b*c*d**2*e)/(6*a*c*e**3 - 3*b**2*e**3 + 6*b*c*d*e**2 - 6*c**2*d**2*e)) + (-a*b*e**3 + 3*a*c*d*e**2 - c**2*d**3 + x*(a*c*e**3 - b**2*e**3 + 3*b*c*d*e**2 - 3*c**2*d**2*e))/(a*c**2 + b*c**2*x + c**3*x**2) + 2*e**3*x/c","B",0
1534,1,340,0,4.354204," ","integrate((2*c*x+b)*(e*x+d)**2/(c*x**2+b*x+a)**2,x)","\left(\frac{e^{2}}{c} - \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 4 a c \left(\frac{e^{2}}{c} - \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{c \left(4 a c - b^{2}\right)}\right) + 4 a e^{2} + b^{2} \left(\frac{e^{2}}{c} - \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{c \left(4 a c - b^{2}\right)}\right) - 2 b d e}{2 b e^{2} - 4 c d e} \right)} + \left(\frac{e^{2}}{c} + \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 4 a c \left(\frac{e^{2}}{c} + \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{c \left(4 a c - b^{2}\right)}\right) + 4 a e^{2} + b^{2} \left(\frac{e^{2}}{c} + \frac{e \sqrt{- 4 a c + b^{2}} \left(b e - 2 c d\right)}{c \left(4 a c - b^{2}\right)}\right) - 2 b d e}{2 b e^{2} - 4 c d e} \right)} + \frac{a e^{2} - c d^{2} + x \left(b e^{2} - 2 c d e\right)}{a c + b c x + c^{2} x^{2}}"," ",0,"(e**2/c - e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(c*(4*a*c - b**2)))*log(x + (-4*a*c*(e**2/c - e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(c*(4*a*c - b**2))) + 4*a*e**2 + b**2*(e**2/c - e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(c*(4*a*c - b**2))) - 2*b*d*e)/(2*b*e**2 - 4*c*d*e)) + (e**2/c + e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(c*(4*a*c - b**2)))*log(x + (-4*a*c*(e**2/c + e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(c*(4*a*c - b**2))) + 4*a*e**2 + b**2*(e**2/c + e*sqrt(-4*a*c + b**2)*(b*e - 2*c*d)/(c*(4*a*c - b**2))) - 2*b*d*e)/(2*b*e**2 - 4*c*d*e)) + (a*e**2 - c*d**2 + x*(b*e**2 - 2*c*d*e))/(a*c + b*c*x + c**2*x**2)","B",0
1535,1,158,0,1.197172," ","integrate((2*c*x+b)*(e*x+d)/(c*x**2+b*x+a)**2,x)","- e \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{- 4 a c e \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} e \sqrt{- \frac{1}{4 a c - b^{2}}} + b e}{2 c e} \right)} + e \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{4 a c e \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} e \sqrt{- \frac{1}{4 a c - b^{2}}} + b e}{2 c e} \right)} + \frac{- d - e x}{a + b x + c x^{2}}"," ",0,"-e*sqrt(-1/(4*a*c - b**2))*log(x + (-4*a*c*e*sqrt(-1/(4*a*c - b**2)) + b**2*e*sqrt(-1/(4*a*c - b**2)) + b*e)/(2*c*e)) + e*sqrt(-1/(4*a*c - b**2))*log(x + (4*a*c*e*sqrt(-1/(4*a*c - b**2)) - b**2*e*sqrt(-1/(4*a*c - b**2)) + b*e)/(2*c*e)) + (-d - e*x)/(a + b*x + c*x**2)","B",0
1536,1,12,0,0.382246," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**2,x)","- \frac{1}{a + b x + c x^{2}}"," ",0,"-1/(a + b*x + c*x**2)","A",0
1537,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1538,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**2/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1539,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**5/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1540,1,1545,0,133.501912," ","integrate((2*c*x+b)*(e*x+d)**4/(c*x**2+b*x+a)**3,x)","\left(\frac{e^{4}}{c^{2}} - \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e^{4}}{c^{2}} - \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 16 a^{2} c e^{4} + 8 a b^{2} c^{2} \left(\frac{e^{4}}{c^{2}} - \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 2 a b^{2} e^{4} - 12 a b c d e^{3} - b^{4} c \left(\frac{e^{4}}{c^{2}} - \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 6 b^{2} c d^{2} e^{2} - 4 b c^{2} d^{3} e}{12 a b c e^{4} - 24 a c^{2} d e^{3} - 2 b^{3} e^{4} + 12 b c^{2} d^{2} e^{2} - 8 c^{3} d^{3} e} \right)} + \left(\frac{e^{4}}{c^{2}} + \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e^{4}}{c^{2}} + \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 16 a^{2} c e^{4} + 8 a b^{2} c^{2} \left(\frac{e^{4}}{c^{2}} + \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - 2 a b^{2} e^{4} - 12 a b c d e^{3} - b^{4} c \left(\frac{e^{4}}{c^{2}} + \frac{e \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(b e - 2 c d\right) \left(6 a c e^{2} - b^{2} e^{2} - 2 b c d e + 2 c^{2} d^{2}\right)}{c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 6 b^{2} c d^{2} e^{2} - 4 b c^{2} d^{3} e}{12 a b c e^{4} - 24 a c^{2} d e^{3} - 2 b^{3} e^{4} + 12 b c^{2} d^{2} e^{2} - 8 c^{3} d^{3} e} \right)} + \frac{12 a^{3} c e^{4} - 5 a^{2} b^{2} e^{4} + 12 a^{2} b c d e^{3} - 24 a^{2} c^{2} d^{2} e^{2} + 4 a b c^{2} d^{3} e - 4 a c^{3} d^{4} + b^{2} c^{2} d^{4} + x^{3} \left(20 a b c^{2} e^{4} - 40 a c^{3} d e^{3} - 6 b^{3} c e^{4} + 16 b^{2} c^{2} d e^{3} - 12 b c^{3} d^{2} e^{2} + 8 c^{4} d^{3} e\right) + x^{2} \left(16 a^{2} c^{2} e^{4} + 10 a b^{2} c e^{4} - 12 a b c^{2} d e^{3} - 48 a c^{3} d^{2} e^{2} - 5 b^{4} e^{4} + 12 b^{3} c d e^{3} - 6 b^{2} c^{2} d^{2} e^{2} + 12 b c^{3} d^{3} e\right) + x \left(28 a^{2} b c e^{4} - 24 a^{2} c^{2} d e^{3} - 10 a b^{3} e^{4} + 24 a b^{2} c d e^{3} - 36 a b c^{2} d^{2} e^{2} - 8 a c^{3} d^{3} e + 8 b^{2} c^{2} d^{3} e\right)}{8 a^{3} c^{3} - 2 a^{2} b^{2} c^{2} + x^{4} \left(8 a c^{5} - 2 b^{2} c^{4}\right) + x^{3} \left(16 a b c^{4} - 4 b^{3} c^{3}\right) + x^{2} \left(16 a^{2} c^{4} + 4 a b^{2} c^{3} - 2 b^{4} c^{2}\right) + x \left(16 a^{2} b c^{3} - 4 a b^{3} c^{2}\right)}"," ",0,"(e**4/c**2 - e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e**4/c**2 - e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 16*a**2*c*e**4 + 8*a*b**2*c**2*(e**4/c**2 - e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 2*a*b**2*e**4 - 12*a*b*c*d*e**3 - b**4*c*(e**4/c**2 - e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 6*b**2*c*d**2*e**2 - 4*b*c**2*d**3*e)/(12*a*b*c*e**4 - 24*a*c**2*d*e**3 - 2*b**3*e**4 + 12*b*c**2*d**2*e**2 - 8*c**3*d**3*e)) + (e**4/c**2 + e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e**4/c**2 + e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 16*a**2*c*e**4 + 8*a*b**2*c**2*(e**4/c**2 + e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - 2*a*b**2*e**4 - 12*a*b*c*d*e**3 - b**4*c*(e**4/c**2 + e*sqrt(-(4*a*c - b**2)**3)*(b*e - 2*c*d)*(6*a*c*e**2 - b**2*e**2 - 2*b*c*d*e + 2*c**2*d**2)/(c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 6*b**2*c*d**2*e**2 - 4*b*c**2*d**3*e)/(12*a*b*c*e**4 - 24*a*c**2*d*e**3 - 2*b**3*e**4 + 12*b*c**2*d**2*e**2 - 8*c**3*d**3*e)) + (12*a**3*c*e**4 - 5*a**2*b**2*e**4 + 12*a**2*b*c*d*e**3 - 24*a**2*c**2*d**2*e**2 + 4*a*b*c**2*d**3*e - 4*a*c**3*d**4 + b**2*c**2*d**4 + x**3*(20*a*b*c**2*e**4 - 40*a*c**3*d*e**3 - 6*b**3*c*e**4 + 16*b**2*c**2*d*e**3 - 12*b*c**3*d**2*e**2 + 8*c**4*d**3*e) + x**2*(16*a**2*c**2*e**4 + 10*a*b**2*c*e**4 - 12*a*b*c**2*d*e**3 - 48*a*c**3*d**2*e**2 - 5*b**4*e**4 + 12*b**3*c*d*e**3 - 6*b**2*c**2*d**2*e**2 + 12*b*c**3*d**3*e) + x*(28*a**2*b*c*e**4 - 24*a**2*c**2*d*e**3 - 10*a*b**3*e**4 + 24*a*b**2*c*d*e**3 - 36*a*b*c**2*d**2*e**2 - 8*a*c**3*d**3*e + 8*b**2*c**2*d**3*e))/(8*a**3*c**3 - 2*a**2*b**2*c**2 + x**4*(8*a*c**5 - 2*b**2*c**4) + x**3*(16*a*b*c**4 - 4*b**3*c**3) + x**2*(16*a**2*c**4 + 4*a*b**2*c**3 - 2*b**4*c**2) + x*(16*a**2*b*c**3 - 4*a*b**3*c**2))","B",0
1541,1,762,0,40.975523," ","integrate((2*c*x+b)*(e*x+d)**3/(c*x**2+b*x+a)**3,x)","- 3 e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{- 48 a^{2} c^{2} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) + 24 a b^{2} c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) + 3 a b e^{3} - 3 b^{4} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) - 3 b^{2} d e^{2} + 3 b c d^{2} e}{6 a c e^{3} - 6 b c d e^{2} + 6 c^{2} d^{2} e} \right)} + 3 e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{48 a^{2} c^{2} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) - 24 a b^{2} c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) + 3 a b e^{3} + 3 b^{4} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(a e^{2} - b d e + c d^{2}\right) - 3 b^{2} d e^{2} + 3 b c d^{2} e}{6 a c e^{3} - 6 b c d e^{2} + 6 c^{2} d^{2} e} \right)} + \frac{3 a^{2} b e^{3} - 12 a^{2} c d e^{2} + 3 a b c d^{2} e - 4 a c^{2} d^{3} + b^{2} c d^{3} + x^{3} \left(- 10 a c^{2} e^{3} + 4 b^{2} c e^{3} - 6 b c^{2} d e^{2} + 6 c^{3} d^{2} e\right) + x^{2} \left(- 3 a b c e^{3} - 24 a c^{2} d e^{2} + 3 b^{3} e^{3} - 3 b^{2} c d e^{2} + 9 b c^{2} d^{2} e\right) + x \left(- 6 a^{2} c e^{3} + 6 a b^{2} e^{3} - 18 a b c d e^{2} - 6 a c^{2} d^{2} e + 6 b^{2} c d^{2} e\right)}{8 a^{3} c^{2} - 2 a^{2} b^{2} c + x^{4} \left(8 a c^{4} - 2 b^{2} c^{3}\right) + x^{3} \left(16 a b c^{3} - 4 b^{3} c^{2}\right) + x^{2} \left(16 a^{2} c^{3} + 4 a b^{2} c^{2} - 2 b^{4} c\right) + x \left(16 a^{2} b c^{2} - 4 a b^{3} c\right)}"," ",0,"-3*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2)*log(x + (-48*a**2*c**2*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) + 24*a*b**2*c*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) + 3*a*b*e**3 - 3*b**4*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) - 3*b**2*d*e**2 + 3*b*c*d**2*e)/(6*a*c*e**3 - 6*b*c*d*e**2 + 6*c**2*d**2*e)) + 3*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2)*log(x + (48*a**2*c**2*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) - 24*a*b**2*c*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) + 3*a*b*e**3 + 3*b**4*e*sqrt(-1/(4*a*c - b**2)**3)*(a*e**2 - b*d*e + c*d**2) - 3*b**2*d*e**2 + 3*b*c*d**2*e)/(6*a*c*e**3 - 6*b*c*d*e**2 + 6*c**2*d**2*e)) + (3*a**2*b*e**3 - 12*a**2*c*d*e**2 + 3*a*b*c*d**2*e - 4*a*c**2*d**3 + b**2*c*d**3 + x**3*(-10*a*c**2*e**3 + 4*b**2*c*e**3 - 6*b*c**2*d*e**2 + 6*c**3*d**2*e) + x**2*(-3*a*b*c*e**3 - 24*a*c**2*d*e**2 + 3*b**3*e**3 - 3*b**2*c*d*e**2 + 9*b*c**2*d**2*e) + x*(-6*a**2*c*e**3 + 6*a*b**2*e**3 - 18*a*b*c*d*e**2 - 6*a*c**2*d**2*e + 6*b**2*c*d**2*e))/(8*a**3*c**2 - 2*a**2*b**2*c + x**4*(8*a*c**4 - 2*b**2*c**3) + x**3*(16*a*b*c**3 - 4*b**3*c**2) + x**2*(16*a**2*c**3 + 4*a*b**2*c**2 - 2*b**4*c) + x*(16*a**2*b*c**2 - 4*a*b**3*c))","B",0
1542,1,530,0,12.583841," ","integrate((2*c*x+b)*(e*x+d)**2/(c*x**2+b*x+a)**3,x)","e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) \log{\left(x + \frac{- 16 a^{2} c^{2} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + 8 a b^{2} c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) - b^{4} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{2} e^{2} - 2 b c d e}{2 b c e^{2} - 4 c^{2} d e} \right)} - e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) \log{\left(x + \frac{16 a^{2} c^{2} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) - 8 a b^{2} c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{4} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(b e - 2 c d\right) + b^{2} e^{2} - 2 b c d e}{2 b c e^{2} - 4 c^{2} d e} \right)} + \frac{- 4 a^{2} e^{2} + 2 a b d e - 4 a c d^{2} + b^{2} d^{2} + x^{3} \left(- 2 b c e^{2} + 4 c^{2} d e\right) + x^{2} \left(- 8 a c e^{2} - b^{2} e^{2} + 6 b c d e\right) + x \left(- 6 a b e^{2} - 4 a c d e + 4 b^{2} d e\right)}{8 a^{3} c - 2 a^{2} b^{2} + x^{4} \left(8 a c^{3} - 2 b^{2} c^{2}\right) + x^{3} \left(16 a b c^{2} - 4 b^{3} c\right) + x^{2} \left(16 a^{2} c^{2} + 4 a b^{2} c - 2 b^{4}\right) + x \left(16 a^{2} b c - 4 a b^{3}\right)}"," ",0,"e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d)*log(x + (-16*a**2*c**2*e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + 8*a*b**2*c*e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) - b**4*e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**2*e**2 - 2*b*c*d*e)/(2*b*c*e**2 - 4*c**2*d*e)) - e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d)*log(x + (16*a**2*c**2*e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) - 8*a*b**2*c*e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**4*e*sqrt(-1/(4*a*c - b**2)**3)*(b*e - 2*c*d) + b**2*e**2 - 2*b*c*d*e)/(2*b*c*e**2 - 4*c**2*d*e)) + (-4*a**2*e**2 + 2*a*b*d*e - 4*a*c*d**2 + b**2*d**2 + x**3*(-2*b*c*e**2 + 4*c**2*d*e) + x**2*(-8*a*c*e**2 - b**2*e**2 + 6*b*c*d*e) + x*(-6*a*b*e**2 - 4*a*c*d*e + 4*b**2*d*e))/(8*a**3*c - 2*a**2*b**2 + x**4*(8*a*c**3 - 2*b**2*c**2) + x**3*(16*a*b*c**2 - 4*b**3*c) + x**2*(16*a**2*c**2 + 4*a*b**2*c - 2*b**4) + x*(16*a**2*b*c - 4*a*b**3))","B",0
1543,1,377,0,3.396427," ","integrate((2*c*x+b)*(e*x+d)/(c*x**2+b*x+a)**3,x)","- c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 16 a^{2} c^{3} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{2} c^{2} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{4} c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c e}{2 c^{2} e} \right)} + c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{16 a^{2} c^{3} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{2} c^{2} e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{4} c e \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c e}{2 c^{2} e} \right)} + \frac{a b e - 4 a c d + b^{2} d + 3 b c e x^{2} + 2 c^{2} e x^{3} + x \left(- 2 a c e + 2 b^{2} e\right)}{8 a^{3} c - 2 a^{2} b^{2} + x^{4} \left(8 a c^{3} - 2 b^{2} c^{2}\right) + x^{3} \left(16 a b c^{2} - 4 b^{3} c\right) + x^{2} \left(16 a^{2} c^{2} + 4 a b^{2} c - 2 b^{4}\right) + x \left(16 a^{2} b c - 4 a b^{3}\right)}"," ",0,"-c*e*sqrt(-1/(4*a*c - b**2)**3)*log(x + (-16*a**2*c**3*e*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**2*c**2*e*sqrt(-1/(4*a*c - b**2)**3) - b**4*c*e*sqrt(-1/(4*a*c - b**2)**3) + b*c*e)/(2*c**2*e)) + c*e*sqrt(-1/(4*a*c - b**2)**3)*log(x + (16*a**2*c**3*e*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**2*c**2*e*sqrt(-1/(4*a*c - b**2)**3) + b**4*c*e*sqrt(-1/(4*a*c - b**2)**3) + b*c*e)/(2*c**2*e)) + (a*b*e - 4*a*c*d + b**2*d + 3*b*c*e*x**2 + 2*c**2*e*x**3 + x*(-2*a*c*e + 2*b**2*e))/(8*a**3*c - 2*a**2*b**2 + x**4*(8*a*c**3 - 2*b**2*c**2) + x**3*(16*a*b*c**2 - 4*b**3*c) + x**2*(16*a**2*c**2 + 4*a*b**2*c - 2*b**4) + x*(16*a**2*b*c - 4*a*b**3))","B",0
1544,1,44,0,0.820693," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**3,x)","- \frac{1}{2 a^{2} + 4 a b x + 4 b c x^{3} + 2 c^{2} x^{4} + x^{2} \left(4 a c + 2 b^{2}\right)}"," ",0,"-1/(2*a**2 + 4*a*b*x + 4*b*c*x**3 + 2*c**2*x**4 + x**2*(4*a*c + 2*b**2))","B",0
1545,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1546,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**4*(c*x**2+b*x+a)**(1/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{4} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**4*sqrt(a + b*x + c*x**2), x)","F",0
1547,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**3*(c*x**2+b*x+a)**(1/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{3} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**3*sqrt(a + b*x + c*x**2), x)","F",0
1548,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**2*(c*x**2+b*x+a)**(1/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{2} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**2*sqrt(a + b*x + c*x**2), x)","F",0
1549,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)*(c*x**2+b*x+a)**(1/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)*sqrt(a + b*x + c*x**2), x)","F",0
1550,1,60,0,0.174423," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2),x)","\frac{2 a \sqrt{a + b x + c x^{2}}}{3} + \frac{2 b x \sqrt{a + b x + c x^{2}}}{3} + \frac{2 c x^{2} \sqrt{a + b x + c x^{2}}}{3}"," ",0,"2*a*sqrt(a + b*x + c*x**2)/3 + 2*b*x*sqrt(a + b*x + c*x**2)/3 + 2*c*x**2*sqrt(a + b*x + c*x**2)/3","B",0
1551,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
1552,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**2,x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**2, x)","F",0
1553,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**3,x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**3, x)","F",0
1554,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**4,x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**4, x)","F",0
1555,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**5,x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**5, x)","F",0
1556,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**6,x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**6, x)","F",0
1557,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**3*(c*x**2+b*x+a)**(3/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**3*(a + b*x + c*x**2)**(3/2), x)","F",0
1558,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**2*(c*x**2+b*x+a)**(3/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**2*(a + b*x + c*x**2)**(3/2), x)","F",0
1559,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)*(c*x**2+b*x+a)**(3/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)*(a + b*x + c*x**2)**(3/2), x)","F",0
1560,1,136,0,0.605054," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2),x)","\frac{2 a^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{4 a b x \sqrt{a + b x + c x^{2}}}{5} + \frac{4 a c x^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{2 b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{5} + \frac{4 b c x^{3} \sqrt{a + b x + c x^{2}}}{5} + \frac{2 c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{5}"," ",0,"2*a**2*sqrt(a + b*x + c*x**2)/5 + 4*a*b*x*sqrt(a + b*x + c*x**2)/5 + 4*a*c*x**2*sqrt(a + b*x + c*x**2)/5 + 2*b**2*x**2*sqrt(a + b*x + c*x**2)/5 + 4*b*c*x**3*sqrt(a + b*x + c*x**2)/5 + 2*c**2*x**4*sqrt(a + b*x + c*x**2)/5","B",0
1561,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d),x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x), x)","F",0
1562,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x)**2, x)","F",0
1563,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x)**3, x)","F",0
1564,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x)**4, x)","F",0
1565,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**3*(c*x**2+b*x+a)**(5/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**3*(a + b*x + c*x**2)**(5/2), x)","F",0
1566,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**2*(c*x**2+b*x+a)**(5/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**2*(a + b*x + c*x**2)**(5/2), x)","F",0
1567,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)*(c*x**2+b*x+a)**(5/2),x)","\int \left(b + 2 c x\right) \left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)*(a + b*x + c*x**2)**(5/2), x)","F",0
1568,1,243,0,2.899560," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(5/2),x)","\frac{2 a^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a^{2} b x \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a^{2} c x^{2} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a b^{2} x^{2} \sqrt{a + b x + c x^{2}}}{7} + \frac{12 a b c x^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 a c^{2} x^{4} \sqrt{a + b x + c x^{2}}}{7} + \frac{2 b^{3} x^{3} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 b^{2} c x^{4} \sqrt{a + b x + c x^{2}}}{7} + \frac{6 b c^{2} x^{5} \sqrt{a + b x + c x^{2}}}{7} + \frac{2 c^{3} x^{6} \sqrt{a + b x + c x^{2}}}{7}"," ",0,"2*a**3*sqrt(a + b*x + c*x**2)/7 + 6*a**2*b*x*sqrt(a + b*x + c*x**2)/7 + 6*a**2*c*x**2*sqrt(a + b*x + c*x**2)/7 + 6*a*b**2*x**2*sqrt(a + b*x + c*x**2)/7 + 12*a*b*c*x**3*sqrt(a + b*x + c*x**2)/7 + 6*a*c**2*x**4*sqrt(a + b*x + c*x**2)/7 + 2*b**3*x**3*sqrt(a + b*x + c*x**2)/7 + 6*b**2*c*x**4*sqrt(a + b*x + c*x**2)/7 + 6*b*c**2*x**5*sqrt(a + b*x + c*x**2)/7 + 2*c**3*x**6*sqrt(a + b*x + c*x**2)/7","B",0
1569,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(5/2)/(e*x+d),x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(5/2)/(d + e*x), x)","F",0
1570,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(5/2)/(d + e*x)**2, x)","F",0
1571,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(5/2)/(d + e*x)**3, x)","F",0
1572,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(5/2)/(d + e*x)**4, x)","F",0
1573,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{3}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**3/sqrt(a + b*x + c*x**2), x)","F",0
1574,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{2}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**2/sqrt(a + b*x + c*x**2), x)","F",0
1575,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)/sqrt(a + b*x + c*x**2), x)","F",0
1576,1,14,0,0.156090," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**(1/2),x)","2 \sqrt{a + b x + c x^{2}}"," ",0,"2*sqrt(a + b*x + c*x**2)","A",0
1577,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
1578,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right)^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)**2*sqrt(a + b*x + c*x**2)), x)","F",0
1579,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right)^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)**3*sqrt(a + b*x + c*x**2)), x)","F",0
1580,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**4/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right)^{4} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)**4*sqrt(a + b*x + c*x**2)), x)","F",0
1581,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**4/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{4}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**4/(a + b*x + c*x**2)**(3/2), x)","F",0
1582,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**3/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{3}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**3/(a + b*x + c*x**2)**(3/2), x)","F",0
1583,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**2/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{2}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**2/(a + b*x + c*x**2)**(3/2), x)","F",0
1584,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
1585,1,15,0,0.919621," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**(3/2),x)","- \frac{2}{\sqrt{a + b x + c x^{2}}}"," ",0,"-2/sqrt(a + b*x + c*x**2)","A",0
1586,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
1587,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**2/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1588,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**4/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1589,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**3/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1590,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1591,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1592,1,58,0,1.699818," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**(5/2),x)","- \frac{2}{3 a \sqrt{a + b x + c x^{2}} + 3 b x \sqrt{a + b x + c x^{2}} + 3 c x^{2} \sqrt{a + b x + c x^{2}}}"," ",0,"-2/(3*a*sqrt(a + b*x + c*x**2) + 3*b*x*sqrt(a + b*x + c*x**2) + 3*c*x**2*sqrt(a + b*x + c*x**2))","B",0
1593,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1594,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1595,1,643,0,4.915137," ","integrate((2*c*x+b)*(e*x+d)**(5/2)*(c*x**2+b*x+a),x)","\begin{cases} \frac{2 a b d^{3} \sqrt{d + e x}}{7 e} + \frac{6 a b d^{2} x \sqrt{d + e x}}{7} + \frac{6 a b d e x^{2} \sqrt{d + e x}}{7} + \frac{2 a b e^{2} x^{3} \sqrt{d + e x}}{7} - \frac{8 a c d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{4 a c d^{3} x \sqrt{d + e x}}{63 e} + \frac{20 a c d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{76 a c d e x^{3} \sqrt{d + e x}}{63} + \frac{4 a c e^{2} x^{4} \sqrt{d + e x}}{9} - \frac{4 b^{2} d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{2 b^{2} d^{3} x \sqrt{d + e x}}{63 e} + \frac{10 b^{2} d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{38 b^{2} d e x^{3} \sqrt{d + e x}}{63} + \frac{2 b^{2} e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{16 b c d^{5} \sqrt{d + e x}}{231 e^{3}} - \frac{8 b c d^{4} x \sqrt{d + e x}}{231 e^{2}} + \frac{2 b c d^{3} x^{2} \sqrt{d + e x}}{77 e} + \frac{226 b c d^{2} x^{3} \sqrt{d + e x}}{231} + \frac{46 b c d e x^{4} \sqrt{d + e x}}{33} + \frac{6 b c e^{2} x^{5} \sqrt{d + e x}}{11} - \frac{64 c^{2} d^{6} \sqrt{d + e x}}{3003 e^{4}} + \frac{32 c^{2} d^{5} x \sqrt{d + e x}}{3003 e^{3}} - \frac{8 c^{2} d^{4} x^{2} \sqrt{d + e x}}{1001 e^{2}} + \frac{20 c^{2} d^{3} x^{3} \sqrt{d + e x}}{3003 e} + \frac{212 c^{2} d^{2} x^{4} \sqrt{d + e x}}{429} + \frac{108 c^{2} d e x^{5} \sqrt{d + e x}}{143} + \frac{4 c^{2} e^{2} x^{6} \sqrt{d + e x}}{13} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(a b x + a c x^{2} + \frac{b^{2} x^{2}}{2} + b c x^{3} + \frac{c^{2} x^{4}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*b*d**3*sqrt(d + e*x)/(7*e) + 6*a*b*d**2*x*sqrt(d + e*x)/7 + 6*a*b*d*e*x**2*sqrt(d + e*x)/7 + 2*a*b*e**2*x**3*sqrt(d + e*x)/7 - 8*a*c*d**4*sqrt(d + e*x)/(63*e**2) + 4*a*c*d**3*x*sqrt(d + e*x)/(63*e) + 20*a*c*d**2*x**2*sqrt(d + e*x)/21 + 76*a*c*d*e*x**3*sqrt(d + e*x)/63 + 4*a*c*e**2*x**4*sqrt(d + e*x)/9 - 4*b**2*d**4*sqrt(d + e*x)/(63*e**2) + 2*b**2*d**3*x*sqrt(d + e*x)/(63*e) + 10*b**2*d**2*x**2*sqrt(d + e*x)/21 + 38*b**2*d*e*x**3*sqrt(d + e*x)/63 + 2*b**2*e**2*x**4*sqrt(d + e*x)/9 + 16*b*c*d**5*sqrt(d + e*x)/(231*e**3) - 8*b*c*d**4*x*sqrt(d + e*x)/(231*e**2) + 2*b*c*d**3*x**2*sqrt(d + e*x)/(77*e) + 226*b*c*d**2*x**3*sqrt(d + e*x)/231 + 46*b*c*d*e*x**4*sqrt(d + e*x)/33 + 6*b*c*e**2*x**5*sqrt(d + e*x)/11 - 64*c**2*d**6*sqrt(d + e*x)/(3003*e**4) + 32*c**2*d**5*x*sqrt(d + e*x)/(3003*e**3) - 8*c**2*d**4*x**2*sqrt(d + e*x)/(1001*e**2) + 20*c**2*d**3*x**3*sqrt(d + e*x)/(3003*e) + 212*c**2*d**2*x**4*sqrt(d + e*x)/429 + 108*c**2*d*e*x**5*sqrt(d + e*x)/143 + 4*c**2*e**2*x**6*sqrt(d + e*x)/13, Ne(e, 0)), (d**(5/2)*(a*b*x + a*c*x**2 + b**2*x**2/2 + b*c*x**3 + c**2*x**4/2), True))","A",0
1596,1,457,0,20.229334," ","integrate((2*c*x+b)*(e*x+d)**(3/2)*(c*x**2+b*x+a),x)","a b d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a b \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 a c d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 a c \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 b^{2} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 b^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 b c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{6 b c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{4 c^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 c^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}}"," ",0,"a*b*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a*b*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*a*c*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*a*c*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*b**2*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*b**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*b*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 6*b*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 4*c**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*c**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4","A",0
1597,1,155,0,5.143889," ","integrate((2*c*x+b)*(c*x**2+b*x+a)*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{2 c^{2} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{3}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(3 b c e - 6 c^{2} d\right)}{7 e^{3}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 a c e^{2} + b^{2} e^{2} - 6 b c d e + 6 c^{2} d^{2}\right)}{5 e^{3}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a b e^{3} - 2 a c d e^{2} - b^{2} d e^{2} + 3 b c d^{2} e - 2 c^{2} d^{3}\right)}{3 e^{3}}\right)}{e}"," ",0,"2*(2*c**2*(d + e*x)**(9/2)/(9*e**3) + (d + e*x)**(7/2)*(3*b*c*e - 6*c**2*d)/(7*e**3) + (d + e*x)**(5/2)*(2*a*c*e**2 + b**2*e**2 - 6*b*c*d*e + 6*c**2*d**2)/(5*e**3) + (d + e*x)**(3/2)*(a*b*e**3 - 2*a*c*d*e**2 - b**2*d*e**2 + 3*b*c*d**2*e - 2*c**2*d**3)/(3*e**3))/e","A",0
1598,1,427,0,45.951196," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a b d}{\sqrt{d + e x}} - 2 a b \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 a c d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 a c \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 b^{2} d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 b^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{6 b c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 b c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{4 c^{2} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{4 c^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{\left(a + b x + c x^{2}\right)^{2}}{2 \sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*b*d/sqrt(d + e*x) - 2*a*b*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a*c*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*a*c*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*b**2*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*b**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 6*b*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*b*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 4*c**2*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 4*c**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3)/e, Ne(e, 0)), ((a + b*x + c*x**2)**2/(2*sqrt(d)), True))","A",0
1599,1,128,0,28.766673," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**(3/2),x)","\frac{4 c^{2} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 b c e - 12 c^{2} d\right)}{3 e^{4}} + \frac{\sqrt{d + e x} \left(4 a c e^{2} + 2 b^{2} e^{2} - 12 b c d e + 12 c^{2} d^{2}\right)}{e^{4}} - \frac{2 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)}{e^{4} \sqrt{d + e x}}"," ",0,"4*c**2*(d + e*x)**(5/2)/(5*e**4) + (d + e*x)**(3/2)*(6*b*c*e - 12*c**2*d)/(3*e**4) + sqrt(d + e*x)*(4*a*c*e**2 + 2*b**2*e**2 - 12*b*c*d*e + 12*c**2*d**2)/e**4 - 2*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)/(e**4*sqrt(d + e*x))","A",0
1600,1,536,0,1.652602," ","integrate((2*c*x+b)*(c*x**2+b*x+a)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 a b e^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{8 a c d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 a c e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{4 b^{2} d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{6 b^{2} e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{48 b c d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{72 b c d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{18 b c e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{64 c^{2} d^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{96 c^{2} d^{2} e x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{24 c^{2} d e^{2} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{4 c^{2} e^{3} x^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a b x + a c x^{2} + \frac{b^{2} x^{2}}{2} + b c x^{3} + \frac{c^{2} x^{4}}{2}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*b*e**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 8*a*c*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*a*c*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 4*b**2*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 6*b**2*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 48*b*c*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 72*b*c*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 18*b*c*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 64*c**2*d**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 96*c**2*d**2*e*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 24*c**2*d*e**2*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 4*c**2*e**3*x**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)), Ne(e, 0)), ((a*b*x + a*c*x**2 + b**2*x**2/2 + b*c*x**3 + c**2*x**4/2)/d**(5/2), True))","A",0
1601,1,1860,0,70.394343," ","integrate((2*c*x+b)*(e*x+d)**(5/2)*(c*x**2+b*x+a)**2,x)","a^{2} b d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{2} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{2} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{4 a^{2} c d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{8 a^{2} c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 a^{2} c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{4 a b^{2} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{8 a b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 a b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{12 a b c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{24 a b c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 a b c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{8 a c^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{16 a c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{8 a c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 b^{3} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{8 b^{2} c d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{16 b^{2} c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{8 b^{2} c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{10 b c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{20 b c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{10 b c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{4 c^{3} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{8 c^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{4 c^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}}"," ",0,"a**2*b*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**2*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**2*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 4*a**2*c*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 8*a**2*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*a**2*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 4*a*b**2*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 8*a*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*a*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*a*b*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 24*a*b*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*a*b*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 8*a*c**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 16*a*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 8*a*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*b**3*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 8*b**2*c*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 16*b**2*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 8*b**2*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 10*b*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 20*b*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 10*b*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 4*c**3*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 8*c**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 4*c**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6","A",0
1602,1,1093,0,43.463165," ","integrate((2*c*x+b)*(e*x+d)**(3/2)*(c*x**2+b*x+a)**2,x)","a^{2} b d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{2} b \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 a^{2} c d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 a^{2} c \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 a b^{2} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 a b^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{12 a b c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 a b c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{8 a c^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 a c^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 b^{3} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 b^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{8 b^{2} c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 b^{2} c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{10 b c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{10 b c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{4 c^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{4 c^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}}"," ",0,"a**2*b*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**2*b*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*a**2*c*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*a**2*c*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*a*b**2*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*a*b**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 12*a*b*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*a*b*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 8*a*c**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*a*c**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*b**3*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*b**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 8*b**2*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*b**2*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 10*b*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 10*b*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 4*c**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 4*c**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6","A",0
1603,1,405,0,8.783138," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{2 c^{3} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{5}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(5 b c^{2} e - 10 c^{3} d\right)}{11 e^{5}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(4 a c^{2} e^{2} + 4 b^{2} c e^{2} - 20 b c^{2} d e + 20 c^{3} d^{2}\right)}{9 e^{5}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 a b c e^{3} - 12 a c^{2} d e^{2} + b^{3} e^{3} - 12 b^{2} c d e^{2} + 30 b c^{2} d^{2} e - 20 c^{3} d^{3}\right)}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 a^{2} c e^{4} + 2 a b^{2} e^{4} - 12 a b c d e^{3} + 12 a c^{2} d^{2} e^{2} - 2 b^{3} d e^{3} + 12 b^{2} c d^{2} e^{2} - 20 b c^{2} d^{3} e + 10 c^{3} d^{4}\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{2} b e^{5} - 2 a^{2} c d e^{4} - 2 a b^{2} d e^{4} + 6 a b c d^{2} e^{3} - 4 a c^{2} d^{3} e^{2} + b^{3} d^{2} e^{3} - 4 b^{2} c d^{3} e^{2} + 5 b c^{2} d^{4} e - 2 c^{3} d^{5}\right)}{3 e^{5}}\right)}{e}"," ",0,"2*(2*c**3*(d + e*x)**(13/2)/(13*e**5) + (d + e*x)**(11/2)*(5*b*c**2*e - 10*c**3*d)/(11*e**5) + (d + e*x)**(9/2)*(4*a*c**2*e**2 + 4*b**2*c*e**2 - 20*b*c**2*d*e + 20*c**3*d**2)/(9*e**5) + (d + e*x)**(7/2)*(6*a*b*c*e**3 - 12*a*c**2*d*e**2 + b**3*e**3 - 12*b**2*c*d*e**2 + 30*b*c**2*d**2*e - 20*c**3*d**3)/(7*e**5) + (d + e*x)**(5/2)*(2*a**2*c*e**4 + 2*a*b**2*e**4 - 12*a*b*c*d*e**3 + 12*a*c**2*d**2*e**2 - 2*b**3*d*e**3 + 12*b**2*c*d**2*e**2 - 20*b*c**2*d**3*e + 10*c**3*d**4)/(5*e**5) + (d + e*x)**(3/2)*(a**2*b*e**5 - 2*a**2*c*d*e**4 - 2*a*b**2*d*e**4 + 6*a*b*c*d**2*e**3 - 4*a*c**2*d**3*e**2 + b**3*d**2*e**3 - 4*b**2*c*d**3*e**2 + 5*b*c**2*d**4*e - 2*c**3*d**5)/(3*e**5))/e","A",0
1604,1,1025,0,121.363073," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{2} b d}{\sqrt{d + e x}} - 2 a^{2} b \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 a^{2} c d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 a^{2} c \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{4 a b^{2} d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 a b^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{12 a b c d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{12 a b c \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{8 a c^{2} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{8 a c^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 b^{3} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 b^{3} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{8 b^{2} c d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{8 b^{2} c \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{10 b c^{2} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{10 b c^{2} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{4 c^{3} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{4 c^{3} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}}}{e} & \text{for}\: e \neq 0 \\\frac{\left(a + b x + c x^{2}\right)^{3}}{3 \sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*b*d/sqrt(d + e*x) - 2*a**2*b*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*a**2*c*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*a**2*c*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 4*a*b**2*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*a*b**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 12*a*b*c*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 12*a*b*c*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 8*a*c**2*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 8*a*c**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*b**3*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*b**3*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 8*b**2*c*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 8*b**2*c*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 10*b*c**2*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 10*b*c**2*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 4*c**3*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 4*c**3*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5)/e, Ne(e, 0)), ((a + b*x + c*x**2)**3/(3*sqrt(d)), True))","A",0
1605,1,316,0,90.272049," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**(3/2),x)","\frac{4 c^{3} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(10 b c^{2} e - 20 c^{3} d\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(8 a c^{2} e^{2} + 8 b^{2} c e^{2} - 40 b c^{2} d e + 40 c^{3} d^{2}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(12 a b c e^{3} - 24 a c^{2} d e^{2} + 2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(4 a^{2} c e^{4} + 4 a b^{2} e^{4} - 24 a b c d e^{3} + 24 a c^{2} d^{2} e^{2} - 4 b^{3} d e^{3} + 24 b^{2} c d^{2} e^{2} - 40 b c^{2} d^{3} e + 20 c^{3} d^{4}\right)}{e^{6}} - \frac{2 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{2}}{e^{6} \sqrt{d + e x}}"," ",0,"4*c**3*(d + e*x)**(9/2)/(9*e**6) + (d + e*x)**(7/2)*(10*b*c**2*e - 20*c**3*d)/(7*e**6) + (d + e*x)**(5/2)*(8*a*c**2*e**2 + 8*b**2*c*e**2 - 40*b*c**2*d*e + 40*c**3*d**2)/(5*e**6) + (d + e*x)**(3/2)*(12*a*b*c*e**3 - 24*a*c**2*d*e**2 + 2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/(3*e**6) + sqrt(d + e*x)*(4*a**2*c*e**4 + 4*a*b**2*e**4 - 24*a*b*c*d*e**3 + 24*a*c**2*d**2*e**2 - 4*b**3*d*e**3 + 24*b**2*c*d**2*e**2 - 40*b*c**2*d**3*e + 20*c**3*d**4)/e**6 - 2*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**2/(e**6*sqrt(d + e*x))","A",0
1606,1,274,0,113.801790," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**2/(e*x+d)**(5/2),x)","\frac{4 c^{3} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(10 b c^{2} e - 20 c^{3} d\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(8 a c^{2} e^{2} + 8 b^{2} c e^{2} - 40 b c^{2} d e + 40 c^{3} d^{2}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(12 a b c e^{3} - 24 a c^{2} d e^{2} + 2 b^{3} e^{3} - 24 b^{2} c d e^{2} + 60 b c^{2} d^{2} e - 40 c^{3} d^{3}\right)}{e^{6}} - \frac{4 \left(a e^{2} - b d e + c d^{2}\right) \left(a c e^{2} + b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right)}{e^{6} \sqrt{d + e x}} - \frac{2 \left(b e - 2 c d\right) \left(a e^{2} - b d e + c d^{2}\right)^{2}}{3 e^{6} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"4*c**3*(d + e*x)**(7/2)/(7*e**6) + (d + e*x)**(5/2)*(10*b*c**2*e - 20*c**3*d)/(5*e**6) + (d + e*x)**(3/2)*(8*a*c**2*e**2 + 8*b**2*c*e**2 - 40*b*c**2*d*e + 40*c**3*d**2)/(3*e**6) + sqrt(d + e*x)*(12*a*b*c*e**3 - 24*a*c**2*d*e**2 + 2*b**3*e**3 - 24*b**2*c*d*e**2 + 60*b*c**2*d**2*e - 40*c**3*d**3)/e**6 - 4*(a*e**2 - b*d*e + c*d**2)*(a*c*e**2 + b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)/(e**6*sqrt(d + e*x)) - 2*(b*e - 2*c*d)*(a*e**2 - b*d*e + c*d**2)**2/(3*e**6*(d + e*x)**(3/2))","A",0
1607,1,3529,0,126.017638," ","integrate((2*c*x+b)*(e*x+d)**(5/2)*(c*x**2+b*x+a)**3,x)","a^{3} b d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{3} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{3} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{4 a^{3} c d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{8 a^{3} c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 a^{3} c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{6 a^{2} b^{2} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{12 a^{2} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 a^{2} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{18 a^{2} b c d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{36 a^{2} b c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{18 a^{2} b c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{12 a^{2} c^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{24 a^{2} c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{12 a^{2} c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{6 a b^{3} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 a b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{6 a b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{24 a b^{2} c d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{48 a b^{2} c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{24 a b^{2} c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{30 a b c^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{60 a b c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{30 a b c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{12 a c^{3} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{24 a c^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{12 a c^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{2 b^{4} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{4 b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{10 b^{3} c d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{20 b^{3} c d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{10 b^{3} c \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{18 b^{2} c^{2} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{36 b^{2} c^{2} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{18 b^{2} c^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{14 b c^{3} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{28 b c^{3} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{14 b c^{3} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{4 c^{4} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{8 c^{4} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}} + \frac{4 c^{4} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{8}}"," ",0,"a**3*b*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**3*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**3*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 4*a**3*c*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 8*a**3*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*a**3*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 6*a**2*b**2*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 12*a**2*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*a**2*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 18*a**2*b*c*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 36*a**2*b*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 18*a**2*b*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 12*a**2*c**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 24*a**2*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 12*a**2*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 6*a*b**3*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*a*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 6*a*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 24*a*b**2*c*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 48*a*b**2*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 24*a*b**2*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 30*a*b*c**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 60*a*b*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 30*a*b*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 12*a*c**3*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 24*a*c**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 12*a*c**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 2*b**4*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 4*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 10*b**3*c*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 20*b**3*c*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 10*b**3*c*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 18*b**2*c**2*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 36*b**2*c**2*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 18*b**2*c**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 14*b*c**3*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 28*b*c**3*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 14*b*c**3*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 4*c**4*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 8*c**4*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8 + 4*c**4*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**8","A",0
1608,1,2122,0,77.354356," ","integrate((2*c*x+b)*(e*x+d)**(3/2)*(c*x**2+b*x+a)**3,x)","a^{3} b d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{3} b \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 a^{3} c d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 a^{3} c \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 a^{2} b^{2} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{6 a^{2} b^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{18 a^{2} b c d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{18 a^{2} b c \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 a^{2} c^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{12 a^{2} c^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{6 a b^{3} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{6 a b^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{24 a b^{2} c d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{24 a b^{2} c \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{30 a b c^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{30 a b c^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{12 a c^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{12 a c^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 b^{4} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 b^{4} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{10 b^{3} c d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{10 b^{3} c \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{18 b^{2} c^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{18 b^{2} c^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{14 b c^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{14 b c^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{4 c^{4} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{4 c^{4} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}}"," ",0,"a**3*b*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**3*b*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*a**3*c*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*a**3*c*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*a**2*b**2*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 6*a**2*b**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 18*a**2*b*c*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 18*a**2*b*c*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*a**2*c**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 12*a**2*c**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 6*a*b**3*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 6*a*b**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 24*a*b**2*c*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 24*a*b**2*c*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 30*a*b*c**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 30*a*b*c**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 12*a*c**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 12*a*c**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*b**4*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*b**4*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 10*b**3*c*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 10*b**3*c*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 18*b**2*c**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 18*b**2*c**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 14*b*c**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 14*b*c**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 4*c**4*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 4*c**4*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8","A",0
1609,1,843,0,13.405895," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{2 c^{4} \left(d + e x\right)^{\frac{17}{2}}}{17 e^{7}} + \frac{\left(d + e x\right)^{\frac{15}{2}} \left(7 b c^{3} e - 14 c^{4} d\right)}{15 e^{7}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(6 a c^{3} e^{2} + 9 b^{2} c^{2} e^{2} - 42 b c^{3} d e + 42 c^{4} d^{2}\right)}{13 e^{7}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(15 a b c^{2} e^{3} - 30 a c^{3} d e^{2} + 5 b^{3} c e^{3} - 45 b^{2} c^{2} d e^{2} + 105 b c^{3} d^{2} e - 70 c^{4} d^{3}\right)}{11 e^{7}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(6 a^{2} c^{2} e^{4} + 12 a b^{2} c e^{4} - 60 a b c^{2} d e^{3} + 60 a c^{3} d^{2} e^{2} + b^{4} e^{4} - 20 b^{3} c d e^{3} + 90 b^{2} c^{2} d^{2} e^{2} - 140 b c^{3} d^{3} e + 70 c^{4} d^{4}\right)}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(9 a^{2} b c e^{5} - 18 a^{2} c^{2} d e^{4} + 3 a b^{3} e^{5} - 36 a b^{2} c d e^{4} + 90 a b c^{2} d^{2} e^{3} - 60 a c^{3} d^{3} e^{2} - 3 b^{4} d e^{4} + 30 b^{3} c d^{2} e^{3} - 90 b^{2} c^{2} d^{3} e^{2} + 105 b c^{3} d^{4} e - 42 c^{4} d^{5}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 a^{3} c e^{6} + 3 a^{2} b^{2} e^{6} - 18 a^{2} b c d e^{5} + 18 a^{2} c^{2} d^{2} e^{4} - 6 a b^{3} d e^{5} + 36 a b^{2} c d^{2} e^{4} - 60 a b c^{2} d^{3} e^{3} + 30 a c^{3} d^{4} e^{2} + 3 b^{4} d^{2} e^{4} - 20 b^{3} c d^{3} e^{3} + 45 b^{2} c^{2} d^{4} e^{2} - 42 b c^{3} d^{5} e + 14 c^{4} d^{6}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{3} b e^{7} - 2 a^{3} c d e^{6} - 3 a^{2} b^{2} d e^{6} + 9 a^{2} b c d^{2} e^{5} - 6 a^{2} c^{2} d^{3} e^{4} + 3 a b^{3} d^{2} e^{5} - 12 a b^{2} c d^{3} e^{4} + 15 a b c^{2} d^{4} e^{3} - 6 a c^{3} d^{5} e^{2} - b^{4} d^{3} e^{4} + 5 b^{3} c d^{4} e^{3} - 9 b^{2} c^{2} d^{5} e^{2} + 7 b c^{3} d^{6} e - 2 c^{4} d^{7}\right)}{3 e^{7}}\right)}{e}"," ",0,"2*(2*c**4*(d + e*x)**(17/2)/(17*e**7) + (d + e*x)**(15/2)*(7*b*c**3*e - 14*c**4*d)/(15*e**7) + (d + e*x)**(13/2)*(6*a*c**3*e**2 + 9*b**2*c**2*e**2 - 42*b*c**3*d*e + 42*c**4*d**2)/(13*e**7) + (d + e*x)**(11/2)*(15*a*b*c**2*e**3 - 30*a*c**3*d*e**2 + 5*b**3*c*e**3 - 45*b**2*c**2*d*e**2 + 105*b*c**3*d**2*e - 70*c**4*d**3)/(11*e**7) + (d + e*x)**(9/2)*(6*a**2*c**2*e**4 + 12*a*b**2*c*e**4 - 60*a*b*c**2*d*e**3 + 60*a*c**3*d**2*e**2 + b**4*e**4 - 20*b**3*c*d*e**3 + 90*b**2*c**2*d**2*e**2 - 140*b*c**3*d**3*e + 70*c**4*d**4)/(9*e**7) + (d + e*x)**(7/2)*(9*a**2*b*c*e**5 - 18*a**2*c**2*d*e**4 + 3*a*b**3*e**5 - 36*a*b**2*c*d*e**4 + 90*a*b*c**2*d**2*e**3 - 60*a*c**3*d**3*e**2 - 3*b**4*d*e**4 + 30*b**3*c*d**2*e**3 - 90*b**2*c**2*d**3*e**2 + 105*b*c**3*d**4*e - 42*c**4*d**5)/(7*e**7) + (d + e*x)**(5/2)*(2*a**3*c*e**6 + 3*a**2*b**2*e**6 - 18*a**2*b*c*d*e**5 + 18*a**2*c**2*d**2*e**4 - 6*a*b**3*d*e**5 + 36*a*b**2*c*d**2*e**4 - 60*a*b*c**2*d**3*e**3 + 30*a*c**3*d**4*e**2 + 3*b**4*d**2*e**4 - 20*b**3*c*d**3*e**3 + 45*b**2*c**2*d**4*e**2 - 42*b*c**3*d**5*e + 14*c**4*d**6)/(5*e**7) + (d + e*x)**(3/2)*(a**3*b*e**7 - 2*a**3*c*d*e**6 - 3*a**2*b**2*d*e**6 + 9*a**2*b*c*d**2*e**5 - 6*a**2*c**2*d**3*e**4 + 3*a*b**3*d**2*e**5 - 12*a*b**2*c*d**3*e**4 + 15*a*b*c**2*d**4*e**3 - 6*a*c**3*d**5*e**2 - b**4*d**3*e**4 + 5*b**3*c*d**4*e**3 - 9*b**2*c**2*d**5*e**2 + 7*b*c**3*d**6*e - 2*c**4*d**7)/(3*e**7))/e","A",0
1610,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1611,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1612,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**3/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1613,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1614,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1615,-1,0,0,0.000000," ","integrate((2*c*x+b)/(c*x**2+b*x+a)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1616,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1617,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(5/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1618,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(5/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1619,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1620,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1621,-1,0,0,0.000000," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**2/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1622,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1623,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(7/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1624,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(5/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1625,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1626,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1627,-1,0,0,0.000000," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1628,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(b + 2 c x\right) \sqrt{d + e x} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(d + e*x)*sqrt(a + b*x + c*x**2), x)","F",0
1629,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/sqrt(d + e*x), x)","F",0
1630,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**(3/2), x)","F",0
1631,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**(5/2), x)","F",0
1632,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\left(b + 2 c x\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**(7/2), x)","F",0
1633,-1,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1634,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x)**(3/2), x)","F",0
1635,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x)**(5/2), x)","F",0
1636,0,0,0,0.000000," ","integrate((2*c*x+b)*(c*x**2+b*x+a)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(b + 2 c x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x)**(7/2), x)","F",0
1637,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{\frac{5}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**(5/2)/sqrt(a + b*x + c*x**2), x)","F",0
1638,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{\frac{3}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**(3/2)/sqrt(a + b*x + c*x**2), x)","F",0
1639,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(b + 2 c x\right) \sqrt{d + e x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(d + e*x)/sqrt(a + b*x + c*x**2), x)","F",0
1640,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\sqrt{d + e x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/(sqrt(d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
1641,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)**(3/2)*sqrt(a + b*x + c*x**2)), x)","F",0
1642,0,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{b + 2 c x}{\left(d + e x\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((b + 2*c*x)/((d + e*x)**(5/2)*sqrt(a + b*x + c*x**2)), x)","F",0
1643,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(7/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1644,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(5/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1645,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1646,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(b + 2 c x\right) \sqrt{d + e x}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b + 2*c*x)*sqrt(d + e*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
1647,-1,0,0,0.000000," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1648,-1,0,0,0.000000," ","integrate((2*c*x+b)/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1649,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(7/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1650,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(5/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1651,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1652,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1653,-1,0,0,0.000000," ","integrate((2*c*x+b)/(c*x**2+b*x+a)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1654,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**m*(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1655,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**m*(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1656,1,4760,0,4.713310," ","integrate((2*c*x+b)*(e*x+d)**m*(c*x**2+b*x+a),x)","\begin{cases} d^{m} \left(a b x + a c x^{2} + \frac{b^{2} x^{2}}{2} + b c x^{3} + \frac{c^{2} x^{4}}{2}\right) & \text{for}\: e = 0 \\- \frac{2 a b e^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 a c d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 a c e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{b^{2} d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 b^{2} e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 b c d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{18 b c d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{18 b c e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{12 c^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{22 c^{2} d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{36 c^{2} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{54 c^{2} d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{36 c^{2} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{36 c^{2} d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{12 c^{2} e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{a b e^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 a c d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{4 a c e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{b^{2} d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 b^{2} e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 b c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{9 b c d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{12 b c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{12 b c d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 b c e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{18 c^{2} d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{24 c^{2} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{24 c^{2} d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c^{2} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 c^{2} e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\- \frac{a b e^{3}}{d e^{4} + e^{5} x} + \frac{2 a c d e^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} + \frac{2 a c d e^{2}}{d e^{4} + e^{5} x} + \frac{2 a c e^{3} x \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} + \frac{b^{2} d e^{2} \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} + \frac{b^{2} d e^{2}}{d e^{4} + e^{5} x} + \frac{b^{2} e^{3} x \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} - \frac{6 b c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} - \frac{6 b c d^{2} e}{d e^{4} + e^{5} x} - \frac{6 b c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} + \frac{3 b c e^{3} x^{2}}{d e^{4} + e^{5} x} + \frac{6 c^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} + \frac{6 c^{2} d^{3}}{d e^{4} + e^{5} x} + \frac{6 c^{2} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{d e^{4} + e^{5} x} - \frac{3 c^{2} d e^{2} x^{2}}{d e^{4} + e^{5} x} + \frac{c^{2} e^{3} x^{3}}{d e^{4} + e^{5} x} & \text{for}\: m = -2 \\\frac{a b \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{2 a c d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{2 a c x}{e} - \frac{b^{2} d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{b^{2} x}{e} + \frac{3 b c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{3 b c d x}{e^{2}} + \frac{3 b c x^{2}}{2 e} - \frac{2 c^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{2 c^{2} d^{2} x}{e^{3}} - \frac{c^{2} d x^{2}}{e^{2}} + \frac{2 c^{2} x^{3}}{3 e} & \text{for}\: m = -1 \\\frac{a b d e^{3} m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 a b d e^{3} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 a b d e^{3} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a b d e^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a b e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 a b e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 a b e^{4} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a b e^{4} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 a c d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{14 a c d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{24 a c d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 a c d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 a c d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a c d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 a c e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{16 a c e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{38 a c e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a c e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{b^{2} d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 b^{2} d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 b^{2} d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b^{2} d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 b^{2} d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 b^{2} d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b^{2} e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 b^{2} e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 b^{2} e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 b^{2} e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 b c d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 b c d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 b c d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{24 b c d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 b c d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{15 b c d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 b c d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 b c e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{21 b c e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{42 b c e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 b c e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 c^{2} d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 c^{2} d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 c^{2} d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 c^{2} d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 c^{2} d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c^{2} d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 c^{2} d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 c^{2} e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 c^{2} e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{22 c^{2} e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 c^{2} e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a*b*x + a*c*x**2 + b**2*x**2/2 + b*c*x**3 + c**2*x**4/2), Eq(e, 0)), (-2*a*b*e**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*a*c*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*a*c*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - b**2*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*b**2*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*b*c*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 18*b*c*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 18*b*c*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 12*c**2*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 22*c**2*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 36*c**2*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 54*c**2*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 36*c**2*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 36*c**2*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 12*c**2*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-a*b*e**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*a*c*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 4*a*c*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - b**2*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*b**2*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*b*c*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 9*b*c*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 12*b*c*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 12*b*c*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*b*c*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c**2*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 18*c**2*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 24*c**2*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 24*c**2*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c**2*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*c**2*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (-a*b*e**3/(d*e**4 + e**5*x) + 2*a*c*d*e**2*log(d/e + x)/(d*e**4 + e**5*x) + 2*a*c*d*e**2/(d*e**4 + e**5*x) + 2*a*c*e**3*x*log(d/e + x)/(d*e**4 + e**5*x) + b**2*d*e**2*log(d/e + x)/(d*e**4 + e**5*x) + b**2*d*e**2/(d*e**4 + e**5*x) + b**2*e**3*x*log(d/e + x)/(d*e**4 + e**5*x) - 6*b*c*d**2*e*log(d/e + x)/(d*e**4 + e**5*x) - 6*b*c*d**2*e/(d*e**4 + e**5*x) - 6*b*c*d*e**2*x*log(d/e + x)/(d*e**4 + e**5*x) + 3*b*c*e**3*x**2/(d*e**4 + e**5*x) + 6*c**2*d**3*log(d/e + x)/(d*e**4 + e**5*x) + 6*c**2*d**3/(d*e**4 + e**5*x) + 6*c**2*d**2*e*x*log(d/e + x)/(d*e**4 + e**5*x) - 3*c**2*d*e**2*x**2/(d*e**4 + e**5*x) + c**2*e**3*x**3/(d*e**4 + e**5*x), Eq(m, -2)), (a*b*log(d/e + x)/e - 2*a*c*d*log(d/e + x)/e**2 + 2*a*c*x/e - b**2*d*log(d/e + x)/e**2 + b**2*x/e + 3*b*c*d**2*log(d/e + x)/e**3 - 3*b*c*d*x/e**2 + 3*b*c*x**2/(2*e) - 2*c**2*d**3*log(d/e + x)/e**4 + 2*c**2*d**2*x/e**3 - c**2*d*x**2/e**2 + 2*c**2*x**3/(3*e), Eq(m, -1)), (a*b*d*e**3*m**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*a*b*d*e**3*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*a*b*d*e**3*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*b*d*e**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*b*e**4*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*a*b*e**4*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*a*b*e**4*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*b*e**4*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*a*c*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 14*a*c*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 24*a*c*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*a*c*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*a*c*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*c*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*a*c*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 16*a*c*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 38*a*c*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*c*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - b**2*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*b**2*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*b**2*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b**2*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*b**2*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*b**2*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b**2*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*b**2*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*b**2*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*b**2*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*b*c*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*b*c*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*b*c*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 24*b*c*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*b*c*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 15*b*c*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*b*c*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*b*c*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 21*b*c*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 42*b*c*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*b*c*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*c**2*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*c**2*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*c**2*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*c**2*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*c**2*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c**2*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*c**2*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*c**2*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*c**2*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 22*c**2*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*c**2*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
1657,0,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**m/(c*x**2+b*x+a),x)","\int \frac{\left(b + 2 c x\right) \left(d + e x\right)^{m}}{a + b x + c x^{2}}\, dx"," ",0,"Integral((b + 2*c*x)*(d + e*x)**m/(a + b*x + c*x**2), x)","F",0
1658,-1,0,0,0.000000," ","integrate((2*c*x+b)*(e*x+d)**m/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1659,1,481,0,0.132072," ","integrate((B*x+A)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} d^{5} x + \frac{B b^{2} e^{5} x^{9}}{9} + x^{8} \left(\frac{A b^{2} e^{5}}{8} + \frac{B a b e^{5}}{4} + \frac{5 B b^{2} d e^{4}}{8}\right) + x^{7} \left(\frac{2 A a b e^{5}}{7} + \frac{5 A b^{2} d e^{4}}{7} + \frac{B a^{2} e^{5}}{7} + \frac{10 B a b d e^{4}}{7} + \frac{10 B b^{2} d^{2} e^{3}}{7}\right) + x^{6} \left(\frac{A a^{2} e^{5}}{6} + \frac{5 A a b d e^{4}}{3} + \frac{5 A b^{2} d^{2} e^{3}}{3} + \frac{5 B a^{2} d e^{4}}{6} + \frac{10 B a b d^{2} e^{3}}{3} + \frac{5 B b^{2} d^{3} e^{2}}{3}\right) + x^{5} \left(A a^{2} d e^{4} + 4 A a b d^{2} e^{3} + 2 A b^{2} d^{3} e^{2} + 2 B a^{2} d^{2} e^{3} + 4 B a b d^{3} e^{2} + B b^{2} d^{4} e\right) + x^{4} \left(\frac{5 A a^{2} d^{2} e^{3}}{2} + 5 A a b d^{3} e^{2} + \frac{5 A b^{2} d^{4} e}{4} + \frac{5 B a^{2} d^{3} e^{2}}{2} + \frac{5 B a b d^{4} e}{2} + \frac{B b^{2} d^{5}}{4}\right) + x^{3} \left(\frac{10 A a^{2} d^{3} e^{2}}{3} + \frac{10 A a b d^{4} e}{3} + \frac{A b^{2} d^{5}}{3} + \frac{5 B a^{2} d^{4} e}{3} + \frac{2 B a b d^{5}}{3}\right) + x^{2} \left(\frac{5 A a^{2} d^{4} e}{2} + A a b d^{5} + \frac{B a^{2} d^{5}}{2}\right)"," ",0,"A*a**2*d**5*x + B*b**2*e**5*x**9/9 + x**8*(A*b**2*e**5/8 + B*a*b*e**5/4 + 5*B*b**2*d*e**4/8) + x**7*(2*A*a*b*e**5/7 + 5*A*b**2*d*e**4/7 + B*a**2*e**5/7 + 10*B*a*b*d*e**4/7 + 10*B*b**2*d**2*e**3/7) + x**6*(A*a**2*e**5/6 + 5*A*a*b*d*e**4/3 + 5*A*b**2*d**2*e**3/3 + 5*B*a**2*d*e**4/6 + 10*B*a*b*d**2*e**3/3 + 5*B*b**2*d**3*e**2/3) + x**5*(A*a**2*d*e**4 + 4*A*a*b*d**2*e**3 + 2*A*b**2*d**3*e**2 + 2*B*a**2*d**2*e**3 + 4*B*a*b*d**3*e**2 + B*b**2*d**4*e) + x**4*(5*A*a**2*d**2*e**3/2 + 5*A*a*b*d**3*e**2 + 5*A*b**2*d**4*e/4 + 5*B*a**2*d**3*e**2/2 + 5*B*a*b*d**4*e/2 + B*b**2*d**5/4) + x**3*(10*A*a**2*d**3*e**2/3 + 10*A*a*b*d**4*e/3 + A*b**2*d**5/3 + 5*B*a**2*d**4*e/3 + 2*B*a*b*d**5/3) + x**2*(5*A*a**2*d**4*e/2 + A*a*b*d**5 + B*a**2*d**5/2)","B",0
1660,1,384,0,0.117679," ","integrate((B*x+A)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} d^{4} x + \frac{B b^{2} e^{4} x^{8}}{8} + x^{7} \left(\frac{A b^{2} e^{4}}{7} + \frac{2 B a b e^{4}}{7} + \frac{4 B b^{2} d e^{3}}{7}\right) + x^{6} \left(\frac{A a b e^{4}}{3} + \frac{2 A b^{2} d e^{3}}{3} + \frac{B a^{2} e^{4}}{6} + \frac{4 B a b d e^{3}}{3} + B b^{2} d^{2} e^{2}\right) + x^{5} \left(\frac{A a^{2} e^{4}}{5} + \frac{8 A a b d e^{3}}{5} + \frac{6 A b^{2} d^{2} e^{2}}{5} + \frac{4 B a^{2} d e^{3}}{5} + \frac{12 B a b d^{2} e^{2}}{5} + \frac{4 B b^{2} d^{3} e}{5}\right) + x^{4} \left(A a^{2} d e^{3} + 3 A a b d^{2} e^{2} + A b^{2} d^{3} e + \frac{3 B a^{2} d^{2} e^{2}}{2} + 2 B a b d^{3} e + \frac{B b^{2} d^{4}}{4}\right) + x^{3} \left(2 A a^{2} d^{2} e^{2} + \frac{8 A a b d^{3} e}{3} + \frac{A b^{2} d^{4}}{3} + \frac{4 B a^{2} d^{3} e}{3} + \frac{2 B a b d^{4}}{3}\right) + x^{2} \left(2 A a^{2} d^{3} e + A a b d^{4} + \frac{B a^{2} d^{4}}{2}\right)"," ",0,"A*a**2*d**4*x + B*b**2*e**4*x**8/8 + x**7*(A*b**2*e**4/7 + 2*B*a*b*e**4/7 + 4*B*b**2*d*e**3/7) + x**6*(A*a*b*e**4/3 + 2*A*b**2*d*e**3/3 + B*a**2*e**4/6 + 4*B*a*b*d*e**3/3 + B*b**2*d**2*e**2) + x**5*(A*a**2*e**4/5 + 8*A*a*b*d*e**3/5 + 6*A*b**2*d**2*e**2/5 + 4*B*a**2*d*e**3/5 + 12*B*a*b*d**2*e**2/5 + 4*B*b**2*d**3*e/5) + x**4*(A*a**2*d*e**3 + 3*A*a*b*d**2*e**2 + A*b**2*d**3*e + 3*B*a**2*d**2*e**2/2 + 2*B*a*b*d**3*e + B*b**2*d**4/4) + x**3*(2*A*a**2*d**2*e**2 + 8*A*a*b*d**3*e/3 + A*b**2*d**4/3 + 4*B*a**2*d**3*e/3 + 2*B*a*b*d**4/3) + x**2*(2*A*a**2*d**3*e + A*a*b*d**4 + B*a**2*d**4/2)","B",0
1661,1,296,0,0.106190," ","integrate((B*x+A)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} d^{3} x + \frac{B b^{2} e^{3} x^{7}}{7} + x^{6} \left(\frac{A b^{2} e^{3}}{6} + \frac{B a b e^{3}}{3} + \frac{B b^{2} d e^{2}}{2}\right) + x^{5} \left(\frac{2 A a b e^{3}}{5} + \frac{3 A b^{2} d e^{2}}{5} + \frac{B a^{2} e^{3}}{5} + \frac{6 B a b d e^{2}}{5} + \frac{3 B b^{2} d^{2} e}{5}\right) + x^{4} \left(\frac{A a^{2} e^{3}}{4} + \frac{3 A a b d e^{2}}{2} + \frac{3 A b^{2} d^{2} e}{4} + \frac{3 B a^{2} d e^{2}}{4} + \frac{3 B a b d^{2} e}{2} + \frac{B b^{2} d^{3}}{4}\right) + x^{3} \left(A a^{2} d e^{2} + 2 A a b d^{2} e + \frac{A b^{2} d^{3}}{3} + B a^{2} d^{2} e + \frac{2 B a b d^{3}}{3}\right) + x^{2} \left(\frac{3 A a^{2} d^{2} e}{2} + A a b d^{3} + \frac{B a^{2} d^{3}}{2}\right)"," ",0,"A*a**2*d**3*x + B*b**2*e**3*x**7/7 + x**6*(A*b**2*e**3/6 + B*a*b*e**3/3 + B*b**2*d*e**2/2) + x**5*(2*A*a*b*e**3/5 + 3*A*b**2*d*e**2/5 + B*a**2*e**3/5 + 6*B*a*b*d*e**2/5 + 3*B*b**2*d**2*e/5) + x**4*(A*a**2*e**3/4 + 3*A*a*b*d*e**2/2 + 3*A*b**2*d**2*e/4 + 3*B*a**2*d*e**2/4 + 3*B*a*b*d**2*e/2 + B*b**2*d**3/4) + x**3*(A*a**2*d*e**2 + 2*A*a*b*d**2*e + A*b**2*d**3/3 + B*a**2*d**2*e + 2*B*a*b*d**3/3) + x**2*(3*A*a**2*d**2*e/2 + A*a*b*d**3 + B*a**2*d**3/2)","B",0
1662,1,202,0,0.094139," ","integrate((B*x+A)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} d^{2} x + \frac{B b^{2} e^{2} x^{6}}{6} + x^{5} \left(\frac{A b^{2} e^{2}}{5} + \frac{2 B a b e^{2}}{5} + \frac{2 B b^{2} d e}{5}\right) + x^{4} \left(\frac{A a b e^{2}}{2} + \frac{A b^{2} d e}{2} + \frac{B a^{2} e^{2}}{4} + B a b d e + \frac{B b^{2} d^{2}}{4}\right) + x^{3} \left(\frac{A a^{2} e^{2}}{3} + \frac{4 A a b d e}{3} + \frac{A b^{2} d^{2}}{3} + \frac{2 B a^{2} d e}{3} + \frac{2 B a b d^{2}}{3}\right) + x^{2} \left(A a^{2} d e + A a b d^{2} + \frac{B a^{2} d^{2}}{2}\right)"," ",0,"A*a**2*d**2*x + B*b**2*e**2*x**6/6 + x**5*(A*b**2*e**2/5 + 2*B*a*b*e**2/5 + 2*B*b**2*d*e/5) + x**4*(A*a*b*e**2/2 + A*b**2*d*e/2 + B*a**2*e**2/4 + B*a*b*d*e + B*b**2*d**2/4) + x**3*(A*a**2*e**2/3 + 4*A*a*b*d*e/3 + A*b**2*d**2/3 + 2*B*a**2*d*e/3 + 2*B*a*b*d**2/3) + x**2*(A*a**2*d*e + A*a*b*d**2 + B*a**2*d**2/2)","A",0
1663,1,116,0,0.078090," ","integrate((B*x+A)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} d x + \frac{B b^{2} e x^{5}}{5} + x^{4} \left(\frac{A b^{2} e}{4} + \frac{B a b e}{2} + \frac{B b^{2} d}{4}\right) + x^{3} \left(\frac{2 A a b e}{3} + \frac{A b^{2} d}{3} + \frac{B a^{2} e}{3} + \frac{2 B a b d}{3}\right) + x^{2} \left(\frac{A a^{2} e}{2} + A a b d + \frac{B a^{2} d}{2}\right)"," ",0,"A*a**2*d*x + B*b**2*e*x**5/5 + x**4*(A*b**2*e/4 + B*a*b*e/2 + B*b**2*d/4) + x**3*(2*A*a*b*e/3 + A*b**2*d/3 + B*a**2*e/3 + 2*B*a*b*d/3) + x**2*(A*a**2*e/2 + A*a*b*d + B*a**2*d/2)","A",0
1664,1,49,0,0.068904," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} x + \frac{B b^{2} x^{4}}{4} + x^{3} \left(\frac{A b^{2}}{3} + \frac{2 B a b}{3}\right) + x^{2} \left(A a b + \frac{B a^{2}}{2}\right)"," ",0,"A*a**2*x + B*b**2*x**4/4 + x**3*(A*b**2/3 + 2*B*a*b/3) + x**2*(A*a*b + B*a**2/2)","A",0
1665,1,117,0,0.433334," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d),x)","\frac{B b^{2} x^{3}}{3 e} + x^{2} \left(\frac{A b^{2}}{2 e} + \frac{B a b}{e} - \frac{B b^{2} d}{2 e^{2}}\right) + x \left(\frac{2 A a b}{e} - \frac{A b^{2} d}{e^{2}} + \frac{B a^{2}}{e} - \frac{2 B a b d}{e^{2}} + \frac{B b^{2} d^{2}}{e^{3}}\right) - \frac{\left(- A e + B d\right) \left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*b**2*x**3/(3*e) + x**2*(A*b**2/(2*e) + B*a*b/e - B*b**2*d/(2*e**2)) + x*(2*A*a*b/e - A*b**2*d/e**2 + B*a**2/e - 2*B*a*b*d/e**2 + B*b**2*d**2/e**3) - (-A*e + B*d)*(a*e - b*d)**2*log(d + e*x)/e**4","A",0
1666,1,151,0,0.882037," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**2,x)","\frac{B b^{2} x^{2}}{2 e^{2}} + x \left(\frac{A b^{2}}{e^{2}} + \frac{2 B a b}{e^{2}} - \frac{2 B b^{2} d}{e^{3}}\right) + \frac{- A a^{2} e^{3} + 2 A a b d e^{2} - A b^{2} d^{2} e + B a^{2} d e^{2} - 2 B a b d^{2} e + B b^{2} d^{3}}{d e^{4} + e^{5} x} + \frac{\left(a e - b d\right) \left(2 A b e + B a e - 3 B b d\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*b**2*x**2/(2*e**2) + x*(A*b**2/e**2 + 2*B*a*b/e**2 - 2*B*b**2*d/e**3) + (-A*a**2*e**3 + 2*A*a*b*d*e**2 - A*b**2*d**2*e + B*a**2*d*e**2 - 2*B*a*b*d**2*e + B*b**2*d**3)/(d*e**4 + e**5*x) + (a*e - b*d)*(2*A*b*e + B*a*e - 3*B*b*d)*log(d + e*x)/e**4","A",0
1667,1,187,0,2.414813," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**3,x)","\frac{B b^{2} x}{e^{3}} + \frac{b \left(A b e + 2 B a e - 3 B b d\right) \log{\left(d + e x \right)}}{e^{4}} + \frac{- A a^{2} e^{3} - 2 A a b d e^{2} + 3 A b^{2} d^{2} e - B a^{2} d e^{2} + 6 B a b d^{2} e - 5 B b^{2} d^{3} + x \left(- 4 A a b e^{3} + 4 A b^{2} d e^{2} - 2 B a^{2} e^{3} + 8 B a b d e^{2} - 6 B b^{2} d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}}"," ",0,"B*b**2*x/e**3 + b*(A*b*e + 2*B*a*e - 3*B*b*d)*log(d + e*x)/e**4 + (-A*a**2*e**3 - 2*A*a*b*d*e**2 + 3*A*b**2*d**2*e - B*a**2*d*e**2 + 6*B*a*b*d**2*e - 5*B*b**2*d**3 + x*(-4*A*a*b*e**3 + 4*A*b**2*d*e**2 - 2*B*a**2*e**3 + 8*B*a*b*d*e**2 - 6*B*b**2*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2)","A",0
1668,1,211,0,5.764467," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**4,x)","\frac{B b^{2} \log{\left(d + e x \right)}}{e^{4}} + \frac{- 2 A a^{2} e^{3} - 2 A a b d e^{2} - 2 A b^{2} d^{2} e - B a^{2} d e^{2} - 4 B a b d^{2} e + 11 B b^{2} d^{3} + x^{2} \left(- 6 A b^{2} e^{3} - 12 B a b e^{3} + 18 B b^{2} d e^{2}\right) + x \left(- 6 A a b e^{3} - 6 A b^{2} d e^{2} - 3 B a^{2} e^{3} - 12 B a b d e^{2} + 27 B b^{2} d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"B*b**2*log(d + e*x)/e**4 + (-2*A*a**2*e**3 - 2*A*a*b*d*e**2 - 2*A*b**2*d**2*e - B*a**2*d*e**2 - 4*B*a*b*d**2*e + 11*B*b**2*d**3 + x**2*(-6*A*b**2*e**3 - 12*B*a*b*e**3 + 18*B*b**2*d*e**2) + x*(-6*A*a*b*e**3 - 6*A*b**2*d*e**2 - 3*B*a**2*e**3 - 12*B*a*b*d*e**2 + 27*B*b**2*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","B",0
1669,1,223,0,11.665182," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**5,x)","\frac{- 3 A a^{2} e^{3} - 2 A a b d e^{2} - A b^{2} d^{2} e - B a^{2} d e^{2} - 2 B a b d^{2} e - 3 B b^{2} d^{3} - 12 B b^{2} e^{3} x^{3} + x^{2} \left(- 6 A b^{2} e^{3} - 12 B a b e^{3} - 18 B b^{2} d e^{2}\right) + x \left(- 8 A a b e^{3} - 4 A b^{2} d e^{2} - 4 B a^{2} e^{3} - 8 B a b d e^{2} - 12 B b^{2} d^{2} e\right)}{12 d^{4} e^{4} + 48 d^{3} e^{5} x + 72 d^{2} e^{6} x^{2} + 48 d e^{7} x^{3} + 12 e^{8} x^{4}}"," ",0,"(-3*A*a**2*e**3 - 2*A*a*b*d*e**2 - A*b**2*d**2*e - B*a**2*d*e**2 - 2*B*a*b*d**2*e - 3*B*b**2*d**3 - 12*B*b**2*e**3*x**3 + x**2*(-6*A*b**2*e**3 - 12*B*a*b*e**3 - 18*B*b**2*d*e**2) + x*(-8*A*a*b*e**3 - 4*A*b**2*d*e**2 - 4*B*a**2*e**3 - 8*B*a*b*d*e**2 - 12*B*b**2*d**2*e))/(12*d**4*e**4 + 48*d**3*e**5*x + 72*d**2*e**6*x**2 + 48*d*e**7*x**3 + 12*e**8*x**4)","B",0
1670,1,238,0,21.111081," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**6,x)","\frac{- 12 A a^{2} e^{3} - 6 A a b d e^{2} - 2 A b^{2} d^{2} e - 3 B a^{2} d e^{2} - 4 B a b d^{2} e - 3 B b^{2} d^{3} - 30 B b^{2} e^{3} x^{3} + x^{2} \left(- 20 A b^{2} e^{3} - 40 B a b e^{3} - 30 B b^{2} d e^{2}\right) + x \left(- 30 A a b e^{3} - 10 A b^{2} d e^{2} - 15 B a^{2} e^{3} - 20 B a b d e^{2} - 15 B b^{2} d^{2} e\right)}{60 d^{5} e^{4} + 300 d^{4} e^{5} x + 600 d^{3} e^{6} x^{2} + 600 d^{2} e^{7} x^{3} + 300 d e^{8} x^{4} + 60 e^{9} x^{5}}"," ",0,"(-12*A*a**2*e**3 - 6*A*a*b*d*e**2 - 2*A*b**2*d**2*e - 3*B*a**2*d*e**2 - 4*B*a*b*d**2*e - 3*B*b**2*d**3 - 30*B*b**2*e**3*x**3 + x**2*(-20*A*b**2*e**3 - 40*B*a*b*e**3 - 30*B*b**2*d*e**2) + x*(-30*A*a*b*e**3 - 10*A*b**2*d*e**2 - 15*B*a**2*e**3 - 20*B*a*b*d*e**2 - 15*B*b**2*d**2*e))/(60*d**5*e**4 + 300*d**4*e**5*x + 600*d**3*e**6*x**2 + 600*d**2*e**7*x**3 + 300*d*e**8*x**4 + 60*e**9*x**5)","B",0
1671,1,246,0,36.793746," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**7,x)","\frac{- 10 A a^{2} e^{3} - 4 A a b d e^{2} - A b^{2} d^{2} e - 2 B a^{2} d e^{2} - 2 B a b d^{2} e - B b^{2} d^{3} - 20 B b^{2} e^{3} x^{3} + x^{2} \left(- 15 A b^{2} e^{3} - 30 B a b e^{3} - 15 B b^{2} d e^{2}\right) + x \left(- 24 A a b e^{3} - 6 A b^{2} d e^{2} - 12 B a^{2} e^{3} - 12 B a b d e^{2} - 6 B b^{2} d^{2} e\right)}{60 d^{6} e^{4} + 360 d^{5} e^{5} x + 900 d^{4} e^{6} x^{2} + 1200 d^{3} e^{7} x^{3} + 900 d^{2} e^{8} x^{4} + 360 d e^{9} x^{5} + 60 e^{10} x^{6}}"," ",0,"(-10*A*a**2*e**3 - 4*A*a*b*d*e**2 - A*b**2*d**2*e - 2*B*a**2*d*e**2 - 2*B*a*b*d**2*e - B*b**2*d**3 - 20*B*b**2*e**3*x**3 + x**2*(-15*A*b**2*e**3 - 30*B*a*b*e**3 - 15*B*b**2*d*e**2) + x*(-24*A*a*b*e**3 - 6*A*b**2*d*e**2 - 12*B*a**2*e**3 - 12*B*a*b*d*e**2 - 6*B*b**2*d**2*e))/(60*d**6*e**4 + 360*d**5*e**5*x + 900*d**4*e**6*x**2 + 1200*d**3*e**7*x**3 + 900*d**2*e**8*x**4 + 360*d*e**9*x**5 + 60*e**10*x**6)","B",0
1672,1,262,0,60.721041," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**8,x)","\frac{- 60 A a^{2} e^{3} - 20 A a b d e^{2} - 4 A b^{2} d^{2} e - 10 B a^{2} d e^{2} - 8 B a b d^{2} e - 3 B b^{2} d^{3} - 105 B b^{2} e^{3} x^{3} + x^{2} \left(- 84 A b^{2} e^{3} - 168 B a b e^{3} - 63 B b^{2} d e^{2}\right) + x \left(- 140 A a b e^{3} - 28 A b^{2} d e^{2} - 70 B a^{2} e^{3} - 56 B a b d e^{2} - 21 B b^{2} d^{2} e\right)}{420 d^{7} e^{4} + 2940 d^{6} e^{5} x + 8820 d^{5} e^{6} x^{2} + 14700 d^{4} e^{7} x^{3} + 14700 d^{3} e^{8} x^{4} + 8820 d^{2} e^{9} x^{5} + 2940 d e^{10} x^{6} + 420 e^{11} x^{7}}"," ",0,"(-60*A*a**2*e**3 - 20*A*a*b*d*e**2 - 4*A*b**2*d**2*e - 10*B*a**2*d*e**2 - 8*B*a*b*d**2*e - 3*B*b**2*d**3 - 105*B*b**2*e**3*x**3 + x**2*(-84*A*b**2*e**3 - 168*B*a*b*e**3 - 63*B*b**2*d*e**2) + x*(-140*A*a*b*e**3 - 28*A*b**2*d*e**2 - 70*B*a**2*e**3 - 56*B*a*b*d*e**2 - 21*B*b**2*d**2*e))/(420*d**7*e**4 + 2940*d**6*e**5*x + 8820*d**5*e**6*x**2 + 14700*d**4*e**7*x**3 + 14700*d**3*e**8*x**4 + 8820*d**2*e**9*x**5 + 2940*d*e**10*x**6 + 420*e**11*x**7)","B",0
1673,1,1210,0,0.217505," ","integrate((B*x+A)*(e*x+d)**7*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{7} x + \frac{B b^{4} e^{7} x^{13}}{13} + x^{12} \left(\frac{A b^{4} e^{7}}{12} + \frac{B a b^{3} e^{7}}{3} + \frac{7 B b^{4} d e^{6}}{12}\right) + x^{11} \left(\frac{4 A a b^{3} e^{7}}{11} + \frac{7 A b^{4} d e^{6}}{11} + \frac{6 B a^{2} b^{2} e^{7}}{11} + \frac{28 B a b^{3} d e^{6}}{11} + \frac{21 B b^{4} d^{2} e^{5}}{11}\right) + x^{10} \left(\frac{3 A a^{2} b^{2} e^{7}}{5} + \frac{14 A a b^{3} d e^{6}}{5} + \frac{21 A b^{4} d^{2} e^{5}}{10} + \frac{2 B a^{3} b e^{7}}{5} + \frac{21 B a^{2} b^{2} d e^{6}}{5} + \frac{42 B a b^{3} d^{2} e^{5}}{5} + \frac{7 B b^{4} d^{3} e^{4}}{2}\right) + x^{9} \left(\frac{4 A a^{3} b e^{7}}{9} + \frac{14 A a^{2} b^{2} d e^{6}}{3} + \frac{28 A a b^{3} d^{2} e^{5}}{3} + \frac{35 A b^{4} d^{3} e^{4}}{9} + \frac{B a^{4} e^{7}}{9} + \frac{28 B a^{3} b d e^{6}}{9} + 14 B a^{2} b^{2} d^{2} e^{5} + \frac{140 B a b^{3} d^{3} e^{4}}{9} + \frac{35 B b^{4} d^{4} e^{3}}{9}\right) + x^{8} \left(\frac{A a^{4} e^{7}}{8} + \frac{7 A a^{3} b d e^{6}}{2} + \frac{63 A a^{2} b^{2} d^{2} e^{5}}{4} + \frac{35 A a b^{3} d^{3} e^{4}}{2} + \frac{35 A b^{4} d^{4} e^{3}}{8} + \frac{7 B a^{4} d e^{6}}{8} + \frac{21 B a^{3} b d^{2} e^{5}}{2} + \frac{105 B a^{2} b^{2} d^{3} e^{4}}{4} + \frac{35 B a b^{3} d^{4} e^{3}}{2} + \frac{21 B b^{4} d^{5} e^{2}}{8}\right) + x^{7} \left(A a^{4} d e^{6} + 12 A a^{3} b d^{2} e^{5} + 30 A a^{2} b^{2} d^{3} e^{4} + 20 A a b^{3} d^{4} e^{3} + 3 A b^{4} d^{5} e^{2} + 3 B a^{4} d^{2} e^{5} + 20 B a^{3} b d^{3} e^{4} + 30 B a^{2} b^{2} d^{4} e^{3} + 12 B a b^{3} d^{5} e^{2} + B b^{4} d^{6} e\right) + x^{6} \left(\frac{7 A a^{4} d^{2} e^{5}}{2} + \frac{70 A a^{3} b d^{3} e^{4}}{3} + 35 A a^{2} b^{2} d^{4} e^{3} + 14 A a b^{3} d^{5} e^{2} + \frac{7 A b^{4} d^{6} e}{6} + \frac{35 B a^{4} d^{3} e^{4}}{6} + \frac{70 B a^{3} b d^{4} e^{3}}{3} + 21 B a^{2} b^{2} d^{5} e^{2} + \frac{14 B a b^{3} d^{6} e}{3} + \frac{B b^{4} d^{7}}{6}\right) + x^{5} \left(7 A a^{4} d^{3} e^{4} + 28 A a^{3} b d^{4} e^{3} + \frac{126 A a^{2} b^{2} d^{5} e^{2}}{5} + \frac{28 A a b^{3} d^{6} e}{5} + \frac{A b^{4} d^{7}}{5} + 7 B a^{4} d^{4} e^{3} + \frac{84 B a^{3} b d^{5} e^{2}}{5} + \frac{42 B a^{2} b^{2} d^{6} e}{5} + \frac{4 B a b^{3} d^{7}}{5}\right) + x^{4} \left(\frac{35 A a^{4} d^{4} e^{3}}{4} + 21 A a^{3} b d^{5} e^{2} + \frac{21 A a^{2} b^{2} d^{6} e}{2} + A a b^{3} d^{7} + \frac{21 B a^{4} d^{5} e^{2}}{4} + 7 B a^{3} b d^{6} e + \frac{3 B a^{2} b^{2} d^{7}}{2}\right) + x^{3} \left(7 A a^{4} d^{5} e^{2} + \frac{28 A a^{3} b d^{6} e}{3} + 2 A a^{2} b^{2} d^{7} + \frac{7 B a^{4} d^{6} e}{3} + \frac{4 B a^{3} b d^{7}}{3}\right) + x^{2} \left(\frac{7 A a^{4} d^{6} e}{2} + 2 A a^{3} b d^{7} + \frac{B a^{4} d^{7}}{2}\right)"," ",0,"A*a**4*d**7*x + B*b**4*e**7*x**13/13 + x**12*(A*b**4*e**7/12 + B*a*b**3*e**7/3 + 7*B*b**4*d*e**6/12) + x**11*(4*A*a*b**3*e**7/11 + 7*A*b**4*d*e**6/11 + 6*B*a**2*b**2*e**7/11 + 28*B*a*b**3*d*e**6/11 + 21*B*b**4*d**2*e**5/11) + x**10*(3*A*a**2*b**2*e**7/5 + 14*A*a*b**3*d*e**6/5 + 21*A*b**4*d**2*e**5/10 + 2*B*a**3*b*e**7/5 + 21*B*a**2*b**2*d*e**6/5 + 42*B*a*b**3*d**2*e**5/5 + 7*B*b**4*d**3*e**4/2) + x**9*(4*A*a**3*b*e**7/9 + 14*A*a**2*b**2*d*e**6/3 + 28*A*a*b**3*d**2*e**5/3 + 35*A*b**4*d**3*e**4/9 + B*a**4*e**7/9 + 28*B*a**3*b*d*e**6/9 + 14*B*a**2*b**2*d**2*e**5 + 140*B*a*b**3*d**3*e**4/9 + 35*B*b**4*d**4*e**3/9) + x**8*(A*a**4*e**7/8 + 7*A*a**3*b*d*e**6/2 + 63*A*a**2*b**2*d**2*e**5/4 + 35*A*a*b**3*d**3*e**4/2 + 35*A*b**4*d**4*e**3/8 + 7*B*a**4*d*e**6/8 + 21*B*a**3*b*d**2*e**5/2 + 105*B*a**2*b**2*d**3*e**4/4 + 35*B*a*b**3*d**4*e**3/2 + 21*B*b**4*d**5*e**2/8) + x**7*(A*a**4*d*e**6 + 12*A*a**3*b*d**2*e**5 + 30*A*a**2*b**2*d**3*e**4 + 20*A*a*b**3*d**4*e**3 + 3*A*b**4*d**5*e**2 + 3*B*a**4*d**2*e**5 + 20*B*a**3*b*d**3*e**4 + 30*B*a**2*b**2*d**4*e**3 + 12*B*a*b**3*d**5*e**2 + B*b**4*d**6*e) + x**6*(7*A*a**4*d**2*e**5/2 + 70*A*a**3*b*d**3*e**4/3 + 35*A*a**2*b**2*d**4*e**3 + 14*A*a*b**3*d**5*e**2 + 7*A*b**4*d**6*e/6 + 35*B*a**4*d**3*e**4/6 + 70*B*a**3*b*d**4*e**3/3 + 21*B*a**2*b**2*d**5*e**2 + 14*B*a*b**3*d**6*e/3 + B*b**4*d**7/6) + x**5*(7*A*a**4*d**3*e**4 + 28*A*a**3*b*d**4*e**3 + 126*A*a**2*b**2*d**5*e**2/5 + 28*A*a*b**3*d**6*e/5 + A*b**4*d**7/5 + 7*B*a**4*d**4*e**3 + 84*B*a**3*b*d**5*e**2/5 + 42*B*a**2*b**2*d**6*e/5 + 4*B*a*b**3*d**7/5) + x**4*(35*A*a**4*d**4*e**3/4 + 21*A*a**3*b*d**5*e**2 + 21*A*a**2*b**2*d**6*e/2 + A*a*b**3*d**7 + 21*B*a**4*d**5*e**2/4 + 7*B*a**3*b*d**6*e + 3*B*a**2*b**2*d**7/2) + x**3*(7*A*a**4*d**5*e**2 + 28*A*a**3*b*d**6*e/3 + 2*A*a**2*b**2*d**7 + 7*B*a**4*d**6*e/3 + 4*B*a**3*b*d**7/3) + x**2*(7*A*a**4*d**6*e/2 + 2*A*a**3*b*d**7 + B*a**4*d**7/2)","B",0
1674,1,1035,0,0.196641," ","integrate((B*x+A)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{6} x + \frac{B b^{4} e^{6} x^{12}}{12} + x^{11} \left(\frac{A b^{4} e^{6}}{11} + \frac{4 B a b^{3} e^{6}}{11} + \frac{6 B b^{4} d e^{5}}{11}\right) + x^{10} \left(\frac{2 A a b^{3} e^{6}}{5} + \frac{3 A b^{4} d e^{5}}{5} + \frac{3 B a^{2} b^{2} e^{6}}{5} + \frac{12 B a b^{3} d e^{5}}{5} + \frac{3 B b^{4} d^{2} e^{4}}{2}\right) + x^{9} \left(\frac{2 A a^{2} b^{2} e^{6}}{3} + \frac{8 A a b^{3} d e^{5}}{3} + \frac{5 A b^{4} d^{2} e^{4}}{3} + \frac{4 B a^{3} b e^{6}}{9} + 4 B a^{2} b^{2} d e^{5} + \frac{20 B a b^{3} d^{2} e^{4}}{3} + \frac{20 B b^{4} d^{3} e^{3}}{9}\right) + x^{8} \left(\frac{A a^{3} b e^{6}}{2} + \frac{9 A a^{2} b^{2} d e^{5}}{2} + \frac{15 A a b^{3} d^{2} e^{4}}{2} + \frac{5 A b^{4} d^{3} e^{3}}{2} + \frac{B a^{4} e^{6}}{8} + 3 B a^{3} b d e^{5} + \frac{45 B a^{2} b^{2} d^{2} e^{4}}{4} + 10 B a b^{3} d^{3} e^{3} + \frac{15 B b^{4} d^{4} e^{2}}{8}\right) + x^{7} \left(\frac{A a^{4} e^{6}}{7} + \frac{24 A a^{3} b d e^{5}}{7} + \frac{90 A a^{2} b^{2} d^{2} e^{4}}{7} + \frac{80 A a b^{3} d^{3} e^{3}}{7} + \frac{15 A b^{4} d^{4} e^{2}}{7} + \frac{6 B a^{4} d e^{5}}{7} + \frac{60 B a^{3} b d^{2} e^{4}}{7} + \frac{120 B a^{2} b^{2} d^{3} e^{3}}{7} + \frac{60 B a b^{3} d^{4} e^{2}}{7} + \frac{6 B b^{4} d^{5} e}{7}\right) + x^{6} \left(A a^{4} d e^{5} + 10 A a^{3} b d^{2} e^{4} + 20 A a^{2} b^{2} d^{3} e^{3} + 10 A a b^{3} d^{4} e^{2} + A b^{4} d^{5} e + \frac{5 B a^{4} d^{2} e^{4}}{2} + \frac{40 B a^{3} b d^{3} e^{3}}{3} + 15 B a^{2} b^{2} d^{4} e^{2} + 4 B a b^{3} d^{5} e + \frac{B b^{4} d^{6}}{6}\right) + x^{5} \left(3 A a^{4} d^{2} e^{4} + 16 A a^{3} b d^{3} e^{3} + 18 A a^{2} b^{2} d^{4} e^{2} + \frac{24 A a b^{3} d^{5} e}{5} + \frac{A b^{4} d^{6}}{5} + 4 B a^{4} d^{3} e^{3} + 12 B a^{3} b d^{4} e^{2} + \frac{36 B a^{2} b^{2} d^{5} e}{5} + \frac{4 B a b^{3} d^{6}}{5}\right) + x^{4} \left(5 A a^{4} d^{3} e^{3} + 15 A a^{3} b d^{4} e^{2} + 9 A a^{2} b^{2} d^{5} e + A a b^{3} d^{6} + \frac{15 B a^{4} d^{4} e^{2}}{4} + 6 B a^{3} b d^{5} e + \frac{3 B a^{2} b^{2} d^{6}}{2}\right) + x^{3} \left(5 A a^{4} d^{4} e^{2} + 8 A a^{3} b d^{5} e + 2 A a^{2} b^{2} d^{6} + 2 B a^{4} d^{5} e + \frac{4 B a^{3} b d^{6}}{3}\right) + x^{2} \left(3 A a^{4} d^{5} e + 2 A a^{3} b d^{6} + \frac{B a^{4} d^{6}}{2}\right)"," ",0,"A*a**4*d**6*x + B*b**4*e**6*x**12/12 + x**11*(A*b**4*e**6/11 + 4*B*a*b**3*e**6/11 + 6*B*b**4*d*e**5/11) + x**10*(2*A*a*b**3*e**6/5 + 3*A*b**4*d*e**5/5 + 3*B*a**2*b**2*e**6/5 + 12*B*a*b**3*d*e**5/5 + 3*B*b**4*d**2*e**4/2) + x**9*(2*A*a**2*b**2*e**6/3 + 8*A*a*b**3*d*e**5/3 + 5*A*b**4*d**2*e**4/3 + 4*B*a**3*b*e**6/9 + 4*B*a**2*b**2*d*e**5 + 20*B*a*b**3*d**2*e**4/3 + 20*B*b**4*d**3*e**3/9) + x**8*(A*a**3*b*e**6/2 + 9*A*a**2*b**2*d*e**5/2 + 15*A*a*b**3*d**2*e**4/2 + 5*A*b**4*d**3*e**3/2 + B*a**4*e**6/8 + 3*B*a**3*b*d*e**5 + 45*B*a**2*b**2*d**2*e**4/4 + 10*B*a*b**3*d**3*e**3 + 15*B*b**4*d**4*e**2/8) + x**7*(A*a**4*e**6/7 + 24*A*a**3*b*d*e**5/7 + 90*A*a**2*b**2*d**2*e**4/7 + 80*A*a*b**3*d**3*e**3/7 + 15*A*b**4*d**4*e**2/7 + 6*B*a**4*d*e**5/7 + 60*B*a**3*b*d**2*e**4/7 + 120*B*a**2*b**2*d**3*e**3/7 + 60*B*a*b**3*d**4*e**2/7 + 6*B*b**4*d**5*e/7) + x**6*(A*a**4*d*e**5 + 10*A*a**3*b*d**2*e**4 + 20*A*a**2*b**2*d**3*e**3 + 10*A*a*b**3*d**4*e**2 + A*b**4*d**5*e + 5*B*a**4*d**2*e**4/2 + 40*B*a**3*b*d**3*e**3/3 + 15*B*a**2*b**2*d**4*e**2 + 4*B*a*b**3*d**5*e + B*b**4*d**6/6) + x**5*(3*A*a**4*d**2*e**4 + 16*A*a**3*b*d**3*e**3 + 18*A*a**2*b**2*d**4*e**2 + 24*A*a*b**3*d**5*e/5 + A*b**4*d**6/5 + 4*B*a**4*d**3*e**3 + 12*B*a**3*b*d**4*e**2 + 36*B*a**2*b**2*d**5*e/5 + 4*B*a*b**3*d**6/5) + x**4*(5*A*a**4*d**3*e**3 + 15*A*a**3*b*d**4*e**2 + 9*A*a**2*b**2*d**5*e + A*a*b**3*d**6 + 15*B*a**4*d**4*e**2/4 + 6*B*a**3*b*d**5*e + 3*B*a**2*b**2*d**6/2) + x**3*(5*A*a**4*d**4*e**2 + 8*A*a**3*b*d**5*e + 2*A*a**2*b**2*d**6 + 2*B*a**4*d**5*e + 4*B*a**3*b*d**6/3) + x**2*(3*A*a**4*d**5*e + 2*A*a**3*b*d**6 + B*a**4*d**6/2)","B",0
1675,1,884,0,0.178978," ","integrate((B*x+A)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{5} x + \frac{B b^{4} e^{5} x^{11}}{11} + x^{10} \left(\frac{A b^{4} e^{5}}{10} + \frac{2 B a b^{3} e^{5}}{5} + \frac{B b^{4} d e^{4}}{2}\right) + x^{9} \left(\frac{4 A a b^{3} e^{5}}{9} + \frac{5 A b^{4} d e^{4}}{9} + \frac{2 B a^{2} b^{2} e^{5}}{3} + \frac{20 B a b^{3} d e^{4}}{9} + \frac{10 B b^{4} d^{2} e^{3}}{9}\right) + x^{8} \left(\frac{3 A a^{2} b^{2} e^{5}}{4} + \frac{5 A a b^{3} d e^{4}}{2} + \frac{5 A b^{4} d^{2} e^{3}}{4} + \frac{B a^{3} b e^{5}}{2} + \frac{15 B a^{2} b^{2} d e^{4}}{4} + 5 B a b^{3} d^{2} e^{3} + \frac{5 B b^{4} d^{3} e^{2}}{4}\right) + x^{7} \left(\frac{4 A a^{3} b e^{5}}{7} + \frac{30 A a^{2} b^{2} d e^{4}}{7} + \frac{40 A a b^{3} d^{2} e^{3}}{7} + \frac{10 A b^{4} d^{3} e^{2}}{7} + \frac{B a^{4} e^{5}}{7} + \frac{20 B a^{3} b d e^{4}}{7} + \frac{60 B a^{2} b^{2} d^{2} e^{3}}{7} + \frac{40 B a b^{3} d^{3} e^{2}}{7} + \frac{5 B b^{4} d^{4} e}{7}\right) + x^{6} \left(\frac{A a^{4} e^{5}}{6} + \frac{10 A a^{3} b d e^{4}}{3} + 10 A a^{2} b^{2} d^{2} e^{3} + \frac{20 A a b^{3} d^{3} e^{2}}{3} + \frac{5 A b^{4} d^{4} e}{6} + \frac{5 B a^{4} d e^{4}}{6} + \frac{20 B a^{3} b d^{2} e^{3}}{3} + 10 B a^{2} b^{2} d^{3} e^{2} + \frac{10 B a b^{3} d^{4} e}{3} + \frac{B b^{4} d^{5}}{6}\right) + x^{5} \left(A a^{4} d e^{4} + 8 A a^{3} b d^{2} e^{3} + 12 A a^{2} b^{2} d^{3} e^{2} + 4 A a b^{3} d^{4} e + \frac{A b^{4} d^{5}}{5} + 2 B a^{4} d^{2} e^{3} + 8 B a^{3} b d^{3} e^{2} + 6 B a^{2} b^{2} d^{4} e + \frac{4 B a b^{3} d^{5}}{5}\right) + x^{4} \left(\frac{5 A a^{4} d^{2} e^{3}}{2} + 10 A a^{3} b d^{3} e^{2} + \frac{15 A a^{2} b^{2} d^{4} e}{2} + A a b^{3} d^{5} + \frac{5 B a^{4} d^{3} e^{2}}{2} + 5 B a^{3} b d^{4} e + \frac{3 B a^{2} b^{2} d^{5}}{2}\right) + x^{3} \left(\frac{10 A a^{4} d^{3} e^{2}}{3} + \frac{20 A a^{3} b d^{4} e}{3} + 2 A a^{2} b^{2} d^{5} + \frac{5 B a^{4} d^{4} e}{3} + \frac{4 B a^{3} b d^{5}}{3}\right) + x^{2} \left(\frac{5 A a^{4} d^{4} e}{2} + 2 A a^{3} b d^{5} + \frac{B a^{4} d^{5}}{2}\right)"," ",0,"A*a**4*d**5*x + B*b**4*e**5*x**11/11 + x**10*(A*b**4*e**5/10 + 2*B*a*b**3*e**5/5 + B*b**4*d*e**4/2) + x**9*(4*A*a*b**3*e**5/9 + 5*A*b**4*d*e**4/9 + 2*B*a**2*b**2*e**5/3 + 20*B*a*b**3*d*e**4/9 + 10*B*b**4*d**2*e**3/9) + x**8*(3*A*a**2*b**2*e**5/4 + 5*A*a*b**3*d*e**4/2 + 5*A*b**4*d**2*e**3/4 + B*a**3*b*e**5/2 + 15*B*a**2*b**2*d*e**4/4 + 5*B*a*b**3*d**2*e**3 + 5*B*b**4*d**3*e**2/4) + x**7*(4*A*a**3*b*e**5/7 + 30*A*a**2*b**2*d*e**4/7 + 40*A*a*b**3*d**2*e**3/7 + 10*A*b**4*d**3*e**2/7 + B*a**4*e**5/7 + 20*B*a**3*b*d*e**4/7 + 60*B*a**2*b**2*d**2*e**3/7 + 40*B*a*b**3*d**3*e**2/7 + 5*B*b**4*d**4*e/7) + x**6*(A*a**4*e**5/6 + 10*A*a**3*b*d*e**4/3 + 10*A*a**2*b**2*d**2*e**3 + 20*A*a*b**3*d**3*e**2/3 + 5*A*b**4*d**4*e/6 + 5*B*a**4*d*e**4/6 + 20*B*a**3*b*d**2*e**3/3 + 10*B*a**2*b**2*d**3*e**2 + 10*B*a*b**3*d**4*e/3 + B*b**4*d**5/6) + x**5*(A*a**4*d*e**4 + 8*A*a**3*b*d**2*e**3 + 12*A*a**2*b**2*d**3*e**2 + 4*A*a*b**3*d**4*e + A*b**4*d**5/5 + 2*B*a**4*d**2*e**3 + 8*B*a**3*b*d**3*e**2 + 6*B*a**2*b**2*d**4*e + 4*B*a*b**3*d**5/5) + x**4*(5*A*a**4*d**2*e**3/2 + 10*A*a**3*b*d**3*e**2 + 15*A*a**2*b**2*d**4*e/2 + A*a*b**3*d**5 + 5*B*a**4*d**3*e**2/2 + 5*B*a**3*b*d**4*e + 3*B*a**2*b**2*d**5/2) + x**3*(10*A*a**4*d**3*e**2/3 + 20*A*a**3*b*d**4*e/3 + 2*A*a**2*b**2*d**5 + 5*B*a**4*d**4*e/3 + 4*B*a**3*b*d**5/3) + x**2*(5*A*a**4*d**4*e/2 + 2*A*a**3*b*d**5 + B*a**4*d**5/2)","B",0
1676,1,717,0,0.159955," ","integrate((B*x+A)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{4} x + \frac{B b^{4} e^{4} x^{10}}{10} + x^{9} \left(\frac{A b^{4} e^{4}}{9} + \frac{4 B a b^{3} e^{4}}{9} + \frac{4 B b^{4} d e^{3}}{9}\right) + x^{8} \left(\frac{A a b^{3} e^{4}}{2} + \frac{A b^{4} d e^{3}}{2} + \frac{3 B a^{2} b^{2} e^{4}}{4} + 2 B a b^{3} d e^{3} + \frac{3 B b^{4} d^{2} e^{2}}{4}\right) + x^{7} \left(\frac{6 A a^{2} b^{2} e^{4}}{7} + \frac{16 A a b^{3} d e^{3}}{7} + \frac{6 A b^{4} d^{2} e^{2}}{7} + \frac{4 B a^{3} b e^{4}}{7} + \frac{24 B a^{2} b^{2} d e^{3}}{7} + \frac{24 B a b^{3} d^{2} e^{2}}{7} + \frac{4 B b^{4} d^{3} e}{7}\right) + x^{6} \left(\frac{2 A a^{3} b e^{4}}{3} + 4 A a^{2} b^{2} d e^{3} + 4 A a b^{3} d^{2} e^{2} + \frac{2 A b^{4} d^{3} e}{3} + \frac{B a^{4} e^{4}}{6} + \frac{8 B a^{3} b d e^{3}}{3} + 6 B a^{2} b^{2} d^{2} e^{2} + \frac{8 B a b^{3} d^{3} e}{3} + \frac{B b^{4} d^{4}}{6}\right) + x^{5} \left(\frac{A a^{4} e^{4}}{5} + \frac{16 A a^{3} b d e^{3}}{5} + \frac{36 A a^{2} b^{2} d^{2} e^{2}}{5} + \frac{16 A a b^{3} d^{3} e}{5} + \frac{A b^{4} d^{4}}{5} + \frac{4 B a^{4} d e^{3}}{5} + \frac{24 B a^{3} b d^{2} e^{2}}{5} + \frac{24 B a^{2} b^{2} d^{3} e}{5} + \frac{4 B a b^{3} d^{4}}{5}\right) + x^{4} \left(A a^{4} d e^{3} + 6 A a^{3} b d^{2} e^{2} + 6 A a^{2} b^{2} d^{3} e + A a b^{3} d^{4} + \frac{3 B a^{4} d^{2} e^{2}}{2} + 4 B a^{3} b d^{3} e + \frac{3 B a^{2} b^{2} d^{4}}{2}\right) + x^{3} \left(2 A a^{4} d^{2} e^{2} + \frac{16 A a^{3} b d^{3} e}{3} + 2 A a^{2} b^{2} d^{4} + \frac{4 B a^{4} d^{3} e}{3} + \frac{4 B a^{3} b d^{4}}{3}\right) + x^{2} \left(2 A a^{4} d^{3} e + 2 A a^{3} b d^{4} + \frac{B a^{4} d^{4}}{2}\right)"," ",0,"A*a**4*d**4*x + B*b**4*e**4*x**10/10 + x**9*(A*b**4*e**4/9 + 4*B*a*b**3*e**4/9 + 4*B*b**4*d*e**3/9) + x**8*(A*a*b**3*e**4/2 + A*b**4*d*e**3/2 + 3*B*a**2*b**2*e**4/4 + 2*B*a*b**3*d*e**3 + 3*B*b**4*d**2*e**2/4) + x**7*(6*A*a**2*b**2*e**4/7 + 16*A*a*b**3*d*e**3/7 + 6*A*b**4*d**2*e**2/7 + 4*B*a**3*b*e**4/7 + 24*B*a**2*b**2*d*e**3/7 + 24*B*a*b**3*d**2*e**2/7 + 4*B*b**4*d**3*e/7) + x**6*(2*A*a**3*b*e**4/3 + 4*A*a**2*b**2*d*e**3 + 4*A*a*b**3*d**2*e**2 + 2*A*b**4*d**3*e/3 + B*a**4*e**4/6 + 8*B*a**3*b*d*e**3/3 + 6*B*a**2*b**2*d**2*e**2 + 8*B*a*b**3*d**3*e/3 + B*b**4*d**4/6) + x**5*(A*a**4*e**4/5 + 16*A*a**3*b*d*e**3/5 + 36*A*a**2*b**2*d**2*e**2/5 + 16*A*a*b**3*d**3*e/5 + A*b**4*d**4/5 + 4*B*a**4*d*e**3/5 + 24*B*a**3*b*d**2*e**2/5 + 24*B*a**2*b**2*d**3*e/5 + 4*B*a*b**3*d**4/5) + x**4*(A*a**4*d*e**3 + 6*A*a**3*b*d**2*e**2 + 6*A*a**2*b**2*d**3*e + A*a*b**3*d**4 + 3*B*a**4*d**2*e**2/2 + 4*B*a**3*b*d**3*e + 3*B*a**2*b**2*d**4/2) + x**3*(2*A*a**4*d**2*e**2 + 16*A*a**3*b*d**3*e/3 + 2*A*a**2*b**2*d**4 + 4*B*a**4*d**3*e/3 + 4*B*a**3*b*d**4/3) + x**2*(2*A*a**4*d**3*e + 2*A*a**3*b*d**4 + B*a**4*d**4/2)","B",0
1677,1,546,0,0.140148," ","integrate((B*x+A)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{3} x + \frac{B b^{4} e^{3} x^{9}}{9} + x^{8} \left(\frac{A b^{4} e^{3}}{8} + \frac{B a b^{3} e^{3}}{2} + \frac{3 B b^{4} d e^{2}}{8}\right) + x^{7} \left(\frac{4 A a b^{3} e^{3}}{7} + \frac{3 A b^{4} d e^{2}}{7} + \frac{6 B a^{2} b^{2} e^{3}}{7} + \frac{12 B a b^{3} d e^{2}}{7} + \frac{3 B b^{4} d^{2} e}{7}\right) + x^{6} \left(A a^{2} b^{2} e^{3} + 2 A a b^{3} d e^{2} + \frac{A b^{4} d^{2} e}{2} + \frac{2 B a^{3} b e^{3}}{3} + 3 B a^{2} b^{2} d e^{2} + 2 B a b^{3} d^{2} e + \frac{B b^{4} d^{3}}{6}\right) + x^{5} \left(\frac{4 A a^{3} b e^{3}}{5} + \frac{18 A a^{2} b^{2} d e^{2}}{5} + \frac{12 A a b^{3} d^{2} e}{5} + \frac{A b^{4} d^{3}}{5} + \frac{B a^{4} e^{3}}{5} + \frac{12 B a^{3} b d e^{2}}{5} + \frac{18 B a^{2} b^{2} d^{2} e}{5} + \frac{4 B a b^{3} d^{3}}{5}\right) + x^{4} \left(\frac{A a^{4} e^{3}}{4} + 3 A a^{3} b d e^{2} + \frac{9 A a^{2} b^{2} d^{2} e}{2} + A a b^{3} d^{3} + \frac{3 B a^{4} d e^{2}}{4} + 3 B a^{3} b d^{2} e + \frac{3 B a^{2} b^{2} d^{3}}{2}\right) + x^{3} \left(A a^{4} d e^{2} + 4 A a^{3} b d^{2} e + 2 A a^{2} b^{2} d^{3} + B a^{4} d^{2} e + \frac{4 B a^{3} b d^{3}}{3}\right) + x^{2} \left(\frac{3 A a^{4} d^{2} e}{2} + 2 A a^{3} b d^{3} + \frac{B a^{4} d^{3}}{2}\right)"," ",0,"A*a**4*d**3*x + B*b**4*e**3*x**9/9 + x**8*(A*b**4*e**3/8 + B*a*b**3*e**3/2 + 3*B*b**4*d*e**2/8) + x**7*(4*A*a*b**3*e**3/7 + 3*A*b**4*d*e**2/7 + 6*B*a**2*b**2*e**3/7 + 12*B*a*b**3*d*e**2/7 + 3*B*b**4*d**2*e/7) + x**6*(A*a**2*b**2*e**3 + 2*A*a*b**3*d*e**2 + A*b**4*d**2*e/2 + 2*B*a**3*b*e**3/3 + 3*B*a**2*b**2*d*e**2 + 2*B*a*b**3*d**2*e + B*b**4*d**3/6) + x**5*(4*A*a**3*b*e**3/5 + 18*A*a**2*b**2*d*e**2/5 + 12*A*a*b**3*d**2*e/5 + A*b**4*d**3/5 + B*a**4*e**3/5 + 12*B*a**3*b*d*e**2/5 + 18*B*a**2*b**2*d**2*e/5 + 4*B*a*b**3*d**3/5) + x**4*(A*a**4*e**3/4 + 3*A*a**3*b*d*e**2 + 9*A*a**2*b**2*d**2*e/2 + A*a*b**3*d**3 + 3*B*a**4*d*e**2/4 + 3*B*a**3*b*d**2*e + 3*B*a**2*b**2*d**3/2) + x**3*(A*a**4*d*e**2 + 4*A*a**3*b*d**2*e + 2*A*a**2*b**2*d**3 + B*a**4*d**2*e + 4*B*a**3*b*d**3/3) + x**2*(3*A*a**4*d**2*e/2 + 2*A*a**3*b*d**3 + B*a**4*d**3/2)","B",0
1678,1,384,0,0.120606," ","integrate((B*x+A)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{2} x + \frac{B b^{4} e^{2} x^{8}}{8} + x^{7} \left(\frac{A b^{4} e^{2}}{7} + \frac{4 B a b^{3} e^{2}}{7} + \frac{2 B b^{4} d e}{7}\right) + x^{6} \left(\frac{2 A a b^{3} e^{2}}{3} + \frac{A b^{4} d e}{3} + B a^{2} b^{2} e^{2} + \frac{4 B a b^{3} d e}{3} + \frac{B b^{4} d^{2}}{6}\right) + x^{5} \left(\frac{6 A a^{2} b^{2} e^{2}}{5} + \frac{8 A a b^{3} d e}{5} + \frac{A b^{4} d^{2}}{5} + \frac{4 B a^{3} b e^{2}}{5} + \frac{12 B a^{2} b^{2} d e}{5} + \frac{4 B a b^{3} d^{2}}{5}\right) + x^{4} \left(A a^{3} b e^{2} + 3 A a^{2} b^{2} d e + A a b^{3} d^{2} + \frac{B a^{4} e^{2}}{4} + 2 B a^{3} b d e + \frac{3 B a^{2} b^{2} d^{2}}{2}\right) + x^{3} \left(\frac{A a^{4} e^{2}}{3} + \frac{8 A a^{3} b d e}{3} + 2 A a^{2} b^{2} d^{2} + \frac{2 B a^{4} d e}{3} + \frac{4 B a^{3} b d^{2}}{3}\right) + x^{2} \left(A a^{4} d e + 2 A a^{3} b d^{2} + \frac{B a^{4} d^{2}}{2}\right)"," ",0,"A*a**4*d**2*x + B*b**4*e**2*x**8/8 + x**7*(A*b**4*e**2/7 + 4*B*a*b**3*e**2/7 + 2*B*b**4*d*e/7) + x**6*(2*A*a*b**3*e**2/3 + A*b**4*d*e/3 + B*a**2*b**2*e**2 + 4*B*a*b**3*d*e/3 + B*b**4*d**2/6) + x**5*(6*A*a**2*b**2*e**2/5 + 8*A*a*b**3*d*e/5 + A*b**4*d**2/5 + 4*B*a**3*b*e**2/5 + 12*B*a**2*b**2*d*e/5 + 4*B*a*b**3*d**2/5) + x**4*(A*a**3*b*e**2 + 3*A*a**2*b**2*d*e + A*a*b**3*d**2 + B*a**4*e**2/4 + 2*B*a**3*b*d*e + 3*B*a**2*b**2*d**2/2) + x**3*(A*a**4*e**2/3 + 8*A*a**3*b*d*e/3 + 2*A*a**2*b**2*d**2 + 2*B*a**4*d*e/3 + 4*B*a**3*b*d**2/3) + x**2*(A*a**4*d*e + 2*A*a**3*b*d**2 + B*a**4*d**2/2)","B",0
1679,1,226,0,0.098894," ","integrate((B*x+A)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d x + \frac{B b^{4} e x^{7}}{7} + x^{6} \left(\frac{A b^{4} e}{6} + \frac{2 B a b^{3} e}{3} + \frac{B b^{4} d}{6}\right) + x^{5} \left(\frac{4 A a b^{3} e}{5} + \frac{A b^{4} d}{5} + \frac{6 B a^{2} b^{2} e}{5} + \frac{4 B a b^{3} d}{5}\right) + x^{4} \left(\frac{3 A a^{2} b^{2} e}{2} + A a b^{3} d + B a^{3} b e + \frac{3 B a^{2} b^{2} d}{2}\right) + x^{3} \left(\frac{4 A a^{3} b e}{3} + 2 A a^{2} b^{2} d + \frac{B a^{4} e}{3} + \frac{4 B a^{3} b d}{3}\right) + x^{2} \left(\frac{A a^{4} e}{2} + 2 A a^{3} b d + \frac{B a^{4} d}{2}\right)"," ",0,"A*a**4*d*x + B*b**4*e*x**7/7 + x**6*(A*b**4*e/6 + 2*B*a*b**3*e/3 + B*b**4*d/6) + x**5*(4*A*a*b**3*e/5 + A*b**4*d/5 + 6*B*a**2*b**2*e/5 + 4*B*a*b**3*d/5) + x**4*(3*A*a**2*b**2*e/2 + A*a*b**3*d + B*a**3*b*e + 3*B*a**2*b**2*d/2) + x**3*(4*A*a**3*b*e/3 + 2*A*a**2*b**2*d + B*a**4*e/3 + 4*B*a**3*b*d/3) + x**2*(A*a**4*e/2 + 2*A*a**3*b*d + B*a**4*d/2)","B",0
1680,1,100,0,0.083189," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} x + \frac{B b^{4} x^{6}}{6} + x^{5} \left(\frac{A b^{4}}{5} + \frac{4 B a b^{3}}{5}\right) + x^{4} \left(A a b^{3} + \frac{3 B a^{2} b^{2}}{2}\right) + x^{3} \left(2 A a^{2} b^{2} + \frac{4 B a^{3} b}{3}\right) + x^{2} \left(2 A a^{3} b + \frac{B a^{4}}{2}\right)"," ",0,"A*a**4*x + B*b**4*x**6/6 + x**5*(A*b**4/5 + 4*B*a*b**3/5) + x**4*(A*a*b**3 + 3*B*a**2*b**2/2) + x**3*(2*A*a**2*b**2 + 4*B*a**3*b/3) + x**2*(2*A*a**3*b + B*a**4/2)","B",0
1681,1,352,0,0.920125," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d),x)","\frac{B b^{4} x^{5}}{5 e} + x^{4} \left(\frac{A b^{4}}{4 e} + \frac{B a b^{3}}{e} - \frac{B b^{4} d}{4 e^{2}}\right) + x^{3} \left(\frac{4 A a b^{3}}{3 e} - \frac{A b^{4} d}{3 e^{2}} + \frac{2 B a^{2} b^{2}}{e} - \frac{4 B a b^{3} d}{3 e^{2}} + \frac{B b^{4} d^{2}}{3 e^{3}}\right) + x^{2} \left(\frac{3 A a^{2} b^{2}}{e} - \frac{2 A a b^{3} d}{e^{2}} + \frac{A b^{4} d^{2}}{2 e^{3}} + \frac{2 B a^{3} b}{e} - \frac{3 B a^{2} b^{2} d}{e^{2}} + \frac{2 B a b^{3} d^{2}}{e^{3}} - \frac{B b^{4} d^{3}}{2 e^{4}}\right) + x \left(\frac{4 A a^{3} b}{e} - \frac{6 A a^{2} b^{2} d}{e^{2}} + \frac{4 A a b^{3} d^{2}}{e^{3}} - \frac{A b^{4} d^{3}}{e^{4}} + \frac{B a^{4}}{e} - \frac{4 B a^{3} b d}{e^{2}} + \frac{6 B a^{2} b^{2} d^{2}}{e^{3}} - \frac{4 B a b^{3} d^{3}}{e^{4}} + \frac{B b^{4} d^{4}}{e^{5}}\right) - \frac{\left(- A e + B d\right) \left(a e - b d\right)^{4} \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*b**4*x**5/(5*e) + x**4*(A*b**4/(4*e) + B*a*b**3/e - B*b**4*d/(4*e**2)) + x**3*(4*A*a*b**3/(3*e) - A*b**4*d/(3*e**2) + 2*B*a**2*b**2/e - 4*B*a*b**3*d/(3*e**2) + B*b**4*d**2/(3*e**3)) + x**2*(3*A*a**2*b**2/e - 2*A*a*b**3*d/e**2 + A*b**4*d**2/(2*e**3) + 2*B*a**3*b/e - 3*B*a**2*b**2*d/e**2 + 2*B*a*b**3*d**2/e**3 - B*b**4*d**3/(2*e**4)) + x*(4*A*a**3*b/e - 6*A*a**2*b**2*d/e**2 + 4*A*a*b**3*d**2/e**3 - A*b**4*d**3/e**4 + B*a**4/e - 4*B*a**3*b*d/e**2 + 6*B*a**2*b**2*d**2/e**3 - 4*B*a*b**3*d**3/e**4 + B*b**4*d**4/e**5) - (-A*e + B*d)*(a*e - b*d)**4*log(d + e*x)/e**6","B",0
1682,1,396,0,2.088154," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**2,x)","\frac{B b^{4} x^{4}}{4 e^{2}} + x^{3} \left(\frac{A b^{4}}{3 e^{2}} + \frac{4 B a b^{3}}{3 e^{2}} - \frac{2 B b^{4} d}{3 e^{3}}\right) + x^{2} \left(\frac{2 A a b^{3}}{e^{2}} - \frac{A b^{4} d}{e^{3}} + \frac{3 B a^{2} b^{2}}{e^{2}} - \frac{4 B a b^{3} d}{e^{3}} + \frac{3 B b^{4} d^{2}}{2 e^{4}}\right) + x \left(\frac{6 A a^{2} b^{2}}{e^{2}} - \frac{8 A a b^{3} d}{e^{3}} + \frac{3 A b^{4} d^{2}}{e^{4}} + \frac{4 B a^{3} b}{e^{2}} - \frac{12 B a^{2} b^{2} d}{e^{3}} + \frac{12 B a b^{3} d^{2}}{e^{4}} - \frac{4 B b^{4} d^{3}}{e^{5}}\right) + \frac{- A a^{4} e^{5} + 4 A a^{3} b d e^{4} - 6 A a^{2} b^{2} d^{2} e^{3} + 4 A a b^{3} d^{3} e^{2} - A b^{4} d^{4} e + B a^{4} d e^{4} - 4 B a^{3} b d^{2} e^{3} + 6 B a^{2} b^{2} d^{3} e^{2} - 4 B a b^{3} d^{4} e + B b^{4} d^{5}}{d e^{6} + e^{7} x} + \frac{\left(a e - b d\right)^{3} \left(4 A b e + B a e - 5 B b d\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*b**4*x**4/(4*e**2) + x**3*(A*b**4/(3*e**2) + 4*B*a*b**3/(3*e**2) - 2*B*b**4*d/(3*e**3)) + x**2*(2*A*a*b**3/e**2 - A*b**4*d/e**3 + 3*B*a**2*b**2/e**2 - 4*B*a*b**3*d/e**3 + 3*B*b**4*d**2/(2*e**4)) + x*(6*A*a**2*b**2/e**2 - 8*A*a*b**3*d/e**3 + 3*A*b**4*d**2/e**4 + 4*B*a**3*b/e**2 - 12*B*a**2*b**2*d/e**3 + 12*B*a*b**3*d**2/e**4 - 4*B*b**4*d**3/e**5) + (-A*a**4*e**5 + 4*A*a**3*b*d*e**4 - 6*A*a**2*b**2*d**2*e**3 + 4*A*a*b**3*d**3*e**2 - A*b**4*d**4*e + B*a**4*d*e**4 - 4*B*a**3*b*d**2*e**3 + 6*B*a**2*b**2*d**3*e**2 - 4*B*a*b**3*d**4*e + B*b**4*d**5)/(d*e**6 + e**7*x) + (a*e - b*d)**3*(4*A*b*e + B*a*e - 5*B*b*d)*log(d + e*x)/e**6","B",0
1683,1,444,0,7.274903," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**3,x)","\frac{B b^{4} x^{3}}{3 e^{3}} + \frac{2 b \left(a e - b d\right)^{2} \left(3 A b e + 2 B a e - 5 B b d\right) \log{\left(d + e x \right)}}{e^{6}} + x^{2} \left(\frac{A b^{4}}{2 e^{3}} + \frac{2 B a b^{3}}{e^{3}} - \frac{3 B b^{4} d}{2 e^{4}}\right) + x \left(\frac{4 A a b^{3}}{e^{3}} - \frac{3 A b^{4} d}{e^{4}} + \frac{6 B a^{2} b^{2}}{e^{3}} - \frac{12 B a b^{3} d}{e^{4}} + \frac{6 B b^{4} d^{2}}{e^{5}}\right) + \frac{- A a^{4} e^{5} - 4 A a^{3} b d e^{4} + 18 A a^{2} b^{2} d^{2} e^{3} - 20 A a b^{3} d^{3} e^{2} + 7 A b^{4} d^{4} e - B a^{4} d e^{4} + 12 B a^{3} b d^{2} e^{3} - 30 B a^{2} b^{2} d^{3} e^{2} + 28 B a b^{3} d^{4} e - 9 B b^{4} d^{5} + x \left(- 8 A a^{3} b e^{5} + 24 A a^{2} b^{2} d e^{4} - 24 A a b^{3} d^{2} e^{3} + 8 A b^{4} d^{3} e^{2} - 2 B a^{4} e^{5} + 16 B a^{3} b d e^{4} - 36 B a^{2} b^{2} d^{2} e^{3} + 32 B a b^{3} d^{3} e^{2} - 10 B b^{4} d^{4} e\right)}{2 d^{2} e^{6} + 4 d e^{7} x + 2 e^{8} x^{2}}"," ",0,"B*b**4*x**3/(3*e**3) + 2*b*(a*e - b*d)**2*(3*A*b*e + 2*B*a*e - 5*B*b*d)*log(d + e*x)/e**6 + x**2*(A*b**4/(2*e**3) + 2*B*a*b**3/e**3 - 3*B*b**4*d/(2*e**4)) + x*(4*A*a*b**3/e**3 - 3*A*b**4*d/e**4 + 6*B*a**2*b**2/e**3 - 12*B*a*b**3*d/e**4 + 6*B*b**4*d**2/e**5) + (-A*a**4*e**5 - 4*A*a**3*b*d*e**4 + 18*A*a**2*b**2*d**2*e**3 - 20*A*a*b**3*d**3*e**2 + 7*A*b**4*d**4*e - B*a**4*d*e**4 + 12*B*a**3*b*d**2*e**3 - 30*B*a**2*b**2*d**3*e**2 + 28*B*a*b**3*d**4*e - 9*B*b**4*d**5 + x*(-8*A*a**3*b*e**5 + 24*A*a**2*b**2*d*e**4 - 24*A*a*b**3*d**2*e**3 + 8*A*b**4*d**3*e**2 - 2*B*a**4*e**5 + 16*B*a**3*b*d*e**4 - 36*B*a**2*b**2*d**2*e**3 + 32*B*a*b**3*d**3*e**2 - 10*B*b**4*d**4*e))/(2*d**2*e**6 + 4*d*e**7*x + 2*e**8*x**2)","B",0
1684,1,486,0,21.583622," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**4,x)","\frac{B b^{4} x^{2}}{2 e^{4}} + \frac{2 b^{2} \left(a e - b d\right) \left(2 A b e + 3 B a e - 5 B b d\right) \log{\left(d + e x \right)}}{e^{6}} + x \left(\frac{A b^{4}}{e^{4}} + \frac{4 B a b^{3}}{e^{4}} - \frac{4 B b^{4} d}{e^{5}}\right) + \frac{- 2 A a^{4} e^{5} - 4 A a^{3} b d e^{4} - 12 A a^{2} b^{2} d^{2} e^{3} + 44 A a b^{3} d^{3} e^{2} - 26 A b^{4} d^{4} e - B a^{4} d e^{4} - 8 B a^{3} b d^{2} e^{3} + 66 B a^{2} b^{2} d^{3} e^{2} - 104 B a b^{3} d^{4} e + 47 B b^{4} d^{5} + x^{2} \left(- 36 A a^{2} b^{2} e^{5} + 72 A a b^{3} d e^{4} - 36 A b^{4} d^{2} e^{3} - 24 B a^{3} b e^{5} + 108 B a^{2} b^{2} d e^{4} - 144 B a b^{3} d^{2} e^{3} + 60 B b^{4} d^{3} e^{2}\right) + x \left(- 12 A a^{3} b e^{5} - 36 A a^{2} b^{2} d e^{4} + 108 A a b^{3} d^{2} e^{3} - 60 A b^{4} d^{3} e^{2} - 3 B a^{4} e^{5} - 24 B a^{3} b d e^{4} + 162 B a^{2} b^{2} d^{2} e^{3} - 240 B a b^{3} d^{3} e^{2} + 105 B b^{4} d^{4} e\right)}{6 d^{3} e^{6} + 18 d^{2} e^{7} x + 18 d e^{8} x^{2} + 6 e^{9} x^{3}}"," ",0,"B*b**4*x**2/(2*e**4) + 2*b**2*(a*e - b*d)*(2*A*b*e + 3*B*a*e - 5*B*b*d)*log(d + e*x)/e**6 + x*(A*b**4/e**4 + 4*B*a*b**3/e**4 - 4*B*b**4*d/e**5) + (-2*A*a**4*e**5 - 4*A*a**3*b*d*e**4 - 12*A*a**2*b**2*d**2*e**3 + 44*A*a*b**3*d**3*e**2 - 26*A*b**4*d**4*e - B*a**4*d*e**4 - 8*B*a**3*b*d**2*e**3 + 66*B*a**2*b**2*d**3*e**2 - 104*B*a*b**3*d**4*e + 47*B*b**4*d**5 + x**2*(-36*A*a**2*b**2*e**5 + 72*A*a*b**3*d*e**4 - 36*A*b**4*d**2*e**3 - 24*B*a**3*b*e**5 + 108*B*a**2*b**2*d*e**4 - 144*B*a*b**3*d**2*e**3 + 60*B*b**4*d**3*e**2) + x*(-12*A*a**3*b*e**5 - 36*A*a**2*b**2*d*e**4 + 108*A*a*b**3*d**2*e**3 - 60*A*b**4*d**3*e**2 - 3*B*a**4*e**5 - 24*B*a**3*b*d*e**4 + 162*B*a**2*b**2*d**2*e**3 - 240*B*a*b**3*d**3*e**2 + 105*B*b**4*d**4*e))/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3)","B",0
1685,1,518,0,62.238700," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**5,x)","\frac{B b^{4} x}{e^{5}} + \frac{b^{3} \left(A b e + 4 B a e - 5 B b d\right) \log{\left(d + e x \right)}}{e^{6}} + \frac{- 3 A a^{4} e^{5} - 4 A a^{3} b d e^{4} - 6 A a^{2} b^{2} d^{2} e^{3} - 12 A a b^{3} d^{3} e^{2} + 25 A b^{4} d^{4} e - B a^{4} d e^{4} - 4 B a^{3} b d^{2} e^{3} - 18 B a^{2} b^{2} d^{3} e^{2} + 100 B a b^{3} d^{4} e - 77 B b^{4} d^{5} + x^{3} \left(- 48 A a b^{3} e^{5} + 48 A b^{4} d e^{4} - 72 B a^{2} b^{2} e^{5} + 192 B a b^{3} d e^{4} - 120 B b^{4} d^{2} e^{3}\right) + x^{2} \left(- 36 A a^{2} b^{2} e^{5} - 72 A a b^{3} d e^{4} + 108 A b^{4} d^{2} e^{3} - 24 B a^{3} b e^{5} - 108 B a^{2} b^{2} d e^{4} + 432 B a b^{3} d^{2} e^{3} - 300 B b^{4} d^{3} e^{2}\right) + x \left(- 16 A a^{3} b e^{5} - 24 A a^{2} b^{2} d e^{4} - 48 A a b^{3} d^{2} e^{3} + 88 A b^{4} d^{3} e^{2} - 4 B a^{4} e^{5} - 16 B a^{3} b d e^{4} - 72 B a^{2} b^{2} d^{2} e^{3} + 352 B a b^{3} d^{3} e^{2} - 260 B b^{4} d^{4} e\right)}{12 d^{4} e^{6} + 48 d^{3} e^{7} x + 72 d^{2} e^{8} x^{2} + 48 d e^{9} x^{3} + 12 e^{10} x^{4}}"," ",0,"B*b**4*x/e**5 + b**3*(A*b*e + 4*B*a*e - 5*B*b*d)*log(d + e*x)/e**6 + (-3*A*a**4*e**5 - 4*A*a**3*b*d*e**4 - 6*A*a**2*b**2*d**2*e**3 - 12*A*a*b**3*d**3*e**2 + 25*A*b**4*d**4*e - B*a**4*d*e**4 - 4*B*a**3*b*d**2*e**3 - 18*B*a**2*b**2*d**3*e**2 + 100*B*a*b**3*d**4*e - 77*B*b**4*d**5 + x**3*(-48*A*a*b**3*e**5 + 48*A*b**4*d*e**4 - 72*B*a**2*b**2*e**5 + 192*B*a*b**3*d*e**4 - 120*B*b**4*d**2*e**3) + x**2*(-36*A*a**2*b**2*e**5 - 72*A*a*b**3*d*e**4 + 108*A*b**4*d**2*e**3 - 24*B*a**3*b*e**5 - 108*B*a**2*b**2*d*e**4 + 432*B*a*b**3*d**2*e**3 - 300*B*b**4*d**3*e**2) + x*(-16*A*a**3*b*e**5 - 24*A*a**2*b**2*d*e**4 - 48*A*a*b**3*d**2*e**3 + 88*A*b**4*d**3*e**2 - 4*B*a**4*e**5 - 16*B*a**3*b*d*e**4 - 72*B*a**2*b**2*d**2*e**3 + 352*B*a*b**3*d**3*e**2 - 260*B*b**4*d**4*e))/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4)","B",0
1686,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1687,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1688,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1689,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1690,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1691,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1692,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**12,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1693,1,396,0,2.077855," ","integrate((B*x+A)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B e^{4} x^{4}}{4 b^{2}} + x^{3} \left(\frac{A e^{4}}{3 b^{2}} - \frac{2 B a e^{4}}{3 b^{3}} + \frac{4 B d e^{3}}{3 b^{2}}\right) + x^{2} \left(- \frac{A a e^{4}}{b^{3}} + \frac{2 A d e^{3}}{b^{2}} + \frac{3 B a^{2} e^{4}}{2 b^{4}} - \frac{4 B a d e^{3}}{b^{3}} + \frac{3 B d^{2} e^{2}}{b^{2}}\right) + x \left(\frac{3 A a^{2} e^{4}}{b^{4}} - \frac{8 A a d e^{3}}{b^{3}} + \frac{6 A d^{2} e^{2}}{b^{2}} - \frac{4 B a^{3} e^{4}}{b^{5}} + \frac{12 B a^{2} d e^{3}}{b^{4}} - \frac{12 B a d^{2} e^{2}}{b^{3}} + \frac{4 B d^{3} e}{b^{2}}\right) + \frac{- A a^{4} b e^{4} + 4 A a^{3} b^{2} d e^{3} - 6 A a^{2} b^{3} d^{2} e^{2} + 4 A a b^{4} d^{3} e - A b^{5} d^{4} + B a^{5} e^{4} - 4 B a^{4} b d e^{3} + 6 B a^{3} b^{2} d^{2} e^{2} - 4 B a^{2} b^{3} d^{3} e + B a b^{4} d^{4}}{a b^{6} + b^{7} x} + \frac{\left(a e - b d\right)^{3} \left(- 4 A b e + 5 B a e - B b d\right) \log{\left(a + b x \right)}}{b^{6}}"," ",0,"B*e**4*x**4/(4*b**2) + x**3*(A*e**4/(3*b**2) - 2*B*a*e**4/(3*b**3) + 4*B*d*e**3/(3*b**2)) + x**2*(-A*a*e**4/b**3 + 2*A*d*e**3/b**2 + 3*B*a**2*e**4/(2*b**4) - 4*B*a*d*e**3/b**3 + 3*B*d**2*e**2/b**2) + x*(3*A*a**2*e**4/b**4 - 8*A*a*d*e**3/b**3 + 6*A*d**2*e**2/b**2 - 4*B*a**3*e**4/b**5 + 12*B*a**2*d*e**3/b**4 - 12*B*a*d**2*e**2/b**3 + 4*B*d**3*e/b**2) + (-A*a**4*b*e**4 + 4*A*a**3*b**2*d*e**3 - 6*A*a**2*b**3*d**2*e**2 + 4*A*a*b**4*d**3*e - A*b**5*d**4 + B*a**5*e**4 - 4*B*a**4*b*d*e**3 + 6*B*a**3*b**2*d**2*e**2 - 4*B*a**2*b**3*d**3*e + B*a*b**4*d**4)/(a*b**6 + b**7*x) + (a*e - b*d)**3*(-4*A*b*e + 5*B*a*e - B*b*d)*log(a + b*x)/b**6","B",0
1694,1,257,0,1.430449," ","integrate((B*x+A)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B e^{3} x^{3}}{3 b^{2}} + x^{2} \left(\frac{A e^{3}}{2 b^{2}} - \frac{B a e^{3}}{b^{3}} + \frac{3 B d e^{2}}{2 b^{2}}\right) + x \left(- \frac{2 A a e^{3}}{b^{3}} + \frac{3 A d e^{2}}{b^{2}} + \frac{3 B a^{2} e^{3}}{b^{4}} - \frac{6 B a d e^{2}}{b^{3}} + \frac{3 B d^{2} e}{b^{2}}\right) + \frac{A a^{3} b e^{3} - 3 A a^{2} b^{2} d e^{2} + 3 A a b^{3} d^{2} e - A b^{4} d^{3} - B a^{4} e^{3} + 3 B a^{3} b d e^{2} - 3 B a^{2} b^{2} d^{2} e + B a b^{3} d^{3}}{a b^{5} + b^{6} x} - \frac{\left(a e - b d\right)^{2} \left(- 3 A b e + 4 B a e - B b d\right) \log{\left(a + b x \right)}}{b^{5}}"," ",0,"B*e**3*x**3/(3*b**2) + x**2*(A*e**3/(2*b**2) - B*a*e**3/b**3 + 3*B*d*e**2/(2*b**2)) + x*(-2*A*a*e**3/b**3 + 3*A*d*e**2/b**2 + 3*B*a**2*e**3/b**4 - 6*B*a*d*e**2/b**3 + 3*B*d**2*e/b**2) + (A*a**3*b*e**3 - 3*A*a**2*b**2*d*e**2 + 3*A*a*b**3*d**2*e - A*b**4*d**3 - B*a**4*e**3 + 3*B*a**3*b*d*e**2 - 3*B*a**2*b**2*d**2*e + B*a*b**3*d**3)/(a*b**5 + b**6*x) - (a*e - b*d)**2*(-3*A*b*e + 4*B*a*e - B*b*d)*log(a + b*x)/b**5","A",0
1695,1,151,0,0.878847," ","integrate((B*x+A)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B e^{2} x^{2}}{2 b^{2}} + x \left(\frac{A e^{2}}{b^{2}} - \frac{2 B a e^{2}}{b^{3}} + \frac{2 B d e}{b^{2}}\right) + \frac{- A a^{2} b e^{2} + 2 A a b^{2} d e - A b^{3} d^{2} + B a^{3} e^{2} - 2 B a^{2} b d e + B a b^{2} d^{2}}{a b^{4} + b^{5} x} + \frac{\left(a e - b d\right) \left(- 2 A b e + 3 B a e - B b d\right) \log{\left(a + b x \right)}}{b^{4}}"," ",0,"B*e**2*x**2/(2*b**2) + x*(A*e**2/b**2 - 2*B*a*e**2/b**3 + 2*B*d*e/b**2) + (-A*a**2*b*e**2 + 2*A*a*b**2*d*e - A*b**3*d**2 + B*a**3*e**2 - 2*B*a**2*b*d*e + B*a*b**2*d**2)/(a*b**4 + b**5*x) + (a*e - b*d)*(-2*A*b*e + 3*B*a*e - B*b*d)*log(a + b*x)/b**4","A",0
1696,1,71,0,0.432622," ","integrate((B*x+A)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B e x}{b^{2}} + \frac{A a b e - A b^{2} d - B a^{2} e + B a b d}{a b^{3} + b^{4} x} - \frac{\left(- A b e + 2 B a e - B b d\right) \log{\left(a + b x \right)}}{b^{3}}"," ",0,"B*e*x/b**2 + (A*a*b*e - A*b**2*d - B*a**2*e + B*a*b*d)/(a*b**3 + b**4*x) - (-A*b*e + 2*B*a*e - B*b*d)*log(a + b*x)/b**3","A",0
1697,1,27,0,0.179101," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{B \log{\left(a + b x \right)}}{b^{2}} + \frac{- A b + B a}{a b^{2} + b^{3} x}"," ",0,"B*log(a + b*x)/b**2 + (-A*b + B*a)/(a*b**2 + b**3*x)","A",0
1698,1,355,0,1.188405," ","integrate((B*x+A)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{A b - B a}{a^{2} b e - a b^{2} d + x \left(a b^{2} e - b^{3} d\right)} - \frac{\left(- A e + B d\right) \log{\left(x + \frac{- A a e^{2} - A b d e + B a d e + B b d^{2} - \frac{a^{3} e^{3} \left(- A e + B d\right)}{\left(a e - b d\right)^{2}} + \frac{3 a^{2} b d e^{2} \left(- A e + B d\right)}{\left(a e - b d\right)^{2}} - \frac{3 a b^{2} d^{2} e \left(- A e + B d\right)}{\left(a e - b d\right)^{2}} + \frac{b^{3} d^{3} \left(- A e + B d\right)}{\left(a e - b d\right)^{2}}}{- 2 A b e^{2} + 2 B b d e} \right)}}{\left(a e - b d\right)^{2}} + \frac{\left(- A e + B d\right) \log{\left(x + \frac{- A a e^{2} - A b d e + B a d e + B b d^{2} + \frac{a^{3} e^{3} \left(- A e + B d\right)}{\left(a e - b d\right)^{2}} - \frac{3 a^{2} b d e^{2} \left(- A e + B d\right)}{\left(a e - b d\right)^{2}} + \frac{3 a b^{2} d^{2} e \left(- A e + B d\right)}{\left(a e - b d\right)^{2}} - \frac{b^{3} d^{3} \left(- A e + B d\right)}{\left(a e - b d\right)^{2}}}{- 2 A b e^{2} + 2 B b d e} \right)}}{\left(a e - b d\right)^{2}}"," ",0,"(A*b - B*a)/(a**2*b*e - a*b**2*d + x*(a*b**2*e - b**3*d)) - (-A*e + B*d)*log(x + (-A*a*e**2 - A*b*d*e + B*a*d*e + B*b*d**2 - a**3*e**3*(-A*e + B*d)/(a*e - b*d)**2 + 3*a**2*b*d*e**2*(-A*e + B*d)/(a*e - b*d)**2 - 3*a*b**2*d**2*e*(-A*e + B*d)/(a*e - b*d)**2 + b**3*d**3*(-A*e + B*d)/(a*e - b*d)**2)/(-2*A*b*e**2 + 2*B*b*d*e))/(a*e - b*d)**2 + (-A*e + B*d)*log(x + (-A*a*e**2 - A*b*d*e + B*a*d*e + B*b*d**2 + a**3*e**3*(-A*e + B*d)/(a*e - b*d)**2 - 3*a**2*b*d*e**2*(-A*e + B*d)/(a*e - b*d)**2 + 3*a*b**2*d**2*e*(-A*e + B*d)/(a*e - b*d)**2 - b**3*d**3*(-A*e + B*d)/(a*e - b*d)**2)/(-2*A*b*e**2 + 2*B*b*d*e))/(a*e - b*d)**2","B",0
1699,1,706,0,2.287479," ","integrate((B*x+A)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2),x)","\frac{- A a e - A b d + 2 B a d + x \left(- 2 A b e + B a e + B b d\right)}{a^{3} d e^{2} - 2 a^{2} b d^{2} e + a b^{2} d^{3} + x^{2} \left(a^{2} b e^{3} - 2 a b^{2} d e^{2} + b^{3} d^{2} e\right) + x \left(a^{3} e^{3} - a^{2} b d e^{2} - a b^{2} d^{2} e + b^{3} d^{3}\right)} + \frac{\left(- 2 A b e + B a e + B b d\right) \log{\left(x + \frac{- 2 A a b e^{2} - 2 A b^{2} d e + B a^{2} e^{2} + 2 B a b d e + B b^{2} d^{2} - \frac{a^{4} e^{4} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} + \frac{4 a^{3} b d e^{3} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} - \frac{6 a^{2} b^{2} d^{2} e^{2} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} + \frac{4 a b^{3} d^{3} e \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} - \frac{b^{4} d^{4} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}}}{- 4 A b^{2} e^{2} + 2 B a b e^{2} + 2 B b^{2} d e} \right)}}{\left(a e - b d\right)^{3}} - \frac{\left(- 2 A b e + B a e + B b d\right) \log{\left(x + \frac{- 2 A a b e^{2} - 2 A b^{2} d e + B a^{2} e^{2} + 2 B a b d e + B b^{2} d^{2} + \frac{a^{4} e^{4} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} - \frac{4 a^{3} b d e^{3} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} + \frac{6 a^{2} b^{2} d^{2} e^{2} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} - \frac{4 a b^{3} d^{3} e \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}} + \frac{b^{4} d^{4} \left(- 2 A b e + B a e + B b d\right)}{\left(a e - b d\right)^{3}}}{- 4 A b^{2} e^{2} + 2 B a b e^{2} + 2 B b^{2} d e} \right)}}{\left(a e - b d\right)^{3}}"," ",0,"(-A*a*e - A*b*d + 2*B*a*d + x*(-2*A*b*e + B*a*e + B*b*d))/(a**3*d*e**2 - 2*a**2*b*d**2*e + a*b**2*d**3 + x**2*(a**2*b*e**3 - 2*a*b**2*d*e**2 + b**3*d**2*e) + x*(a**3*e**3 - a**2*b*d*e**2 - a*b**2*d**2*e + b**3*d**3)) + (-2*A*b*e + B*a*e + B*b*d)*log(x + (-2*A*a*b*e**2 - 2*A*b**2*d*e + B*a**2*e**2 + 2*B*a*b*d*e + B*b**2*d**2 - a**4*e**4*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 + 4*a**3*b*d*e**3*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 - 6*a**2*b**2*d**2*e**2*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 + 4*a*b**3*d**3*e*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 - b**4*d**4*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3)/(-4*A*b**2*e**2 + 2*B*a*b*e**2 + 2*B*b**2*d*e))/(a*e - b*d)**3 - (-2*A*b*e + B*a*e + B*b*d)*log(x + (-2*A*a*b*e**2 - 2*A*b**2*d*e + B*a**2*e**2 + 2*B*a*b*d*e + B*b**2*d**2 + a**4*e**4*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 - 4*a**3*b*d*e**3*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 + 6*a**2*b**2*d**2*e**2*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 - 4*a*b**3*d**3*e*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3 + b**4*d**4*(-2*A*b*e + B*a*e + B*b*d)/(a*e - b*d)**3)/(-4*A*b**2*e**2 + 2*B*a*b*e**2 + 2*B*b**2*d*e))/(a*e - b*d)**3","B",0
1700,1,1066,0,3.582625," ","integrate((B*x+A)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{b \left(- 3 A b e + 2 B a e + B b d\right) \log{\left(x + \frac{- 3 A a b^{2} e^{2} - 3 A b^{3} d e + 2 B a^{2} b e^{2} + 3 B a b^{2} d e + B b^{3} d^{2} - \frac{a^{5} b e^{5} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} + \frac{5 a^{4} b^{2} d e^{4} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} - \frac{10 a^{3} b^{3} d^{2} e^{3} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} + \frac{10 a^{2} b^{4} d^{3} e^{2} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} - \frac{5 a b^{5} d^{4} e \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} + \frac{b^{6} d^{5} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}}}{- 6 A b^{3} e^{2} + 4 B a b^{2} e^{2} + 2 B b^{3} d e} \right)}}{\left(a e - b d\right)^{4}} + \frac{b \left(- 3 A b e + 2 B a e + B b d\right) \log{\left(x + \frac{- 3 A a b^{2} e^{2} - 3 A b^{3} d e + 2 B a^{2} b e^{2} + 3 B a b^{2} d e + B b^{3} d^{2} + \frac{a^{5} b e^{5} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} - \frac{5 a^{4} b^{2} d e^{4} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} + \frac{10 a^{3} b^{3} d^{2} e^{3} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} - \frac{10 a^{2} b^{4} d^{3} e^{2} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} + \frac{5 a b^{5} d^{4} e \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}} - \frac{b^{6} d^{5} \left(- 3 A b e + 2 B a e + B b d\right)}{\left(a e - b d\right)^{4}}}{- 6 A b^{3} e^{2} + 4 B a b^{2} e^{2} + 2 B b^{3} d e} \right)}}{\left(a e - b d\right)^{4}} + \frac{- A a^{2} e^{2} + 5 A a b d e + 2 A b^{2} d^{2} - B a^{2} d e - 5 B a b d^{2} + x^{2} \left(6 A b^{2} e^{2} - 4 B a b e^{2} - 2 B b^{2} d e\right) + x \left(3 A a b e^{2} + 9 A b^{2} d e - 2 B a^{2} e^{2} - 7 B a b d e - 3 B b^{2} d^{2}\right)}{2 a^{4} d^{2} e^{3} - 6 a^{3} b d^{3} e^{2} + 6 a^{2} b^{2} d^{4} e - 2 a b^{3} d^{5} + x^{3} \left(2 a^{3} b e^{5} - 6 a^{2} b^{2} d e^{4} + 6 a b^{3} d^{2} e^{3} - 2 b^{4} d^{3} e^{2}\right) + x^{2} \left(2 a^{4} e^{5} - 2 a^{3} b d e^{4} - 6 a^{2} b^{2} d^{2} e^{3} + 10 a b^{3} d^{3} e^{2} - 4 b^{4} d^{4} e\right) + x \left(4 a^{4} d e^{4} - 10 a^{3} b d^{2} e^{3} + 6 a^{2} b^{2} d^{3} e^{2} + 2 a b^{3} d^{4} e - 2 b^{4} d^{5}\right)}"," ",0,"-b*(-3*A*b*e + 2*B*a*e + B*b*d)*log(x + (-3*A*a*b**2*e**2 - 3*A*b**3*d*e + 2*B*a**2*b*e**2 + 3*B*a*b**2*d*e + B*b**3*d**2 - a**5*b*e**5*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 + 5*a**4*b**2*d*e**4*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 - 10*a**3*b**3*d**2*e**3*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 + 10*a**2*b**4*d**3*e**2*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 - 5*a*b**5*d**4*e*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 + b**6*d**5*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4)/(-6*A*b**3*e**2 + 4*B*a*b**2*e**2 + 2*B*b**3*d*e))/(a*e - b*d)**4 + b*(-3*A*b*e + 2*B*a*e + B*b*d)*log(x + (-3*A*a*b**2*e**2 - 3*A*b**3*d*e + 2*B*a**2*b*e**2 + 3*B*a*b**2*d*e + B*b**3*d**2 + a**5*b*e**5*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 - 5*a**4*b**2*d*e**4*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 + 10*a**3*b**3*d**2*e**3*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 - 10*a**2*b**4*d**3*e**2*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 + 5*a*b**5*d**4*e*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4 - b**6*d**5*(-3*A*b*e + 2*B*a*e + B*b*d)/(a*e - b*d)**4)/(-6*A*b**3*e**2 + 4*B*a*b**2*e**2 + 2*B*b**3*d*e))/(a*e - b*d)**4 + (-A*a**2*e**2 + 5*A*a*b*d*e + 2*A*b**2*d**2 - B*a**2*d*e - 5*B*a*b*d**2 + x**2*(6*A*b**2*e**2 - 4*B*a*b*e**2 - 2*B*b**2*d*e) + x*(3*A*a*b*e**2 + 9*A*b**2*d*e - 2*B*a**2*e**2 - 7*B*a*b*d*e - 3*B*b**2*d**2))/(2*a**4*d**2*e**3 - 6*a**3*b*d**3*e**2 + 6*a**2*b**2*d**4*e - 2*a*b**3*d**5 + x**3*(2*a**3*b*e**5 - 6*a**2*b**2*d*e**4 + 6*a*b**3*d**2*e**3 - 2*b**4*d**3*e**2) + x**2*(2*a**4*e**5 - 2*a**3*b*d*e**4 - 6*a**2*b**2*d**2*e**3 + 10*a*b**3*d**3*e**2 - 4*b**4*d**4*e) + x*(4*a**4*d*e**4 - 10*a**3*b*d**2*e**3 + 6*a**2*b**2*d**3*e**2 + 2*a*b**3*d**4*e - 2*b**4*d**5))","B",0
1701,1,486,0,21.382483," ","integrate((B*x+A)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B e^{4} x^{2}}{2 b^{4}} + x \left(\frac{A e^{4}}{b^{4}} - \frac{4 B a e^{4}}{b^{5}} + \frac{4 B d e^{3}}{b^{4}}\right) + \frac{- 26 A a^{4} b e^{4} + 44 A a^{3} b^{2} d e^{3} - 12 A a^{2} b^{3} d^{2} e^{2} - 4 A a b^{4} d^{3} e - 2 A b^{5} d^{4} + 47 B a^{5} e^{4} - 104 B a^{4} b d e^{3} + 66 B a^{3} b^{2} d^{2} e^{2} - 8 B a^{2} b^{3} d^{3} e - B a b^{4} d^{4} + x^{2} \left(- 36 A a^{2} b^{3} e^{4} + 72 A a b^{4} d e^{3} - 36 A b^{5} d^{2} e^{2} + 60 B a^{3} b^{2} e^{4} - 144 B a^{2} b^{3} d e^{3} + 108 B a b^{4} d^{2} e^{2} - 24 B b^{5} d^{3} e\right) + x \left(- 60 A a^{3} b^{2} e^{4} + 108 A a^{2} b^{3} d e^{3} - 36 A a b^{4} d^{2} e^{2} - 12 A b^{5} d^{3} e + 105 B a^{4} b e^{4} - 240 B a^{3} b^{2} d e^{3} + 162 B a^{2} b^{3} d^{2} e^{2} - 24 B a b^{4} d^{3} e - 3 B b^{5} d^{4}\right)}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{2 e^{2} \left(a e - b d\right) \left(- 2 A b e + 5 B a e - 3 B b d\right) \log{\left(a + b x \right)}}{b^{6}}"," ",0,"B*e**4*x**2/(2*b**4) + x*(A*e**4/b**4 - 4*B*a*e**4/b**5 + 4*B*d*e**3/b**4) + (-26*A*a**4*b*e**4 + 44*A*a**3*b**2*d*e**3 - 12*A*a**2*b**3*d**2*e**2 - 4*A*a*b**4*d**3*e - 2*A*b**5*d**4 + 47*B*a**5*e**4 - 104*B*a**4*b*d*e**3 + 66*B*a**3*b**2*d**2*e**2 - 8*B*a**2*b**3*d**3*e - B*a*b**4*d**4 + x**2*(-36*A*a**2*b**3*e**4 + 72*A*a*b**4*d*e**3 - 36*A*b**5*d**2*e**2 + 60*B*a**3*b**2*e**4 - 144*B*a**2*b**3*d*e**3 + 108*B*a*b**4*d**2*e**2 - 24*B*b**5*d**3*e) + x*(-60*A*a**3*b**2*e**4 + 108*A*a**2*b**3*d*e**3 - 36*A*a*b**4*d**2*e**2 - 12*A*b**5*d**3*e + 105*B*a**4*b*e**4 - 240*B*a**3*b**2*d*e**3 + 162*B*a**2*b**3*d**2*e**2 - 24*B*a*b**4*d**3*e - 3*B*b**5*d**4))/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 2*e**2*(a*e - b*d)*(-2*A*b*e + 5*B*a*e - 3*B*b*d)*log(a + b*x)/b**6","B",0
1702,1,337,0,12.681980," ","integrate((B*x+A)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B e^{3} x}{b^{4}} + \frac{11 A a^{3} b e^{3} - 6 A a^{2} b^{2} d e^{2} - 3 A a b^{3} d^{2} e - 2 A b^{4} d^{3} - 26 B a^{4} e^{3} + 33 B a^{3} b d e^{2} - 6 B a^{2} b^{2} d^{2} e - B a b^{3} d^{3} + x^{2} \left(18 A a b^{3} e^{3} - 18 A b^{4} d e^{2} - 36 B a^{2} b^{2} e^{3} + 54 B a b^{3} d e^{2} - 18 B b^{4} d^{2} e\right) + x \left(27 A a^{2} b^{2} e^{3} - 18 A a b^{3} d e^{2} - 9 A b^{4} d^{2} e - 60 B a^{3} b e^{3} + 81 B a^{2} b^{2} d e^{2} - 18 B a b^{3} d^{2} e - 3 B b^{4} d^{3}\right)}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{e^{2} \left(- A b e + 4 B a e - 3 B b d\right) \log{\left(a + b x \right)}}{b^{5}}"," ",0,"B*e**3*x/b**4 + (11*A*a**3*b*e**3 - 6*A*a**2*b**2*d*e**2 - 3*A*a*b**3*d**2*e - 2*A*b**4*d**3 - 26*B*a**4*e**3 + 33*B*a**3*b*d*e**2 - 6*B*a**2*b**2*d**2*e - B*a*b**3*d**3 + x**2*(18*A*a*b**3*e**3 - 18*A*b**4*d*e**2 - 36*B*a**2*b**2*e**3 + 54*B*a*b**3*d*e**2 - 18*B*b**4*d**2*e) + x*(27*A*a**2*b**2*e**3 - 18*A*a*b**3*d*e**2 - 9*A*b**4*d**2*e - 60*B*a**3*b*e**3 + 81*B*a**2*b**2*d*e**2 - 18*B*a*b**3*d**2*e - 3*B*b**4*d**3))/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - e**2*(-A*b*e + 4*B*a*e - 3*B*b*d)*log(a + b*x)/b**5","B",0
1703,1,211,0,5.771768," ","integrate((B*x+A)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{B e^{2} \log{\left(a + b x \right)}}{b^{4}} + \frac{- 2 A a^{2} b e^{2} - 2 A a b^{2} d e - 2 A b^{3} d^{2} + 11 B a^{3} e^{2} - 4 B a^{2} b d e - B a b^{2} d^{2} + x^{2} \left(- 6 A b^{3} e^{2} + 18 B a b^{2} e^{2} - 12 B b^{3} d e\right) + x \left(- 6 A a b^{2} e^{2} - 6 A b^{3} d e + 27 B a^{2} b e^{2} - 12 B a b^{2} d e - 3 B b^{3} d^{2}\right)}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}}"," ",0,"B*e**2*log(a + b*x)/b**4 + (-2*A*a**2*b*e**2 - 2*A*a*b**2*d*e - 2*A*b**3*d**2 + 11*B*a**3*e**2 - 4*B*a**2*b*d*e - B*a*b**2*d**2 + x**2*(-6*A*b**3*e**2 + 18*B*a*b**2*e**2 - 12*B*b**3*d*e) + x*(-6*A*a*b**2*e**2 - 6*A*b**3*d*e + 27*B*a**2*b*e**2 - 12*B*a*b**2*d*e - 3*B*b**3*d**2))/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3)","B",0
1704,1,107,0,1.494217," ","integrate((B*x+A)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- A a b e - 2 A b^{2} d - 2 B a^{2} e - B a b d - 6 B b^{2} e x^{2} + x \left(- 3 A b^{2} e - 6 B a b e - 3 B b^{2} d\right)}{6 a^{3} b^{3} + 18 a^{2} b^{4} x + 18 a b^{5} x^{2} + 6 b^{6} x^{3}}"," ",0,"(-A*a*b*e - 2*A*b**2*d - 2*B*a**2*e - B*a*b*d - 6*B*b**2*e*x**2 + x*(-3*A*b**2*e - 6*B*a*b*e - 3*B*b**2*d))/(6*a**3*b**3 + 18*a**2*b**4*x + 18*a*b**5*x**2 + 6*b**6*x**3)","A",0
1705,1,53,0,0.333982," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 2 A b - B a - 3 B b x}{6 a^{3} b^{2} + 18 a^{2} b^{3} x + 18 a b^{4} x^{2} + 6 b^{5} x^{3}}"," ",0,"(-2*A*b - B*a - 3*B*b*x)/(6*a**3*b**2 + 18*a**2*b**3*x + 18*a*b**4*x**2 + 6*b**5*x**3)","A",0
1706,1,818,0,2.810909," ","integrate((B*x+A)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**2,x)","- \frac{e^{2} \left(- A e + B d\right) \log{\left(x + \frac{- A a e^{4} - A b d e^{3} + B a d e^{3} + B b d^{2} e^{2} - \frac{a^{5} e^{7} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} + \frac{5 a^{4} b d e^{6} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} - \frac{10 a^{3} b^{2} d^{2} e^{5} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} + \frac{10 a^{2} b^{3} d^{3} e^{4} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} - \frac{5 a b^{4} d^{4} e^{3} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} + \frac{b^{5} d^{5} e^{2} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}}}{- 2 A b e^{4} + 2 B b d e^{3}} \right)}}{\left(a e - b d\right)^{4}} + \frac{e^{2} \left(- A e + B d\right) \log{\left(x + \frac{- A a e^{4} - A b d e^{3} + B a d e^{3} + B b d^{2} e^{2} + \frac{a^{5} e^{7} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} - \frac{5 a^{4} b d e^{6} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} + \frac{10 a^{3} b^{2} d^{2} e^{5} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} - \frac{10 a^{2} b^{3} d^{3} e^{4} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} + \frac{5 a b^{4} d^{4} e^{3} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}} - \frac{b^{5} d^{5} e^{2} \left(- A e + B d\right)}{\left(a e - b d\right)^{4}}}{- 2 A b e^{4} + 2 B b d e^{3}} \right)}}{\left(a e - b d\right)^{4}} + \frac{11 A a^{2} b e^{2} - 7 A a b^{2} d e + 2 A b^{3} d^{2} - 2 B a^{3} e^{2} - 5 B a^{2} b d e + B a b^{2} d^{2} + x^{2} \left(6 A b^{3} e^{2} - 6 B b^{3} d e\right) + x \left(15 A a b^{2} e^{2} - 3 A b^{3} d e - 15 B a b^{2} d e + 3 B b^{3} d^{2}\right)}{6 a^{6} b e^{3} - 18 a^{5} b^{2} d e^{2} + 18 a^{4} b^{3} d^{2} e - 6 a^{3} b^{4} d^{3} + x^{3} \left(6 a^{3} b^{4} e^{3} - 18 a^{2} b^{5} d e^{2} + 18 a b^{6} d^{2} e - 6 b^{7} d^{3}\right) + x^{2} \left(18 a^{4} b^{3} e^{3} - 54 a^{3} b^{4} d e^{2} + 54 a^{2} b^{5} d^{2} e - 18 a b^{6} d^{3}\right) + x \left(18 a^{5} b^{2} e^{3} - 54 a^{4} b^{3} d e^{2} + 54 a^{3} b^{4} d^{2} e - 18 a^{2} b^{5} d^{3}\right)}"," ",0,"-e**2*(-A*e + B*d)*log(x + (-A*a*e**4 - A*b*d*e**3 + B*a*d*e**3 + B*b*d**2*e**2 - a**5*e**7*(-A*e + B*d)/(a*e - b*d)**4 + 5*a**4*b*d*e**6*(-A*e + B*d)/(a*e - b*d)**4 - 10*a**3*b**2*d**2*e**5*(-A*e + B*d)/(a*e - b*d)**4 + 10*a**2*b**3*d**3*e**4*(-A*e + B*d)/(a*e - b*d)**4 - 5*a*b**4*d**4*e**3*(-A*e + B*d)/(a*e - b*d)**4 + b**5*d**5*e**2*(-A*e + B*d)/(a*e - b*d)**4)/(-2*A*b*e**4 + 2*B*b*d*e**3))/(a*e - b*d)**4 + e**2*(-A*e + B*d)*log(x + (-A*a*e**4 - A*b*d*e**3 + B*a*d*e**3 + B*b*d**2*e**2 + a**5*e**7*(-A*e + B*d)/(a*e - b*d)**4 - 5*a**4*b*d*e**6*(-A*e + B*d)/(a*e - b*d)**4 + 10*a**3*b**2*d**2*e**5*(-A*e + B*d)/(a*e - b*d)**4 - 10*a**2*b**3*d**3*e**4*(-A*e + B*d)/(a*e - b*d)**4 + 5*a*b**4*d**4*e**3*(-A*e + B*d)/(a*e - b*d)**4 - b**5*d**5*e**2*(-A*e + B*d)/(a*e - b*d)**4)/(-2*A*b*e**4 + 2*B*b*d*e**3))/(a*e - b*d)**4 + (11*A*a**2*b*e**2 - 7*A*a*b**2*d*e + 2*A*b**3*d**2 - 2*B*a**3*e**2 - 5*B*a**2*b*d*e + B*a*b**2*d**2 + x**2*(6*A*b**3*e**2 - 6*B*b**3*d*e) + x*(15*A*a*b**2*e**2 - 3*A*b**3*d*e - 15*B*a*b**2*d*e + 3*B*b**3*d**2))/(6*a**6*b*e**3 - 18*a**5*b**2*d*e**2 + 18*a**4*b**3*d**2*e - 6*a**3*b**4*d**3 + x**3*(6*a**3*b**4*e**3 - 18*a**2*b**5*d*e**2 + 18*a*b**6*d**2*e - 6*b**7*d**3) + x**2*(18*a**4*b**3*e**3 - 54*a**3*b**4*d*e**2 + 54*a**2*b**5*d**2*e - 18*a*b**6*d**3) + x*(18*a**5*b**2*e**3 - 54*a**4*b**3*d*e**2 + 54*a**3*b**4*d**2*e - 18*a**2*b**5*d**3))","B",0
1707,1,1445,0,5.353823," ","integrate((B*x+A)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{e^{2} \left(- 4 A b e + B a e + 3 B b d\right) \log{\left(x + \frac{- 4 A a b e^{4} - 4 A b^{2} d e^{3} + B a^{2} e^{4} + 4 B a b d e^{3} + 3 B b^{2} d^{2} e^{2} - \frac{a^{6} e^{8} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} + \frac{6 a^{5} b d e^{7} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} - \frac{15 a^{4} b^{2} d^{2} e^{6} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} + \frac{20 a^{3} b^{3} d^{3} e^{5} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} - \frac{15 a^{2} b^{4} d^{4} e^{4} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} + \frac{6 a b^{5} d^{5} e^{3} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} - \frac{b^{6} d^{6} e^{2} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}}}{- 8 A b^{2} e^{4} + 2 B a b e^{4} + 6 B b^{2} d e^{3}} \right)}}{\left(a e - b d\right)^{5}} - \frac{e^{2} \left(- 4 A b e + B a e + 3 B b d\right) \log{\left(x + \frac{- 4 A a b e^{4} - 4 A b^{2} d e^{3} + B a^{2} e^{4} + 4 B a b d e^{3} + 3 B b^{2} d^{2} e^{2} + \frac{a^{6} e^{8} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} - \frac{6 a^{5} b d e^{7} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} + \frac{15 a^{4} b^{2} d^{2} e^{6} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} - \frac{20 a^{3} b^{3} d^{3} e^{5} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} + \frac{15 a^{2} b^{4} d^{4} e^{4} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} - \frac{6 a b^{5} d^{5} e^{3} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}} + \frac{b^{6} d^{6} e^{2} \left(- 4 A b e + B a e + 3 B b d\right)}{\left(a e - b d\right)^{5}}}{- 8 A b^{2} e^{4} + 2 B a b e^{4} + 6 B b^{2} d e^{3}} \right)}}{\left(a e - b d\right)^{5}} + \frac{- 6 A a^{3} e^{3} - 26 A a^{2} b d e^{2} + 10 A a b^{2} d^{2} e - 2 A b^{3} d^{3} + 17 B a^{3} d e^{2} + 8 B a^{2} b d^{2} e - B a b^{2} d^{3} + x^{3} \left(- 24 A b^{3} e^{3} + 6 B a b^{2} e^{3} + 18 B b^{3} d e^{2}\right) + x^{2} \left(- 60 A a b^{2} e^{3} - 12 A b^{3} d e^{2} + 15 B a^{2} b e^{3} + 48 B a b^{2} d e^{2} + 9 B b^{3} d^{2} e\right) + x \left(- 44 A a^{2} b e^{3} - 32 A a b^{2} d e^{2} + 4 A b^{3} d^{2} e + 11 B a^{3} e^{3} + 41 B a^{2} b d e^{2} + 23 B a b^{2} d^{2} e - 3 B b^{3} d^{3}\right)}{6 a^{7} d e^{4} - 24 a^{6} b d^{2} e^{3} + 36 a^{5} b^{2} d^{3} e^{2} - 24 a^{4} b^{3} d^{4} e + 6 a^{3} b^{4} d^{5} + x^{4} \left(6 a^{4} b^{3} e^{5} - 24 a^{3} b^{4} d e^{4} + 36 a^{2} b^{5} d^{2} e^{3} - 24 a b^{6} d^{3} e^{2} + 6 b^{7} d^{4} e\right) + x^{3} \left(18 a^{5} b^{2} e^{5} - 66 a^{4} b^{3} d e^{4} + 84 a^{3} b^{4} d^{2} e^{3} - 36 a^{2} b^{5} d^{3} e^{2} - 6 a b^{6} d^{4} e + 6 b^{7} d^{5}\right) + x^{2} \left(18 a^{6} b e^{5} - 54 a^{5} b^{2} d e^{4} + 36 a^{4} b^{3} d^{2} e^{3} + 36 a^{3} b^{4} d^{3} e^{2} - 54 a^{2} b^{5} d^{4} e + 18 a b^{6} d^{5}\right) + x \left(6 a^{7} e^{5} - 6 a^{6} b d e^{4} - 36 a^{5} b^{2} d^{2} e^{3} + 84 a^{4} b^{3} d^{3} e^{2} - 66 a^{3} b^{4} d^{4} e + 18 a^{2} b^{5} d^{5}\right)}"," ",0,"e**2*(-4*A*b*e + B*a*e + 3*B*b*d)*log(x + (-4*A*a*b*e**4 - 4*A*b**2*d*e**3 + B*a**2*e**4 + 4*B*a*b*d*e**3 + 3*B*b**2*d**2*e**2 - a**6*e**8*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 + 6*a**5*b*d*e**7*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 - 15*a**4*b**2*d**2*e**6*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 + 20*a**3*b**3*d**3*e**5*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 - 15*a**2*b**4*d**4*e**4*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 + 6*a*b**5*d**5*e**3*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 - b**6*d**6*e**2*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5)/(-8*A*b**2*e**4 + 2*B*a*b*e**4 + 6*B*b**2*d*e**3))/(a*e - b*d)**5 - e**2*(-4*A*b*e + B*a*e + 3*B*b*d)*log(x + (-4*A*a*b*e**4 - 4*A*b**2*d*e**3 + B*a**2*e**4 + 4*B*a*b*d*e**3 + 3*B*b**2*d**2*e**2 + a**6*e**8*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 - 6*a**5*b*d*e**7*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 + 15*a**4*b**2*d**2*e**6*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 - 20*a**3*b**3*d**3*e**5*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 + 15*a**2*b**4*d**4*e**4*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 - 6*a*b**5*d**5*e**3*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5 + b**6*d**6*e**2*(-4*A*b*e + B*a*e + 3*B*b*d)/(a*e - b*d)**5)/(-8*A*b**2*e**4 + 2*B*a*b*e**4 + 6*B*b**2*d*e**3))/(a*e - b*d)**5 + (-6*A*a**3*e**3 - 26*A*a**2*b*d*e**2 + 10*A*a*b**2*d**2*e - 2*A*b**3*d**3 + 17*B*a**3*d*e**2 + 8*B*a**2*b*d**2*e - B*a*b**2*d**3 + x**3*(-24*A*b**3*e**3 + 6*B*a*b**2*e**3 + 18*B*b**3*d*e**2) + x**2*(-60*A*a*b**2*e**3 - 12*A*b**3*d*e**2 + 15*B*a**2*b*e**3 + 48*B*a*b**2*d*e**2 + 9*B*b**3*d**2*e) + x*(-44*A*a**2*b*e**3 - 32*A*a*b**2*d*e**2 + 4*A*b**3*d**2*e + 11*B*a**3*e**3 + 41*B*a**2*b*d*e**2 + 23*B*a*b**2*d**2*e - 3*B*b**3*d**3))/(6*a**7*d*e**4 - 24*a**6*b*d**2*e**3 + 36*a**5*b**2*d**3*e**2 - 24*a**4*b**3*d**4*e + 6*a**3*b**4*d**5 + x**4*(6*a**4*b**3*e**5 - 24*a**3*b**4*d*e**4 + 36*a**2*b**5*d**2*e**3 - 24*a*b**6*d**3*e**2 + 6*b**7*d**4*e) + x**3*(18*a**5*b**2*e**5 - 66*a**4*b**3*d*e**4 + 84*a**3*b**4*d**2*e**3 - 36*a**2*b**5*d**3*e**2 - 6*a*b**6*d**4*e + 6*b**7*d**5) + x**2*(18*a**6*b*e**5 - 54*a**5*b**2*d*e**4 + 36*a**4*b**3*d**2*e**3 + 36*a**3*b**4*d**3*e**2 - 54*a**2*b**5*d**4*e + 18*a*b**6*d**5) + x*(6*a**7*e**5 - 6*a**6*b*d*e**4 - 36*a**5*b**2*d**2*e**3 + 84*a**4*b**3*d**3*e**2 - 66*a**3*b**4*d**4*e + 18*a**2*b**5*d**5))","B",0
1708,1,226,0,0.154374," ","integrate((B*x+A)*(e*x+d)**4*((b*x+a)**2)**(1/2),x)","A a d^{4} x + \frac{B b e^{4} x^{7}}{7} + x^{6} \left(\frac{A b e^{4}}{6} + \frac{B a e^{4}}{6} + \frac{2 B b d e^{3}}{3}\right) + x^{5} \left(\frac{A a e^{4}}{5} + \frac{4 A b d e^{3}}{5} + \frac{4 B a d e^{3}}{5} + \frac{6 B b d^{2} e^{2}}{5}\right) + x^{4} \left(A a d e^{3} + \frac{3 A b d^{2} e^{2}}{2} + \frac{3 B a d^{2} e^{2}}{2} + B b d^{3} e\right) + x^{3} \left(2 A a d^{2} e^{2} + \frac{4 A b d^{3} e}{3} + \frac{4 B a d^{3} e}{3} + \frac{B b d^{4}}{3}\right) + x^{2} \left(2 A a d^{3} e + \frac{A b d^{4}}{2} + \frac{B a d^{4}}{2}\right)"," ",0,"A*a*d**4*x + B*b*e**4*x**7/7 + x**6*(A*b*e**4/6 + B*a*e**4/6 + 2*B*b*d*e**3/3) + x**5*(A*a*e**4/5 + 4*A*b*d*e**3/5 + 4*B*a*d*e**3/5 + 6*B*b*d**2*e**2/5) + x**4*(A*a*d*e**3 + 3*A*b*d**2*e**2/2 + 3*B*a*d**2*e**2/2 + B*b*d**3*e) + x**3*(2*A*a*d**2*e**2 + 4*A*b*d**3*e/3 + 4*B*a*d**3*e/3 + B*b*d**4/3) + x**2*(2*A*a*d**3*e + A*b*d**4/2 + B*a*d**4/2)","A",0
1709,1,168,0,0.138872," ","integrate((B*x+A)*(e*x+d)**3*((b*x+a)**2)**(1/2),x)","A a d^{3} x + \frac{B b e^{3} x^{6}}{6} + x^{5} \left(\frac{A b e^{3}}{5} + \frac{B a e^{3}}{5} + \frac{3 B b d e^{2}}{5}\right) + x^{4} \left(\frac{A a e^{3}}{4} + \frac{3 A b d e^{2}}{4} + \frac{3 B a d e^{2}}{4} + \frac{3 B b d^{2} e}{4}\right) + x^{3} \left(A a d e^{2} + A b d^{2} e + B a d^{2} e + \frac{B b d^{3}}{3}\right) + x^{2} \left(\frac{3 A a d^{2} e}{2} + \frac{A b d^{3}}{2} + \frac{B a d^{3}}{2}\right)"," ",0,"A*a*d**3*x + B*b*e**3*x**6/6 + x**5*(A*b*e**3/5 + B*a*e**3/5 + 3*B*b*d*e**2/5) + x**4*(A*a*e**3/4 + 3*A*b*d*e**2/4 + 3*B*a*d*e**2/4 + 3*B*b*d**2*e/4) + x**3*(A*a*d*e**2 + A*b*d**2*e + B*a*d**2*e + B*b*d**3/3) + x**2*(3*A*a*d**2*e/2 + A*b*d**3/2 + B*a*d**3/2)","A",0
1710,1,116,0,0.122516," ","integrate((B*x+A)*(e*x+d)**2*((b*x+a)**2)**(1/2),x)","A a d^{2} x + \frac{B b e^{2} x^{5}}{5} + x^{4} \left(\frac{A b e^{2}}{4} + \frac{B a e^{2}}{4} + \frac{B b d e}{2}\right) + x^{3} \left(\frac{A a e^{2}}{3} + \frac{2 A b d e}{3} + \frac{2 B a d e}{3} + \frac{B b d^{2}}{3}\right) + x^{2} \left(A a d e + \frac{A b d^{2}}{2} + \frac{B a d^{2}}{2}\right)"," ",0,"A*a*d**2*x + B*b*e**2*x**5/5 + x**4*(A*b*e**2/4 + B*a*e**2/4 + B*b*d*e/2) + x**3*(A*a*e**2/3 + 2*A*b*d*e/3 + 2*B*a*d*e/3 + B*b*d**2/3) + x**2*(A*a*d*e + A*b*d**2/2 + B*a*d**2/2)","A",0
1711,1,63,0,0.104858," ","integrate((B*x+A)*(e*x+d)*((b*x+a)**2)**(1/2),x)","A a d x + \frac{B b e x^{4}}{4} + x^{3} \left(\frac{A b e}{3} + \frac{B a e}{3} + \frac{B b d}{3}\right) + x^{2} \left(\frac{A a e}{2} + \frac{A b d}{2} + \frac{B a d}{2}\right)"," ",0,"A*a*d*x + B*b*e*x**4/4 + x**3*(A*b*e/3 + B*a*e/3 + B*b*d/3) + x**2*(A*a*e/2 + A*b*d/2 + B*a*d/2)","A",0
1712,1,26,0,0.092189," ","integrate((B*x+A)*((b*x+a)**2)**(1/2),x)","A a x + \frac{B b x^{3}}{3} + x^{2} \left(\frac{A b}{2} + \frac{B a}{2}\right)"," ",0,"A*a*x + B*b*x**3/3 + x**2*(A*b/2 + B*a/2)","A",0
1713,1,53,0,0.283144," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d),x)","\frac{B b x^{2}}{2 e} + x \left(\frac{A b}{e} + \frac{B a}{e} - \frac{B b d}{e^{2}}\right) - \frac{\left(- A e + B d\right) \left(a e - b d\right) \log{\left(d + e x \right)}}{e^{3}}"," ",0,"B*b*x**2/(2*e) + x*(A*b/e + B*a/e - B*b*d/e**2) - (-A*e + B*d)*(a*e - b*d)*log(d + e*x)/e**3","A",0
1714,1,71,0,0.458901," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**2,x)","\frac{B b x}{e^{2}} + \frac{- A a e^{2} + A b d e + B a d e - B b d^{2}}{d e^{3} + e^{4} x} + \frac{\left(A b e + B a e - 2 B b d\right) \log{\left(d + e x \right)}}{e^{3}}"," ",0,"B*b*x/e**2 + (-A*a*e**2 + A*b*d*e + B*a*d*e - B*b*d**2)/(d*e**3 + e**4*x) + (A*b*e + B*a*e - 2*B*b*d)*log(d + e*x)/e**3","A",0
1715,1,94,0,0.840483," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**3,x)","\frac{B b \log{\left(d + e x \right)}}{e^{3}} + \frac{- A a e^{2} - A b d e - B a d e + 3 B b d^{2} + x \left(- 2 A b e^{2} - 2 B a e^{2} + 4 B b d e\right)}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"B*b*log(d + e*x)/e**3 + (-A*a*e**2 - A*b*d*e - B*a*d*e + 3*B*b*d**2 + x*(-2*A*b*e**2 - 2*B*a*e**2 + 4*B*b*d*e))/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
1716,1,107,0,1.513496," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**4,x)","\frac{- 2 A a e^{2} - A b d e - B a d e - 2 B b d^{2} - 6 B b e^{2} x^{2} + x \left(- 3 A b e^{2} - 3 B a e^{2} - 6 B b d e\right)}{6 d^{3} e^{3} + 18 d^{2} e^{4} x + 18 d e^{5} x^{2} + 6 e^{6} x^{3}}"," ",0,"(-2*A*a*e**2 - A*b*d*e - B*a*d*e - 2*B*b*d**2 - 6*B*b*e**2*x**2 + x*(-3*A*b*e**2 - 3*B*a*e**2 - 6*B*b*d*e))/(6*d**3*e**3 + 18*d**2*e**4*x + 18*d*e**5*x**2 + 6*e**6*x**3)","A",0
1717,1,117,0,2.619380," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**5,x)","\frac{- 3 A a e^{2} - A b d e - B a d e - B b d^{2} - 6 B b e^{2} x^{2} + x \left(- 4 A b e^{2} - 4 B a e^{2} - 4 B b d e\right)}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-3*A*a*e**2 - A*b*d*e - B*a*d*e - B*b*d**2 - 6*B*b*e**2*x**2 + x*(-4*A*b*e**2 - 4*B*a*e**2 - 4*B*b*d*e))/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
1718,1,134,0,4.359905," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**6,x)","\frac{- 12 A a e^{2} - 3 A b d e - 3 B a d e - 2 B b d^{2} - 20 B b e^{2} x^{2} + x \left(- 15 A b e^{2} - 15 B a e^{2} - 10 B b d e\right)}{60 d^{5} e^{3} + 300 d^{4} e^{4} x + 600 d^{3} e^{5} x^{2} + 600 d^{2} e^{6} x^{3} + 300 d e^{7} x^{4} + 60 e^{8} x^{5}}"," ",0,"(-12*A*a*e**2 - 3*A*b*d*e - 3*B*a*d*e - 2*B*b*d**2 - 20*B*b*e**2*x**2 + x*(-15*A*b*e**2 - 15*B*a*e**2 - 10*B*b*d*e))/(60*d**5*e**3 + 300*d**4*e**4*x + 600*d**3*e**5*x**2 + 600*d**2*e**6*x**3 + 300*d*e**7*x**4 + 60*e**8*x**5)","A",0
1719,1,144,0,6.566242," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**7,x)","\frac{- 10 A a e^{2} - 2 A b d e - 2 B a d e - B b d^{2} - 15 B b e^{2} x^{2} + x \left(- 12 A b e^{2} - 12 B a e^{2} - 6 B b d e\right)}{60 d^{6} e^{3} + 360 d^{5} e^{4} x + 900 d^{4} e^{5} x^{2} + 1200 d^{3} e^{6} x^{3} + 900 d^{2} e^{7} x^{4} + 360 d e^{8} x^{5} + 60 e^{9} x^{6}}"," ",0,"(-10*A*a*e**2 - 2*A*b*d*e - 2*B*a*d*e - B*b*d**2 - 15*B*b*e**2*x**2 + x*(-12*A*b*e**2 - 12*B*a*e**2 - 6*B*b*d*e))/(60*d**6*e**3 + 360*d**5*e**4*x + 900*d**4*e**5*x**2 + 1200*d**3*e**6*x**3 + 900*d**2*e**7*x**4 + 360*d*e**8*x**5 + 60*e**9*x**6)","A",0
1720,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**5*((a + b*x)**2)**(3/2), x)","F",0
1721,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**4*((a + b*x)**2)**(3/2), x)","F",0
1722,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3*((a + b*x)**2)**(3/2), x)","F",0
1723,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2*((a + b*x)**2)**(3/2), x)","F",0
1724,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)*((a + b*x)**2)**(3/2), x)","F",0
1725,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
1726,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x), x)","F",0
1727,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x)**2, x)","F",0
1728,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x)**3, x)","F",0
1729,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x)**4, x)","F",0
1730,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x)**5, x)","F",0
1731,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x)**6, x)","F",0
1732,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(3/2)/(d + e*x)**7, x)","F",0
1733,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1734,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1735,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1736,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1737,-2,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**12,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1738,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{6} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**6*((a + b*x)**2)**(5/2), x)","F",0
1739,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**5*((a + b*x)**2)**(5/2), x)","F",0
1740,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**4*((a + b*x)**2)**(5/2), x)","F",0
1741,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3*((a + b*x)**2)**(5/2), x)","F",0
1742,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2*((a + b*x)**2)**(5/2), x)","F",0
1743,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)*((a + b*x)**2)**(5/2), x)","F",0
1744,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2), x)","F",0
1745,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d),x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/(d + e*x), x)","F",0
1746,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/(d + e*x)**2, x)","F",0
1747,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/(d + e*x)**3, x)","F",0
1748,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/(d + e*x)**4, x)","F",0
1749,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/(d + e*x)**5, x)","F",0
1750,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((A + B*x)*((a + b*x)**2)**(5/2)/(d + e*x)**6, x)","F",0
1751,-2,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**7,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1752,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1753,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1754,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1755,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1756,-2,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1757,-2,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**13,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1758,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**14,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1759,1,221,0,0.705490," ","integrate((B*x+A)*(e*x+d)**3/((b*x+a)**2)**(1/2),x)","\frac{B e^{3} x^{4}}{4 b} + x^{3} \left(\frac{A e^{3}}{3 b} - \frac{B a e^{3}}{3 b^{2}} + \frac{B d e^{2}}{b}\right) + x^{2} \left(- \frac{A a e^{3}}{2 b^{2}} + \frac{3 A d e^{2}}{2 b} + \frac{B a^{2} e^{3}}{2 b^{3}} - \frac{3 B a d e^{2}}{2 b^{2}} + \frac{3 B d^{2} e}{2 b}\right) + x \left(\frac{A a^{2} e^{3}}{b^{3}} - \frac{3 A a d e^{2}}{b^{2}} + \frac{3 A d^{2} e}{b} - \frac{B a^{3} e^{3}}{b^{4}} + \frac{3 B a^{2} d e^{2}}{b^{3}} - \frac{3 B a d^{2} e}{b^{2}} + \frac{B d^{3}}{b}\right) + \frac{\left(- A b + B a\right) \left(a e - b d\right)^{3} \log{\left(a + b x \right)}}{b^{5}}"," ",0,"B*e**3*x**4/(4*b) + x**3*(A*e**3/(3*b) - B*a*e**3/(3*b**2) + B*d*e**2/b) + x**2*(-A*a*e**3/(2*b**2) + 3*A*d*e**2/(2*b) + B*a**2*e**3/(2*b**3) - 3*B*a*d*e**2/(2*b**2) + 3*B*d**2*e/(2*b)) + x*(A*a**2*e**3/b**3 - 3*A*a*d*e**2/b**2 + 3*A*d**2*e/b - B*a**3*e**3/b**4 + 3*B*a**2*d*e**2/b**3 - 3*B*a*d**2*e/b**2 + B*d**3/b) + (-A*b + B*a)*(a*e - b*d)**3*log(a + b*x)/b**5","A",0
1760,1,117,0,0.493496," ","integrate((B*x+A)*(e*x+d)**2/((b*x+a)**2)**(1/2),x)","\frac{B e^{2} x^{3}}{3 b} + x^{2} \left(\frac{A e^{2}}{2 b} - \frac{B a e^{2}}{2 b^{2}} + \frac{B d e}{b}\right) + x \left(- \frac{A a e^{2}}{b^{2}} + \frac{2 A d e}{b} + \frac{B a^{2} e^{2}}{b^{3}} - \frac{2 B a d e}{b^{2}} + \frac{B d^{2}}{b}\right) - \frac{\left(- A b + B a\right) \left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"B*e**2*x**3/(3*b) + x**2*(A*e**2/(2*b) - B*a*e**2/(2*b**2) + B*d*e/b) + x*(-A*a*e**2/b**2 + 2*A*d*e/b + B*a**2*e**2/b**3 - 2*B*a*d*e/b**2 + B*d**2/b) - (-A*b + B*a)*(a*e - b*d)**2*log(a + b*x)/b**4","A",0
1761,1,53,0,0.292486," ","integrate((B*x+A)*(e*x+d)/((b*x+a)**2)**(1/2),x)","\frac{B e x^{2}}{2 b} + x \left(\frac{A e}{b} - \frac{B a e}{b^{2}} + \frac{B d}{b}\right) + \frac{\left(- A b + B a\right) \left(a e - b d\right) \log{\left(a + b x \right)}}{b^{3}}"," ",0,"B*e*x**2/(2*b) + x*(A*e/b - B*a*e/b**2 + B*d/b) + (-A*b + B*a)*(a*e - b*d)*log(a + b*x)/b**3","A",0
1762,1,20,0,0.169438," ","integrate((B*x+A)/((b*x+a)**2)**(1/2),x)","\frac{B x}{b} - \frac{\left(- A b + B a\right) \log{\left(a + b x \right)}}{b^{2}}"," ",0,"B*x/b - (-A*b + B*a)*log(a + b*x)/b**2","A",0
1763,1,226,0,1.447558," ","integrate((B*x+A)/(e*x+d)/((b*x+a)**2)**(1/2),x)","- \frac{\left(- A e + B d\right) \log{\left(x + \frac{- A a e - A b d + 2 B a d - \frac{a^{2} e \left(- A e + B d\right)}{a e - b d} + \frac{2 a b d \left(- A e + B d\right)}{a e - b d} - \frac{b^{2} d^{2} \left(- A e + B d\right)}{e \left(a e - b d\right)}}{- 2 A b e + B a e + B b d} \right)}}{e \left(a e - b d\right)} + \frac{\left(- A b + B a\right) \log{\left(x + \frac{- A a e - A b d + 2 B a d + \frac{a^{2} e^{2} \left(- A b + B a\right)}{b \left(a e - b d\right)} - \frac{2 a d e \left(- A b + B a\right)}{a e - b d} + \frac{b d^{2} \left(- A b + B a\right)}{a e - b d}}{- 2 A b e + B a e + B b d} \right)}}{b \left(a e - b d\right)}"," ",0,"-(-A*e + B*d)*log(x + (-A*a*e - A*b*d + 2*B*a*d - a**2*e*(-A*e + B*d)/(a*e - b*d) + 2*a*b*d*(-A*e + B*d)/(a*e - b*d) - b**2*d**2*(-A*e + B*d)/(e*(a*e - b*d)))/(-2*A*b*e + B*a*e + B*b*d))/(e*(a*e - b*d)) + (-A*b + B*a)*log(x + (-A*a*e - A*b*d + 2*B*a*d + a**2*e**2*(-A*b + B*a)/(b*(a*e - b*d)) - 2*a*d*e*(-A*b + B*a)/(a*e - b*d) + b*d**2*(-A*b + B*a)/(a*e - b*d))/(-2*A*b*e + B*a*e + B*b*d))/(b*(a*e - b*d))","B",0
1764,1,355,0,1.222186," ","integrate((B*x+A)/(e*x+d)**2/((b*x+a)**2)**(1/2),x)","\frac{\left(- A b + B a\right) \log{\left(x + \frac{- A a b e - A b^{2} d + B a^{2} e + B a b d - \frac{a^{3} e^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{2}} + \frac{3 a^{2} b d e^{2} \left(- A b + B a\right)}{\left(a e - b d\right)^{2}} - \frac{3 a b^{2} d^{2} e \left(- A b + B a\right)}{\left(a e - b d\right)^{2}} + \frac{b^{3} d^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{2}}}{- 2 A b^{2} e + 2 B a b e} \right)}}{\left(a e - b d\right)^{2}} - \frac{\left(- A b + B a\right) \log{\left(x + \frac{- A a b e - A b^{2} d + B a^{2} e + B a b d + \frac{a^{3} e^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{2}} - \frac{3 a^{2} b d e^{2} \left(- A b + B a\right)}{\left(a e - b d\right)^{2}} + \frac{3 a b^{2} d^{2} e \left(- A b + B a\right)}{\left(a e - b d\right)^{2}} - \frac{b^{3} d^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{2}}}{- 2 A b^{2} e + 2 B a b e} \right)}}{\left(a e - b d\right)^{2}} + \frac{- A e + B d}{a d e^{2} - b d^{2} e + x \left(a e^{3} - b d e^{2}\right)}"," ",0,"(-A*b + B*a)*log(x + (-A*a*b*e - A*b**2*d + B*a**2*e + B*a*b*d - a**3*e**3*(-A*b + B*a)/(a*e - b*d)**2 + 3*a**2*b*d*e**2*(-A*b + B*a)/(a*e - b*d)**2 - 3*a*b**2*d**2*e*(-A*b + B*a)/(a*e - b*d)**2 + b**3*d**3*(-A*b + B*a)/(a*e - b*d)**2)/(-2*A*b**2*e + 2*B*a*b*e))/(a*e - b*d)**2 - (-A*b + B*a)*log(x + (-A*a*b*e - A*b**2*d + B*a**2*e + B*a*b*d + a**3*e**3*(-A*b + B*a)/(a*e - b*d)**2 - 3*a**2*b*d*e**2*(-A*b + B*a)/(a*e - b*d)**2 + 3*a*b**2*d**2*e*(-A*b + B*a)/(a*e - b*d)**2 - b**3*d**3*(-A*b + B*a)/(a*e - b*d)**2)/(-2*A*b**2*e + 2*B*a*b*e))/(a*e - b*d)**2 + (-A*e + B*d)/(a*d*e**2 - b*d**2*e + x*(a*e**3 - b*d*e**2))","B",0
1765,1,558,0,1.988718," ","integrate((B*x+A)/(e*x+d)**3/((b*x+a)**2)**(1/2),x)","- \frac{b \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{2} e - A b^{3} d + B a^{2} b e + B a b^{2} d - \frac{a^{4} b e^{4} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} + \frac{4 a^{3} b^{2} d e^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} - \frac{6 a^{2} b^{3} d^{2} e^{2} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} + \frac{4 a b^{4} d^{3} e \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} - \frac{b^{5} d^{4} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}}}{- 2 A b^{3} e + 2 B a b^{2} e} \right)}}{\left(a e - b d\right)^{3}} + \frac{b \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{2} e - A b^{3} d + B a^{2} b e + B a b^{2} d + \frac{a^{4} b e^{4} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} - \frac{4 a^{3} b^{2} d e^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} + \frac{6 a^{2} b^{3} d^{2} e^{2} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} - \frac{4 a b^{4} d^{3} e \left(- A b + B a\right)}{\left(a e - b d\right)^{3}} + \frac{b^{5} d^{4} \left(- A b + B a\right)}{\left(a e - b d\right)^{3}}}{- 2 A b^{3} e + 2 B a b^{2} e} \right)}}{\left(a e - b d\right)^{3}} + \frac{- A a e^{2} + 3 A b d e - B a d e - B b d^{2} + x \left(2 A b e^{2} - 2 B a e^{2}\right)}{2 a^{2} d^{2} e^{3} - 4 a b d^{3} e^{2} + 2 b^{2} d^{4} e + x^{2} \left(2 a^{2} e^{5} - 4 a b d e^{4} + 2 b^{2} d^{2} e^{3}\right) + x \left(4 a^{2} d e^{4} - 8 a b d^{2} e^{3} + 4 b^{2} d^{3} e^{2}\right)}"," ",0,"-b*(-A*b + B*a)*log(x + (-A*a*b**2*e - A*b**3*d + B*a**2*b*e + B*a*b**2*d - a**4*b*e**4*(-A*b + B*a)/(a*e - b*d)**3 + 4*a**3*b**2*d*e**3*(-A*b + B*a)/(a*e - b*d)**3 - 6*a**2*b**3*d**2*e**2*(-A*b + B*a)/(a*e - b*d)**3 + 4*a*b**4*d**3*e*(-A*b + B*a)/(a*e - b*d)**3 - b**5*d**4*(-A*b + B*a)/(a*e - b*d)**3)/(-2*A*b**3*e + 2*B*a*b**2*e))/(a*e - b*d)**3 + b*(-A*b + B*a)*log(x + (-A*a*b**2*e - A*b**3*d + B*a**2*b*e + B*a*b**2*d + a**4*b*e**4*(-A*b + B*a)/(a*e - b*d)**3 - 4*a**3*b**2*d*e**3*(-A*b + B*a)/(a*e - b*d)**3 + 6*a**2*b**3*d**2*e**2*(-A*b + B*a)/(a*e - b*d)**3 - 4*a*b**4*d**3*e*(-A*b + B*a)/(a*e - b*d)**3 + b**5*d**4*(-A*b + B*a)/(a*e - b*d)**3)/(-2*A*b**3*e + 2*B*a*b**2*e))/(a*e - b*d)**3 + (-A*a*e**2 + 3*A*b*d*e - B*a*d*e - B*b*d**2 + x*(2*A*b*e**2 - 2*B*a*e**2))/(2*a**2*d**2*e**3 - 4*a*b*d**3*e**2 + 2*b**2*d**4*e + x**2*(2*a**2*e**5 - 4*a*b*d*e**4 + 2*b**2*d**2*e**3) + x*(4*a**2*d*e**4 - 8*a*b*d**2*e**3 + 4*b**2*d**3*e**2))","B",0
1766,1,818,0,2.859466," ","integrate((B*x+A)/(e*x+d)**4/((b*x+a)**2)**(1/2),x)","\frac{b^{2} \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{3} e - A b^{4} d + B a^{2} b^{2} e + B a b^{3} d - \frac{a^{5} b^{2} e^{5} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} + \frac{5 a^{4} b^{3} d e^{4} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} - \frac{10 a^{3} b^{4} d^{2} e^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} + \frac{10 a^{2} b^{5} d^{3} e^{2} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} - \frac{5 a b^{6} d^{4} e \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} + \frac{b^{7} d^{5} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}}}{- 2 A b^{4} e + 2 B a b^{3} e} \right)}}{\left(a e - b d\right)^{4}} - \frac{b^{2} \left(- A b + B a\right) \log{\left(x + \frac{- A a b^{3} e - A b^{4} d + B a^{2} b^{2} e + B a b^{3} d + \frac{a^{5} b^{2} e^{5} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} - \frac{5 a^{4} b^{3} d e^{4} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} + \frac{10 a^{3} b^{4} d^{2} e^{3} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} - \frac{10 a^{2} b^{5} d^{3} e^{2} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} + \frac{5 a b^{6} d^{4} e \left(- A b + B a\right)}{\left(a e - b d\right)^{4}} - \frac{b^{7} d^{5} \left(- A b + B a\right)}{\left(a e - b d\right)^{4}}}{- 2 A b^{4} e + 2 B a b^{3} e} \right)}}{\left(a e - b d\right)^{4}} + \frac{- 2 A a^{2} e^{3} + 7 A a b d e^{2} - 11 A b^{2} d^{2} e - B a^{2} d e^{2} + 5 B a b d^{2} e + 2 B b^{2} d^{3} + x^{2} \left(- 6 A b^{2} e^{3} + 6 B a b e^{3}\right) + x \left(3 A a b e^{3} - 15 A b^{2} d e^{2} - 3 B a^{2} e^{3} + 15 B a b d e^{2}\right)}{6 a^{3} d^{3} e^{4} - 18 a^{2} b d^{4} e^{3} + 18 a b^{2} d^{5} e^{2} - 6 b^{3} d^{6} e + x^{3} \left(6 a^{3} e^{7} - 18 a^{2} b d e^{6} + 18 a b^{2} d^{2} e^{5} - 6 b^{3} d^{3} e^{4}\right) + x^{2} \left(18 a^{3} d e^{6} - 54 a^{2} b d^{2} e^{5} + 54 a b^{2} d^{3} e^{4} - 18 b^{3} d^{4} e^{3}\right) + x \left(18 a^{3} d^{2} e^{5} - 54 a^{2} b d^{3} e^{4} + 54 a b^{2} d^{4} e^{3} - 18 b^{3} d^{5} e^{2}\right)}"," ",0,"b**2*(-A*b + B*a)*log(x + (-A*a*b**3*e - A*b**4*d + B*a**2*b**2*e + B*a*b**3*d - a**5*b**2*e**5*(-A*b + B*a)/(a*e - b*d)**4 + 5*a**4*b**3*d*e**4*(-A*b + B*a)/(a*e - b*d)**4 - 10*a**3*b**4*d**2*e**3*(-A*b + B*a)/(a*e - b*d)**4 + 10*a**2*b**5*d**3*e**2*(-A*b + B*a)/(a*e - b*d)**4 - 5*a*b**6*d**4*e*(-A*b + B*a)/(a*e - b*d)**4 + b**7*d**5*(-A*b + B*a)/(a*e - b*d)**4)/(-2*A*b**4*e + 2*B*a*b**3*e))/(a*e - b*d)**4 - b**2*(-A*b + B*a)*log(x + (-A*a*b**3*e - A*b**4*d + B*a**2*b**2*e + B*a*b**3*d + a**5*b**2*e**5*(-A*b + B*a)/(a*e - b*d)**4 - 5*a**4*b**3*d*e**4*(-A*b + B*a)/(a*e - b*d)**4 + 10*a**3*b**4*d**2*e**3*(-A*b + B*a)/(a*e - b*d)**4 - 10*a**2*b**5*d**3*e**2*(-A*b + B*a)/(a*e - b*d)**4 + 5*a*b**6*d**4*e*(-A*b + B*a)/(a*e - b*d)**4 - b**7*d**5*(-A*b + B*a)/(a*e - b*d)**4)/(-2*A*b**4*e + 2*B*a*b**3*e))/(a*e - b*d)**4 + (-2*A*a**2*e**3 + 7*A*a*b*d*e**2 - 11*A*b**2*d**2*e - B*a**2*d*e**2 + 5*B*a*b*d**2*e + 2*B*b**2*d**3 + x**2*(-6*A*b**2*e**3 + 6*B*a*b*e**3) + x*(3*A*a*b*e**3 - 15*A*b**2*d*e**2 - 3*B*a**2*e**3 + 15*B*a*b*d*e**2))/(6*a**3*d**3*e**4 - 18*a**2*b*d**4*e**3 + 18*a*b**2*d**5*e**2 - 6*b**3*d**6*e + x**3*(6*a**3*e**7 - 18*a**2*b*d*e**6 + 18*a*b**2*d**2*e**5 - 6*b**3*d**3*e**4) + x**2*(18*a**3*d*e**6 - 54*a**2*b*d**2*e**5 + 54*a*b**2*d**3*e**4 - 18*b**3*d**4*e**3) + x*(18*a**3*d**2*e**5 - 54*a**2*b*d**3*e**4 + 54*a*b**2*d**4*e**3 - 18*b**3*d**5*e**2))","B",0
1767,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**4/((a + b*x)**2)**(3/2), x)","F",0
1768,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/((a + b*x)**2)**(3/2), x)","F",0
1769,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/((a + b*x)**2)**(3/2), x)","F",0
1770,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/((a + b*x)**2)**(3/2), x)","F",0
1771,0,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
1772,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{\left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)*((a + b*x)**2)**(3/2)), x)","F",0
1773,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**2*((a + b*x)**2)**(3/2)), x)","F",0
1774,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**3*((a + b*x)**2)**(3/2)), x)","F",0
1775,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**5/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{5}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**5/((a + b*x)**2)**(5/2), x)","F",0
1776,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**4/((a + b*x)**2)**(5/2), x)","F",0
1777,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/((a + b*x)**2)**(5/2), x)","F",0
1778,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/((a + b*x)**2)**(5/2), x)","F",0
1779,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/((a + b*x)**2)**(5/2), x)","F",0
1780,0,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{A + B x}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/((a + b*x)**2)**(5/2), x)","F",0
1781,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{A + B x}{\left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)*((a + b*x)**2)**(5/2)), x)","F",0
1782,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1783,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1784,1,1020,0,9.096282," ","integrate((B*x+A)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \frac{2 A a^{2} d^{4} \sqrt{d + e x}}{9 e} + \frac{8 A a^{2} d^{3} x \sqrt{d + e x}}{9} + \frac{4 A a^{2} d^{2} e x^{2} \sqrt{d + e x}}{3} + \frac{8 A a^{2} d e^{2} x^{3} \sqrt{d + e x}}{9} + \frac{2 A a^{2} e^{3} x^{4} \sqrt{d + e x}}{9} - \frac{8 A a b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{4 A a b d^{4} x \sqrt{d + e x}}{99 e} + \frac{32 A a b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{184 A a b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{136 A a b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{4 A a b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{16 A b^{2} d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{8 A b^{2} d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{2 A b^{2} d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{424 A b^{2} d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{916 A b^{2} d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{80 A b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{2 A b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{4 B a^{2} d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{2 B a^{2} d^{4} x \sqrt{d + e x}}{99 e} + \frac{16 B a^{2} d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{92 B a^{2} d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{68 B a^{2} d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{2 B a^{2} e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{32 B a b d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{16 B a b d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{4 B a b d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{848 B a b d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{1832 B a b d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{160 B a b d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{4 B a b e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{32 B b^{2} d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{16 B b^{2} d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{4 B b^{2} d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{2 B b^{2} d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{320 B b^{2} d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{412 B b^{2} d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{92 B b^{2} d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{2 B b^{2} e^{3} x^{7} \sqrt{d + e x}}{15} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(A a^{2} x + A a b x^{2} + \frac{A b^{2} x^{3}}{3} + \frac{B a^{2} x^{2}}{2} + \frac{2 B a b x^{3}}{3} + \frac{B b^{2} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a**2*d**4*sqrt(d + e*x)/(9*e) + 8*A*a**2*d**3*x*sqrt(d + e*x)/9 + 4*A*a**2*d**2*e*x**2*sqrt(d + e*x)/3 + 8*A*a**2*d*e**2*x**3*sqrt(d + e*x)/9 + 2*A*a**2*e**3*x**4*sqrt(d + e*x)/9 - 8*A*a*b*d**5*sqrt(d + e*x)/(99*e**2) + 4*A*a*b*d**4*x*sqrt(d + e*x)/(99*e) + 32*A*a*b*d**3*x**2*sqrt(d + e*x)/33 + 184*A*a*b*d**2*e*x**3*sqrt(d + e*x)/99 + 136*A*a*b*d*e**2*x**4*sqrt(d + e*x)/99 + 4*A*a*b*e**3*x**5*sqrt(d + e*x)/11 + 16*A*b**2*d**6*sqrt(d + e*x)/(1287*e**3) - 8*A*b**2*d**5*x*sqrt(d + e*x)/(1287*e**2) + 2*A*b**2*d**4*x**2*sqrt(d + e*x)/(429*e) + 424*A*b**2*d**3*x**3*sqrt(d + e*x)/1287 + 916*A*b**2*d**2*e*x**4*sqrt(d + e*x)/1287 + 80*A*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 2*A*b**2*e**3*x**6*sqrt(d + e*x)/13 - 4*B*a**2*d**5*sqrt(d + e*x)/(99*e**2) + 2*B*a**2*d**4*x*sqrt(d + e*x)/(99*e) + 16*B*a**2*d**3*x**2*sqrt(d + e*x)/33 + 92*B*a**2*d**2*e*x**3*sqrt(d + e*x)/99 + 68*B*a**2*d*e**2*x**4*sqrt(d + e*x)/99 + 2*B*a**2*e**3*x**5*sqrt(d + e*x)/11 + 32*B*a*b*d**6*sqrt(d + e*x)/(1287*e**3) - 16*B*a*b*d**5*x*sqrt(d + e*x)/(1287*e**2) + 4*B*a*b*d**4*x**2*sqrt(d + e*x)/(429*e) + 848*B*a*b*d**3*x**3*sqrt(d + e*x)/1287 + 1832*B*a*b*d**2*e*x**4*sqrt(d + e*x)/1287 + 160*B*a*b*d*e**2*x**5*sqrt(d + e*x)/143 + 4*B*a*b*e**3*x**6*sqrt(d + e*x)/13 - 32*B*b**2*d**7*sqrt(d + e*x)/(6435*e**4) + 16*B*b**2*d**6*x*sqrt(d + e*x)/(6435*e**3) - 4*B*b**2*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 2*B*b**2*d**4*x**3*sqrt(d + e*x)/(1287*e) + 320*B*b**2*d**3*x**4*sqrt(d + e*x)/1287 + 412*B*b**2*d**2*e*x**5*sqrt(d + e*x)/715 + 92*B*b**2*d*e**2*x**6*sqrt(d + e*x)/195 + 2*B*b**2*e**3*x**7*sqrt(d + e*x)/15, Ne(e, 0)), (d**(7/2)*(A*a**2*x + A*a*b*x**2 + A*b**2*x**3/3 + B*a**2*x**2/2 + 2*B*a*b*x**3/3 + B*b**2*x**4/4), True))","A",0
1785,1,857,0,4.629428," ","integrate((B*x+A)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \frac{2 A a^{2} d^{3} \sqrt{d + e x}}{7 e} + \frac{6 A a^{2} d^{2} x \sqrt{d + e x}}{7} + \frac{6 A a^{2} d e x^{2} \sqrt{d + e x}}{7} + \frac{2 A a^{2} e^{2} x^{3} \sqrt{d + e x}}{7} - \frac{8 A a b d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{4 A a b d^{3} x \sqrt{d + e x}}{63 e} + \frac{20 A a b d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{76 A a b d e x^{3} \sqrt{d + e x}}{63} + \frac{4 A a b e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{16 A b^{2} d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{8 A b^{2} d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{2 A b^{2} d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{226 A b^{2} d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{46 A b^{2} d e x^{4} \sqrt{d + e x}}{99} + \frac{2 A b^{2} e^{2} x^{5} \sqrt{d + e x}}{11} - \frac{4 B a^{2} d^{4} \sqrt{d + e x}}{63 e^{2}} + \frac{2 B a^{2} d^{3} x \sqrt{d + e x}}{63 e} + \frac{10 B a^{2} d^{2} x^{2} \sqrt{d + e x}}{21} + \frac{38 B a^{2} d e x^{3} \sqrt{d + e x}}{63} + \frac{2 B a^{2} e^{2} x^{4} \sqrt{d + e x}}{9} + \frac{32 B a b d^{5} \sqrt{d + e x}}{693 e^{3}} - \frac{16 B a b d^{4} x \sqrt{d + e x}}{693 e^{2}} + \frac{4 B a b d^{3} x^{2} \sqrt{d + e x}}{231 e} + \frac{452 B a b d^{2} x^{3} \sqrt{d + e x}}{693} + \frac{92 B a b d e x^{4} \sqrt{d + e x}}{99} + \frac{4 B a b e^{2} x^{5} \sqrt{d + e x}}{11} - \frac{32 B b^{2} d^{6} \sqrt{d + e x}}{3003 e^{4}} + \frac{16 B b^{2} d^{5} x \sqrt{d + e x}}{3003 e^{3}} - \frac{4 B b^{2} d^{4} x^{2} \sqrt{d + e x}}{1001 e^{2}} + \frac{10 B b^{2} d^{3} x^{3} \sqrt{d + e x}}{3003 e} + \frac{106 B b^{2} d^{2} x^{4} \sqrt{d + e x}}{429} + \frac{54 B b^{2} d e x^{5} \sqrt{d + e x}}{143} + \frac{2 B b^{2} e^{2} x^{6} \sqrt{d + e x}}{13} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(A a^{2} x + A a b x^{2} + \frac{A b^{2} x^{3}}{3} + \frac{B a^{2} x^{2}}{2} + \frac{2 B a b x^{3}}{3} + \frac{B b^{2} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a**2*d**3*sqrt(d + e*x)/(7*e) + 6*A*a**2*d**2*x*sqrt(d + e*x)/7 + 6*A*a**2*d*e*x**2*sqrt(d + e*x)/7 + 2*A*a**2*e**2*x**3*sqrt(d + e*x)/7 - 8*A*a*b*d**4*sqrt(d + e*x)/(63*e**2) + 4*A*a*b*d**3*x*sqrt(d + e*x)/(63*e) + 20*A*a*b*d**2*x**2*sqrt(d + e*x)/21 + 76*A*a*b*d*e*x**3*sqrt(d + e*x)/63 + 4*A*a*b*e**2*x**4*sqrt(d + e*x)/9 + 16*A*b**2*d**5*sqrt(d + e*x)/(693*e**3) - 8*A*b**2*d**4*x*sqrt(d + e*x)/(693*e**2) + 2*A*b**2*d**3*x**2*sqrt(d + e*x)/(231*e) + 226*A*b**2*d**2*x**3*sqrt(d + e*x)/693 + 46*A*b**2*d*e*x**4*sqrt(d + e*x)/99 + 2*A*b**2*e**2*x**5*sqrt(d + e*x)/11 - 4*B*a**2*d**4*sqrt(d + e*x)/(63*e**2) + 2*B*a**2*d**3*x*sqrt(d + e*x)/(63*e) + 10*B*a**2*d**2*x**2*sqrt(d + e*x)/21 + 38*B*a**2*d*e*x**3*sqrt(d + e*x)/63 + 2*B*a**2*e**2*x**4*sqrt(d + e*x)/9 + 32*B*a*b*d**5*sqrt(d + e*x)/(693*e**3) - 16*B*a*b*d**4*x*sqrt(d + e*x)/(693*e**2) + 4*B*a*b*d**3*x**2*sqrt(d + e*x)/(231*e) + 452*B*a*b*d**2*x**3*sqrt(d + e*x)/693 + 92*B*a*b*d*e*x**4*sqrt(d + e*x)/99 + 4*B*a*b*e**2*x**5*sqrt(d + e*x)/11 - 32*B*b**2*d**6*sqrt(d + e*x)/(3003*e**4) + 16*B*b**2*d**5*x*sqrt(d + e*x)/(3003*e**3) - 4*B*b**2*d**4*x**2*sqrt(d + e*x)/(1001*e**2) + 10*B*b**2*d**3*x**3*sqrt(d + e*x)/(3003*e) + 106*B*b**2*d**2*x**4*sqrt(d + e*x)/429 + 54*B*b**2*d*e*x**5*sqrt(d + e*x)/143 + 2*B*b**2*e**2*x**6*sqrt(d + e*x)/13, Ne(e, 0)), (d**(5/2)*(A*a**2*x + A*a*b*x**2 + A*b**2*x**3/3 + B*a**2*x**2/2 + 2*B*a*b*x**3/3 + B*b**2*x**4/4), True))","A",0
1786,1,586,0,22.383297," ","integrate((B*x+A)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2),x)","A a^{2} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 A a^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{4 A a b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 A a b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 A b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 A b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 B a^{2} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 B a^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{4 B a b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{4 B a b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 B b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 B b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}}"," ",0,"A*a**2*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*A*a**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 4*A*a*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*A*a*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*A*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*A*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*B*a**2*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*B*a**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 4*B*a*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 4*B*a*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*B*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*B*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4","A",0
1787,1,201,0,4.910133," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{B b^{2} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{3}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(A b^{2} e + 2 B a b e - 3 B b^{2} d\right)}{7 e^{3}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 A a b e^{2} - 2 A b^{2} d e + B a^{2} e^{2} - 4 B a b d e + 3 B b^{2} d^{2}\right)}{5 e^{3}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A a^{2} e^{3} - 2 A a b d e^{2} + A b^{2} d^{2} e - B a^{2} d e^{2} + 2 B a b d^{2} e - B b^{2} d^{3}\right)}{3 e^{3}}\right)}{e}"," ",0,"2*(B*b**2*(d + e*x)**(9/2)/(9*e**3) + (d + e*x)**(7/2)*(A*b**2*e + 2*B*a*b*e - 3*B*b**2*d)/(7*e**3) + (d + e*x)**(5/2)*(2*A*a*b*e**2 - 2*A*b**2*d*e + B*a**2*e**2 - 4*B*a*b*d*e + 3*B*b**2*d**2)/(5*e**3) + (d + e*x)**(3/2)*(A*a**2*e**3 - 2*A*a*b*d*e**2 + A*b**2*d**2*e - B*a**2*d*e**2 + 2*B*a*b*d**2*e - B*b**2*d**3)/(3*e**3))/e","A",0
1788,1,583,0,53.774856," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a^{2} d}{\sqrt{d + e x}} - 2 A a^{2} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{4 A a b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{4 A a b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{2 A b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{2 A b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 B a^{2} d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 B a^{2} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{4 B a b d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{4 B a b \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 B b^{2} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 B b^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{A a^{2} x + \frac{B b^{2} x^{4}}{4} + \frac{x^{3} \left(A b^{2} + 2 B a b\right)}{3} + \frac{x^{2} \left(2 A a b + B a^{2}\right)}{2}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a**2*d/sqrt(d + e*x) - 2*A*a**2*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 4*A*a*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 4*A*a*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 2*A*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 2*A*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*B*a**2*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*B*a**2*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 4*B*a*b*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 4*B*a*b*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*B*b**2*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*B*b**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3)/e, Ne(e, 0)), ((A*a**2*x + B*b**2*x**4/4 + x**3*(A*b**2 + 2*B*a*b)/3 + x**2*(2*A*a*b + B*a**2)/2)/sqrt(d), True))","A",0
1789,1,150,0,33.869418," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(3/2),x)","\frac{2 B b^{2} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(2 A b^{2} e + 4 B a b e - 6 B b^{2} d\right)}{3 e^{4}} + \frac{\sqrt{d + e x} \left(4 A a b e^{2} - 4 A b^{2} d e + 2 B a^{2} e^{2} - 8 B a b d e + 6 B b^{2} d^{2}\right)}{e^{4}} + \frac{2 \left(- A e + B d\right) \left(a e - b d\right)^{2}}{e^{4} \sqrt{d + e x}}"," ",0,"2*B*b**2*(d + e*x)**(5/2)/(5*e**4) + (d + e*x)**(3/2)*(2*A*b**2*e + 4*B*a*b*e - 6*B*b**2*d)/(3*e**4) + sqrt(d + e*x)*(4*A*a*b*e**2 - 4*A*b**2*d*e + 2*B*a**2*e**2 - 8*B*a*b*d*e + 6*B*b**2*d**2)/e**4 + 2*(-A*e + B*d)*(a*e - b*d)**2/(e**4*sqrt(d + e*x))","A",0
1790,1,709,0,1.705517," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 A a^{2} e^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{8 A a b d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 A a b e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{16 A b^{2} d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{24 A b^{2} d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{6 A b^{2} e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{4 B a^{2} d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{6 B a^{2} e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{32 B a b d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{48 B a b d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{12 B a b e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{32 B b^{2} d^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{48 B b^{2} d^{2} e x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 B b^{2} d e^{2} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{2 B b^{2} e^{3} x^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{2} x + A a b x^{2} + \frac{A b^{2} x^{3}}{3} + \frac{B a^{2} x^{2}}{2} + \frac{2 B a b x^{3}}{3} + \frac{B b^{2} x^{4}}{4}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a**2*e**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 8*A*a*b*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*A*a*b*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 16*A*b**2*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 24*A*b**2*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 6*A*b**2*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 4*B*a**2*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 6*B*a**2*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 32*B*a*b*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 48*B*a*b*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 12*B*a*b*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 32*B*b**2*d**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 48*B*b**2*d**2*e*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*B*b**2*d*e**2*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 2*B*b**2*e**3*x**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)), Ne(e, 0)), ((A*a**2*x + A*a*b*x**2 + A*b**2*x**3/3 + B*a**2*x**2/2 + 2*B*a*b*x**3/3 + B*b**2*x**4/4)/d**(5/2), True))","A",0
1791,1,1015,0,3.638552," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 A a^{2} e^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{8 A a b d e^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{20 A a b e^{3} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{16 A b^{2} d^{2} e}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{40 A b^{2} d e^{2} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{30 A b^{2} e^{3} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{4 B a^{2} d e^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{10 B a^{2} e^{3} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{32 B a b d^{2} e}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{80 B a b d e^{2} x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} - \frac{60 B a b e^{3} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{96 B b^{2} d^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{240 B b^{2} d^{2} e x}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{180 B b^{2} d e^{2} x^{2}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} + \frac{30 B b^{2} e^{3} x^{3}}{15 d^{2} e^{4} \sqrt{d + e x} + 30 d e^{5} x \sqrt{d + e x} + 15 e^{6} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{2} x + A a b x^{2} + \frac{A b^{2} x^{3}}{3} + \frac{B a^{2} x^{2}}{2} + \frac{2 B a b x^{3}}{3} + \frac{B b^{2} x^{4}}{4}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*a**2*e**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 8*A*a*b*d*e**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 20*A*a*b*e**3*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 16*A*b**2*d**2*e/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 40*A*b**2*d*e**2*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 30*A*b**2*e**3*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 4*B*a**2*d*e**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 10*B*a**2*e**3*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 32*B*a*b*d**2*e/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 80*B*a*b*d*e**2*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) - 60*B*a*b*e**3*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 96*B*b**2*d**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 240*B*b**2*d**2*e*x/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 180*B*b**2*d*e**2*x**2/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)) + 30*B*b**2*e**3*x**3/(15*d**2*e**4*sqrt(d + e*x) + 30*d*e**5*x*sqrt(d + e*x) + 15*e**6*x**2*sqrt(d + e*x)), Ne(e, 0)), ((A*a**2*x + A*a*b*x**2 + A*b**2*x**3/3 + B*a**2*x**2/2 + 2*B*a*b*x**3/3 + B*b**2*x**4/4)/d**(7/2), True))","A",0
1792,1,2091,0,16.307080," ","integrate((B*x+A)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \frac{2 A a^{4} d^{4} \sqrt{d + e x}}{9 e} + \frac{8 A a^{4} d^{3} x \sqrt{d + e x}}{9} + \frac{4 A a^{4} d^{2} e x^{2} \sqrt{d + e x}}{3} + \frac{8 A a^{4} d e^{2} x^{3} \sqrt{d + e x}}{9} + \frac{2 A a^{4} e^{3} x^{4} \sqrt{d + e x}}{9} - \frac{16 A a^{3} b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{8 A a^{3} b d^{4} x \sqrt{d + e x}}{99 e} + \frac{64 A a^{3} b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{368 A a^{3} b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{272 A a^{3} b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{8 A a^{3} b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{32 A a^{2} b^{2} d^{6} \sqrt{d + e x}}{429 e^{3}} - \frac{16 A a^{2} b^{2} d^{5} x \sqrt{d + e x}}{429 e^{2}} + \frac{4 A a^{2} b^{2} d^{4} x^{2} \sqrt{d + e x}}{143 e} + \frac{848 A a^{2} b^{2} d^{3} x^{3} \sqrt{d + e x}}{429} + \frac{1832 A a^{2} b^{2} d^{2} e x^{4} \sqrt{d + e x}}{429} + \frac{480 A a^{2} b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{12 A a^{2} b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{128 A a b^{3} d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{64 A a b^{3} d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{16 A a b^{3} d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{8 A a b^{3} d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{1280 A a b^{3} d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{1648 A a b^{3} d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{368 A a b^{3} d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{8 A a b^{3} e^{3} x^{7} \sqrt{d + e x}}{15} + \frac{256 A b^{4} d^{8} \sqrt{d + e x}}{109395 e^{5}} - \frac{128 A b^{4} d^{7} x \sqrt{d + e x}}{109395 e^{4}} + \frac{32 A b^{4} d^{6} x^{2} \sqrt{d + e x}}{36465 e^{3}} - \frac{16 A b^{4} d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{14 A b^{4} d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{2424 A b^{4} d^{3} x^{5} \sqrt{d + e x}}{12155} + \frac{1604 A b^{4} d^{2} e x^{6} \sqrt{d + e x}}{3315} + \frac{104 A b^{4} d e^{2} x^{7} \sqrt{d + e x}}{255} + \frac{2 A b^{4} e^{3} x^{8} \sqrt{d + e x}}{17} - \frac{4 B a^{4} d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{2 B a^{4} d^{4} x \sqrt{d + e x}}{99 e} + \frac{16 B a^{4} d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{92 B a^{4} d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{68 B a^{4} d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{2 B a^{4} e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{64 B a^{3} b d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{32 B a^{3} b d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{8 B a^{3} b d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{1696 B a^{3} b d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{3664 B a^{3} b d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{320 B a^{3} b d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{8 B a^{3} b e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{64 B a^{2} b^{2} d^{7} \sqrt{d + e x}}{2145 e^{4}} + \frac{32 B a^{2} b^{2} d^{6} x \sqrt{d + e x}}{2145 e^{3}} - \frac{8 B a^{2} b^{2} d^{5} x^{2} \sqrt{d + e x}}{715 e^{2}} + \frac{4 B a^{2} b^{2} d^{4} x^{3} \sqrt{d + e x}}{429 e} + \frac{640 B a^{2} b^{2} d^{3} x^{4} \sqrt{d + e x}}{429} + \frac{2472 B a^{2} b^{2} d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{184 B a^{2} b^{2} d e^{2} x^{6} \sqrt{d + e x}}{65} + \frac{4 B a^{2} b^{2} e^{3} x^{7} \sqrt{d + e x}}{5} + \frac{1024 B a b^{3} d^{8} \sqrt{d + e x}}{109395 e^{5}} - \frac{512 B a b^{3} d^{7} x \sqrt{d + e x}}{109395 e^{4}} + \frac{128 B a b^{3} d^{6} x^{2} \sqrt{d + e x}}{36465 e^{3}} - \frac{64 B a b^{3} d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{56 B a b^{3} d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{9696 B a b^{3} d^{3} x^{5} \sqrt{d + e x}}{12155} + \frac{6416 B a b^{3} d^{2} e x^{6} \sqrt{d + e x}}{3315} + \frac{416 B a b^{3} d e^{2} x^{7} \sqrt{d + e x}}{255} + \frac{8 B a b^{3} e^{3} x^{8} \sqrt{d + e x}}{17} - \frac{512 B b^{4} d^{9} \sqrt{d + e x}}{415701 e^{6}} + \frac{256 B b^{4} d^{8} x \sqrt{d + e x}}{415701 e^{5}} - \frac{64 B b^{4} d^{7} x^{2} \sqrt{d + e x}}{138567 e^{4}} + \frac{160 B b^{4} d^{6} x^{3} \sqrt{d + e x}}{415701 e^{3}} - \frac{140 B b^{4} d^{5} x^{4} \sqrt{d + e x}}{415701 e^{2}} + \frac{14 B b^{4} d^{4} x^{5} \sqrt{d + e x}}{46189 e} + \frac{2096 B b^{4} d^{3} x^{6} \sqrt{d + e x}}{12597} + \frac{404 B b^{4} d^{2} e x^{7} \sqrt{d + e x}}{969} + \frac{116 B b^{4} d e^{2} x^{8} \sqrt{d + e x}}{323} + \frac{2 B b^{4} e^{3} x^{9} \sqrt{d + e x}}{19} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(A a^{4} x + 2 A a^{3} b x^{2} + 2 A a^{2} b^{2} x^{3} + A a b^{3} x^{4} + \frac{A b^{4} x^{5}}{5} + \frac{B a^{4} x^{2}}{2} + \frac{4 B a^{3} b x^{3}}{3} + \frac{3 B a^{2} b^{2} x^{4}}{2} + \frac{4 B a b^{3} x^{5}}{5} + \frac{B b^{4} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a**4*d**4*sqrt(d + e*x)/(9*e) + 8*A*a**4*d**3*x*sqrt(d + e*x)/9 + 4*A*a**4*d**2*e*x**2*sqrt(d + e*x)/3 + 8*A*a**4*d*e**2*x**3*sqrt(d + e*x)/9 + 2*A*a**4*e**3*x**4*sqrt(d + e*x)/9 - 16*A*a**3*b*d**5*sqrt(d + e*x)/(99*e**2) + 8*A*a**3*b*d**4*x*sqrt(d + e*x)/(99*e) + 64*A*a**3*b*d**3*x**2*sqrt(d + e*x)/33 + 368*A*a**3*b*d**2*e*x**3*sqrt(d + e*x)/99 + 272*A*a**3*b*d*e**2*x**4*sqrt(d + e*x)/99 + 8*A*a**3*b*e**3*x**5*sqrt(d + e*x)/11 + 32*A*a**2*b**2*d**6*sqrt(d + e*x)/(429*e**3) - 16*A*a**2*b**2*d**5*x*sqrt(d + e*x)/(429*e**2) + 4*A*a**2*b**2*d**4*x**2*sqrt(d + e*x)/(143*e) + 848*A*a**2*b**2*d**3*x**3*sqrt(d + e*x)/429 + 1832*A*a**2*b**2*d**2*e*x**4*sqrt(d + e*x)/429 + 480*A*a**2*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 12*A*a**2*b**2*e**3*x**6*sqrt(d + e*x)/13 - 128*A*a*b**3*d**7*sqrt(d + e*x)/(6435*e**4) + 64*A*a*b**3*d**6*x*sqrt(d + e*x)/(6435*e**3) - 16*A*a*b**3*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 8*A*a*b**3*d**4*x**3*sqrt(d + e*x)/(1287*e) + 1280*A*a*b**3*d**3*x**4*sqrt(d + e*x)/1287 + 1648*A*a*b**3*d**2*e*x**5*sqrt(d + e*x)/715 + 368*A*a*b**3*d*e**2*x**6*sqrt(d + e*x)/195 + 8*A*a*b**3*e**3*x**7*sqrt(d + e*x)/15 + 256*A*b**4*d**8*sqrt(d + e*x)/(109395*e**5) - 128*A*b**4*d**7*x*sqrt(d + e*x)/(109395*e**4) + 32*A*b**4*d**6*x**2*sqrt(d + e*x)/(36465*e**3) - 16*A*b**4*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 14*A*b**4*d**4*x**4*sqrt(d + e*x)/(21879*e) + 2424*A*b**4*d**3*x**5*sqrt(d + e*x)/12155 + 1604*A*b**4*d**2*e*x**6*sqrt(d + e*x)/3315 + 104*A*b**4*d*e**2*x**7*sqrt(d + e*x)/255 + 2*A*b**4*e**3*x**8*sqrt(d + e*x)/17 - 4*B*a**4*d**5*sqrt(d + e*x)/(99*e**2) + 2*B*a**4*d**4*x*sqrt(d + e*x)/(99*e) + 16*B*a**4*d**3*x**2*sqrt(d + e*x)/33 + 92*B*a**4*d**2*e*x**3*sqrt(d + e*x)/99 + 68*B*a**4*d*e**2*x**4*sqrt(d + e*x)/99 + 2*B*a**4*e**3*x**5*sqrt(d + e*x)/11 + 64*B*a**3*b*d**6*sqrt(d + e*x)/(1287*e**3) - 32*B*a**3*b*d**5*x*sqrt(d + e*x)/(1287*e**2) + 8*B*a**3*b*d**4*x**2*sqrt(d + e*x)/(429*e) + 1696*B*a**3*b*d**3*x**3*sqrt(d + e*x)/1287 + 3664*B*a**3*b*d**2*e*x**4*sqrt(d + e*x)/1287 + 320*B*a**3*b*d*e**2*x**5*sqrt(d + e*x)/143 + 8*B*a**3*b*e**3*x**6*sqrt(d + e*x)/13 - 64*B*a**2*b**2*d**7*sqrt(d + e*x)/(2145*e**4) + 32*B*a**2*b**2*d**6*x*sqrt(d + e*x)/(2145*e**3) - 8*B*a**2*b**2*d**5*x**2*sqrt(d + e*x)/(715*e**2) + 4*B*a**2*b**2*d**4*x**3*sqrt(d + e*x)/(429*e) + 640*B*a**2*b**2*d**3*x**4*sqrt(d + e*x)/429 + 2472*B*a**2*b**2*d**2*e*x**5*sqrt(d + e*x)/715 + 184*B*a**2*b**2*d*e**2*x**6*sqrt(d + e*x)/65 + 4*B*a**2*b**2*e**3*x**7*sqrt(d + e*x)/5 + 1024*B*a*b**3*d**8*sqrt(d + e*x)/(109395*e**5) - 512*B*a*b**3*d**7*x*sqrt(d + e*x)/(109395*e**4) + 128*B*a*b**3*d**6*x**2*sqrt(d + e*x)/(36465*e**3) - 64*B*a*b**3*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 56*B*a*b**3*d**4*x**4*sqrt(d + e*x)/(21879*e) + 9696*B*a*b**3*d**3*x**5*sqrt(d + e*x)/12155 + 6416*B*a*b**3*d**2*e*x**6*sqrt(d + e*x)/3315 + 416*B*a*b**3*d*e**2*x**7*sqrt(d + e*x)/255 + 8*B*a*b**3*e**3*x**8*sqrt(d + e*x)/17 - 512*B*b**4*d**9*sqrt(d + e*x)/(415701*e**6) + 256*B*b**4*d**8*x*sqrt(d + e*x)/(415701*e**5) - 64*B*b**4*d**7*x**2*sqrt(d + e*x)/(138567*e**4) + 160*B*b**4*d**6*x**3*sqrt(d + e*x)/(415701*e**3) - 140*B*b**4*d**5*x**4*sqrt(d + e*x)/(415701*e**2) + 14*B*b**4*d**4*x**5*sqrt(d + e*x)/(46189*e) + 2096*B*b**4*d**3*x**6*sqrt(d + e*x)/12597 + 404*B*b**4*d**2*e*x**7*sqrt(d + e*x)/969 + 116*B*b**4*d*e**2*x**8*sqrt(d + e*x)/323 + 2*B*b**4*e**3*x**9*sqrt(d + e*x)/19, Ne(e, 0)), (d**(7/2)*(A*a**4*x + 2*A*a**3*b*x**2 + 2*A*a**2*b**2*x**3 + A*a*b**3*x**4 + A*b**4*x**5/5 + B*a**4*x**2/2 + 4*B*a**3*b*x**3/3 + 3*B*a**2*b**2*x**4/2 + 4*B*a*b**3*x**5/5 + B*b**4*x**6/6), True))","A",0
1793,1,2193,0,74.115050," ","integrate((B*x+A)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 A a^{4} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 A a^{4} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{8 A a^{3} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{16 A a^{3} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{8 A a^{3} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{12 A a^{2} b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{24 A a^{2} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 A a^{2} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{8 A a b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{16 A a b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{8 A a b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{2 A b^{4} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{4 A b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 A b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 B a^{4} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 B a^{4} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 B a^{4} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{8 B a^{3} b d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{16 B a^{3} b d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{8 B a^{3} b \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{12 B a^{2} b^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{24 B a^{2} b^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{12 B a^{2} b^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{8 B a b^{3} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{16 B a b^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{8 B a b^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 B b^{4} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{4 B b^{4} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 B b^{4} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}}"," ",0,"A*a**4*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*A*a**4*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*A*a**4*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 8*A*a**3*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 16*A*a**3*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 8*A*a**3*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*A*a**2*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 24*A*a**2*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*A*a**2*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 8*A*a*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 16*A*a*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 8*A*a*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 2*A*b**4*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 4*A*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*A*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*B*a**4*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*B*a**4*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*B*a**4*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 8*B*a**3*b*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 16*B*a**3*b*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 8*B*a**3*b*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 12*B*a**2*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 24*B*a**2*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 12*B*a**2*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 8*B*a*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 16*B*a*b**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 8*B*a*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*B*b**4*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 4*B*b**4*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*B*b**4*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6","A",0
1794,1,1297,0,45.216873," ","integrate((B*x+A)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","A a^{4} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 A a^{4} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{8 A a^{3} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{8 A a^{3} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{12 A a^{2} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 A a^{2} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{8 A a b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{8 A a b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 A b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{2 A b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 B a^{4} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 B a^{4} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{8 B a^{3} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{8 B a^{3} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 B a^{2} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{12 B a^{2} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{8 B a b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{8 B a b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 B b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{2 B b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}}"," ",0,"A*a**4*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*A*a**4*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 8*A*a**3*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 8*A*a**3*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 12*A*a**2*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*A*a**2*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 8*A*a*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 8*A*a*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*A*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 2*A*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*B*a**4*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*B*a**4*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 8*B*a**3*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 8*B*a**3*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*B*a**2*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 12*B*a**2*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 8*B*a*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 8*B*a*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*B*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 2*B*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6","A",0
1795,1,517,0,9.115127," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{B b^{4} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{5}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(A b^{4} e + 4 B a b^{3} e - 5 B b^{4} d\right)}{11 e^{5}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(4 A a b^{3} e^{2} - 4 A b^{4} d e + 6 B a^{2} b^{2} e^{2} - 16 B a b^{3} d e + 10 B b^{4} d^{2}\right)}{9 e^{5}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(6 A a^{2} b^{2} e^{3} - 12 A a b^{3} d e^{2} + 6 A b^{4} d^{2} e + 4 B a^{3} b e^{3} - 18 B a^{2} b^{2} d e^{2} + 24 B a b^{3} d^{2} e - 10 B b^{4} d^{3}\right)}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(4 A a^{3} b e^{4} - 12 A a^{2} b^{2} d e^{3} + 12 A a b^{3} d^{2} e^{2} - 4 A b^{4} d^{3} e + B a^{4} e^{4} - 8 B a^{3} b d e^{3} + 18 B a^{2} b^{2} d^{2} e^{2} - 16 B a b^{3} d^{3} e + 5 B b^{4} d^{4}\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A a^{4} e^{5} - 4 A a^{3} b d e^{4} + 6 A a^{2} b^{2} d^{2} e^{3} - 4 A a b^{3} d^{3} e^{2} + A b^{4} d^{4} e - B a^{4} d e^{4} + 4 B a^{3} b d^{2} e^{3} - 6 B a^{2} b^{2} d^{3} e^{2} + 4 B a b^{3} d^{4} e - B b^{4} d^{5}\right)}{3 e^{5}}\right)}{e}"," ",0,"2*(B*b**4*(d + e*x)**(13/2)/(13*e**5) + (d + e*x)**(11/2)*(A*b**4*e + 4*B*a*b**3*e - 5*B*b**4*d)/(11*e**5) + (d + e*x)**(9/2)*(4*A*a*b**3*e**2 - 4*A*b**4*d*e + 6*B*a**2*b**2*e**2 - 16*B*a*b**3*d*e + 10*B*b**4*d**2)/(9*e**5) + (d + e*x)**(7/2)*(6*A*a**2*b**2*e**3 - 12*A*a*b**3*d*e**2 + 6*A*b**4*d**2*e + 4*B*a**3*b*e**3 - 18*B*a**2*b**2*d*e**2 + 24*B*a*b**3*d**2*e - 10*B*b**4*d**3)/(7*e**5) + (d + e*x)**(5/2)*(4*A*a**3*b*e**4 - 12*A*a**2*b**2*d*e**3 + 12*A*a*b**3*d**2*e**2 - 4*A*b**4*d**3*e + B*a**4*e**4 - 8*B*a**3*b*d*e**3 + 18*B*a**2*b**2*d**2*e**2 - 16*B*a*b**3*d**3*e + 5*B*b**4*d**4)/(5*e**5) + (d + e*x)**(3/2)*(A*a**4*e**5 - 4*A*a**3*b*d*e**4 + 6*A*a**2*b**2*d**2*e**3 - 4*A*a*b**3*d**3*e**2 + A*b**4*d**4*e - B*a**4*d*e**4 + 4*B*a**3*b*d**2*e**3 - 6*B*a**2*b**2*d**3*e**2 + 4*B*a*b**3*d**4*e - B*b**4*d**5)/(3*e**5))/e","B",0
1796,1,1311,0,127.178555," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a^{4} d}{\sqrt{d + e x}} - 2 A a^{4} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{8 A a^{3} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{8 A a^{3} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{12 A a^{2} b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{12 A a^{2} b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{8 A a b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{8 A a b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{2 A b^{4} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{2 A b^{4} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 B a^{4} d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{2 B a^{4} \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{8 B a^{3} b d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{8 B a^{3} b \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{12 B a^{2} b^{2} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{12 B a^{2} b^{2} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{8 B a b^{3} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{8 B a b^{3} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 B b^{4} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{2 B b^{4} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}}}{e} & \text{for}\: e \neq 0 \\\frac{A a^{4} x + \frac{B b^{4} x^{6}}{6} + \frac{x^{5} \left(A b^{4} + 4 B a b^{3}\right)}{5} + \frac{x^{4} \left(4 A a b^{3} + 6 B a^{2} b^{2}\right)}{4} + \frac{x^{3} \left(6 A a^{2} b^{2} + 4 B a^{3} b\right)}{3} + \frac{x^{2} \left(4 A a^{3} b + B a^{4}\right)}{2}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a**4*d/sqrt(d + e*x) - 2*A*a**4*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 8*A*a**3*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 8*A*a**3*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 12*A*a**2*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 12*A*a**2*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 8*A*a*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 8*A*a*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 2*A*b**4*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 2*A*b**4*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*B*a**4*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 2*B*a**4*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 8*B*a**3*b*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 8*B*a**3*b*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 12*B*a**2*b**2*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 12*B*a**2*b**2*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 8*B*a*b**3*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 8*B*a*b**3*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*B*b**4*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 2*B*b**4*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5)/e, Ne(e, 0)), ((A*a**4*x + B*b**4*x**6/6 + x**5*(A*b**4 + 4*B*a*b**3)/5 + x**4*(4*A*a*b**3 + 6*B*a**2*b**2)/4 + x**3*(6*A*a**2*b**2 + 4*B*a**3*b)/3 + x**2*(4*A*a**3*b + B*a**4)/2)/sqrt(d), True))","A",0
1797,1,394,0,120.613349," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(3/2),x)","\frac{2 B b^{4} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(2 A b^{4} e + 8 B a b^{3} e - 10 B b^{4} d\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(8 A a b^{3} e^{2} - 8 A b^{4} d e + 12 B a^{2} b^{2} e^{2} - 32 B a b^{3} d e + 20 B b^{4} d^{2}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(12 A a^{2} b^{2} e^{3} - 24 A a b^{3} d e^{2} + 12 A b^{4} d^{2} e + 8 B a^{3} b e^{3} - 36 B a^{2} b^{2} d e^{2} + 48 B a b^{3} d^{2} e - 20 B b^{4} d^{3}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(8 A a^{3} b e^{4} - 24 A a^{2} b^{2} d e^{3} + 24 A a b^{3} d^{2} e^{2} - 8 A b^{4} d^{3} e + 2 B a^{4} e^{4} - 16 B a^{3} b d e^{3} + 36 B a^{2} b^{2} d^{2} e^{2} - 32 B a b^{3} d^{3} e + 10 B b^{4} d^{4}\right)}{e^{6}} + \frac{2 \left(- A e + B d\right) \left(a e - b d\right)^{4}}{e^{6} \sqrt{d + e x}}"," ",0,"2*B*b**4*(d + e*x)**(9/2)/(9*e**6) + (d + e*x)**(7/2)*(2*A*b**4*e + 8*B*a*b**3*e - 10*B*b**4*d)/(7*e**6) + (d + e*x)**(5/2)*(8*A*a*b**3*e**2 - 8*A*b**4*d*e + 12*B*a**2*b**2*e**2 - 32*B*a*b**3*d*e + 20*B*b**4*d**2)/(5*e**6) + (d + e*x)**(3/2)*(12*A*a**2*b**2*e**3 - 24*A*a*b**3*d*e**2 + 12*A*b**4*d**2*e + 8*B*a**3*b*e**3 - 36*B*a**2*b**2*d*e**2 + 48*B*a*b**3*d**2*e - 20*B*b**4*d**3)/(3*e**6) + sqrt(d + e*x)*(8*A*a**3*b*e**4 - 24*A*a**2*b**2*d*e**3 + 24*A*a*b**3*d**2*e**2 - 8*A*b**4*d**3*e + 2*B*a**4*e**4 - 16*B*a**3*b*d*e**3 + 36*B*a**2*b**2*d**2*e**2 - 32*B*a*b**3*d**3*e + 10*B*b**4*d**4)/e**6 + 2*(-A*e + B*d)*(a*e - b*d)**4/(e**6*sqrt(d + e*x))","A",0
1798,1,304,0,139.123499," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(5/2),x)","\frac{2 B b^{4} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(2 A b^{4} e + 8 B a b^{3} e - 10 B b^{4} d\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(8 A a b^{3} e^{2} - 8 A b^{4} d e + 12 B a^{2} b^{2} e^{2} - 32 B a b^{3} d e + 20 B b^{4} d^{2}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(12 A a^{2} b^{2} e^{3} - 24 A a b^{3} d e^{2} + 12 A b^{4} d^{2} e + 8 B a^{3} b e^{3} - 36 B a^{2} b^{2} d e^{2} + 48 B a b^{3} d^{2} e - 20 B b^{4} d^{3}\right)}{e^{6}} - \frac{2 \left(a e - b d\right)^{3} \left(4 A b e + B a e - 5 B b d\right)}{e^{6} \sqrt{d + e x}} + \frac{2 \left(- A e + B d\right) \left(a e - b d\right)^{4}}{3 e^{6} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*B*b**4*(d + e*x)**(7/2)/(7*e**6) + (d + e*x)**(5/2)*(2*A*b**4*e + 8*B*a*b**3*e - 10*B*b**4*d)/(5*e**6) + (d + e*x)**(3/2)*(8*A*a*b**3*e**2 - 8*A*b**4*d*e + 12*B*a**2*b**2*e**2 - 32*B*a*b**3*d*e + 20*B*b**4*d**2)/(3*e**6) + sqrt(d + e*x)*(12*A*a**2*b**2*e**3 - 24*A*a*b**3*d*e**2 + 12*A*b**4*d**2*e + 8*B*a**3*b*e**3 - 36*B*a**2*b**2*d*e**2 + 48*B*a*b**3*d**2*e - 20*B*b**4*d**3)/e**6 - 2*(a*e - b*d)**3*(4*A*b*e + B*a*e - 5*B*b*d)/(e**6*sqrt(d + e*x)) + 2*(-A*e + B*d)*(a*e - b*d)**4/(3*e**6*(d + e*x)**(3/2))","A",0
1799,1,2440,0,5.279458," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 A a^{4} e^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{16 A a^{3} b d e^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{40 A a^{3} b e^{5} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{96 A a^{2} b^{2} d^{2} e^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{240 A a^{2} b^{2} d e^{4} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{180 A a^{2} b^{2} e^{5} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{384 A a b^{3} d^{3} e^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{960 A a b^{3} d^{2} e^{3} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{720 A a b^{3} d e^{4} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{120 A a b^{3} e^{5} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{256 A b^{4} d^{4} e}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{640 A b^{4} d^{3} e^{2} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{480 A b^{4} d^{2} e^{3} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{80 A b^{4} d e^{4} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{10 A b^{4} e^{5} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{4 B a^{4} d e^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{10 B a^{4} e^{5} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{64 B a^{3} b d^{2} e^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{160 B a^{3} b d e^{4} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{120 B a^{3} b e^{5} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{576 B a^{2} b^{2} d^{3} e^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1440 B a^{2} b^{2} d^{2} e^{3} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1080 B a^{2} b^{2} d e^{4} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{180 B a^{2} b^{2} e^{5} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{1024 B a b^{3} d^{4} e}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{2560 B a b^{3} d^{3} e^{2} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{1920 B a b^{3} d^{2} e^{3} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{320 B a b^{3} d e^{4} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{40 B a b^{3} e^{5} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{512 B b^{4} d^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1280 B b^{4} d^{4} e x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{960 B b^{4} d^{3} e^{2} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{160 B b^{4} d^{2} e^{3} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{20 B b^{4} d e^{4} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{6 B b^{4} e^{5} x^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{A a^{4} x + 2 A a^{3} b x^{2} + 2 A a^{2} b^{2} x^{3} + A a b^{3} x^{4} + \frac{A b^{4} x^{5}}{5} + \frac{B a^{4} x^{2}}{2} + \frac{4 B a^{3} b x^{3}}{3} + \frac{3 B a^{2} b^{2} x^{4}}{2} + \frac{4 B a b^{3} x^{5}}{5} + \frac{B b^{4} x^{6}}{6}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*a**4*e**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 16*A*a**3*b*d*e**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 40*A*a**3*b*e**5*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 96*A*a**2*b**2*d**2*e**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 240*A*a**2*b**2*d*e**4*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 180*A*a**2*b**2*e**5*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 384*A*a*b**3*d**3*e**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 960*A*a*b**3*d**2*e**3*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 720*A*a*b**3*d*e**4*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 120*A*a*b**3*e**5*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 256*A*b**4*d**4*e/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 640*A*b**4*d**3*e**2*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 480*A*b**4*d**2*e**3*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 80*A*b**4*d*e**4*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 10*A*b**4*e**5*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 4*B*a**4*d*e**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 10*B*a**4*e**5*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 64*B*a**3*b*d**2*e**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 160*B*a**3*b*d*e**4*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 120*B*a**3*b*e**5*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 576*B*a**2*b**2*d**3*e**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1440*B*a**2*b**2*d**2*e**3*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1080*B*a**2*b**2*d*e**4*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 180*B*a**2*b**2*e**5*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 1024*B*a*b**3*d**4*e/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 2560*B*a*b**3*d**3*e**2*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 1920*B*a*b**3*d**2*e**3*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 320*B*a*b**3*d*e**4*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 40*B*a*b**3*e**5*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 512*B*b**4*d**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1280*B*b**4*d**4*e*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 960*B*b**4*d**3*e**2*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 160*B*b**4*d**2*e**3*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 20*B*b**4*d*e**4*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 6*B*b**4*e**5*x**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)), Ne(e, 0)), ((A*a**4*x + 2*A*a**3*b*x**2 + 2*A*a**2*b**2*x**3 + A*a*b**3*x**4 + A*b**4*x**5/5 + B*a**4*x**2/2 + 4*B*a**3*b*x**3/3 + 3*B*a**2*b**2*x**4/2 + 4*B*a*b**3*x**5/5 + B*b**4*x**6/6)/d**(7/2), True))","A",0
1800,1,5414,0,163.184390," ","integrate((B*x+A)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","A a^{6} d^{3} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{6 A a^{6} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{6 A a^{6} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{2 A a^{6} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e} + \frac{12 A a^{5} b d^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{36 A a^{5} b d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{36 A a^{5} b d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{12 A a^{5} b \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{2}} + \frac{30 A a^{4} b^{2} d^{3} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{90 A a^{4} b^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{90 A a^{4} b^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{30 A a^{4} b^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{3}} + \frac{40 A a^{3} b^{3} d^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{120 A a^{3} b^{3} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{120 A a^{3} b^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{40 A a^{3} b^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{4}} + \frac{30 A a^{2} b^{4} d^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{90 A a^{2} b^{4} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{90 A a^{2} b^{4} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{30 A a^{2} b^{4} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{5}} + \frac{12 A a b^{5} d^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{36 A a b^{5} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{36 A a b^{5} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{12 A a b^{5} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{6}} + \frac{2 A b^{6} d^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{6 A b^{6} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{6 A b^{6} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{2 A b^{6} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{7}} + \frac{2 B a^{6} d^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{6 B a^{6} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 B a^{6} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{2 B a^{6} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{2}} + \frac{12 B a^{5} b d^{3} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{36 B a^{5} b d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{36 B a^{5} b d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{12 B a^{5} b \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{3}} + \frac{30 B a^{4} b^{2} d^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{90 B a^{4} b^{2} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{90 B a^{4} b^{2} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{30 B a^{4} b^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{4}} + \frac{40 B a^{3} b^{3} d^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{120 B a^{3} b^{3} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{120 B a^{3} b^{3} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{40 B a^{3} b^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{5}} + \frac{30 B a^{2} b^{4} d^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{90 B a^{2} b^{4} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{90 B a^{2} b^{4} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{30 B a^{2} b^{4} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{6}} + \frac{12 B a b^{5} d^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{36 B a b^{5} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{36 B a b^{5} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{12 B a b^{5} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{7}} + \frac{2 B b^{6} d^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{6 B b^{6} d^{2} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}} + \frac{6 B b^{6} d \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{8}} + \frac{2 B b^{6} \left(\frac{d^{10} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{9} \left(d + e x\right)^{\frac{5}{2}} + \frac{45 d^{8} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{40 d^{7} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{210 d^{6} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{252 d^{5} \left(d + e x\right)^{\frac{13}{2}}}{13} + 14 d^{4} \left(d + e x\right)^{\frac{15}{2}} - \frac{120 d^{3} \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{45 d^{2} \left(d + e x\right)^{\frac{19}{2}}}{19} - \frac{10 d \left(d + e x\right)^{\frac{21}{2}}}{21} + \frac{\left(d + e x\right)^{\frac{23}{2}}}{23}\right)}{e^{8}}"," ",0,"A*a**6*d**3*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 6*A*a**6*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*A*a**6*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 2*A*a**6*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e + 12*A*a**5*b*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 36*A*a**5*b*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 36*A*a**5*b*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*A*a**5*b*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**2 + 30*A*a**4*b**2*d**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 90*A*a**4*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 90*A*a**4*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 30*A*a**4*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**3 + 40*A*a**3*b**3*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 120*A*a**3*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 120*A*a**3*b**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 40*A*a**3*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 30*A*a**2*b**4*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 90*A*a**2*b**4*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 90*A*a**2*b**4*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 30*A*a**2*b**4*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 12*A*a*b**5*d**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 36*A*a*b**5*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 36*A*a*b**5*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 12*A*a*b**5*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**6 + 2*A*b**6*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 6*A*b**6*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 6*A*b**6*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*A*b**6*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7 + 2*B*a**6*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 6*B*a**6*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*B*a**6*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 2*B*a**6*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**2 + 12*B*a**5*b*d**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 36*B*a**5*b*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 36*B*a**5*b*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 12*B*a**5*b*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**3 + 30*B*a**4*b**2*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 90*B*a**4*b**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 90*B*a**4*b**2*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 30*B*a**4*b**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 40*B*a**3*b**3*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 120*B*a**3*b**3*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 120*B*a**3*b**3*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 40*B*a**3*b**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 30*B*a**2*b**4*d**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 90*B*a**2*b**4*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 90*B*a**2*b**4*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 30*B*a**2*b**4*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**6 + 12*B*a*b**5*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 36*B*a*b**5*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 36*B*a*b**5*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 12*B*a*b**5*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7 + 2*B*b**6*d**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 6*B*b**6*d**2*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8 + 6*B*b**6*d*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**8 + 2*B*b**6*(d**10*(d + e*x)**(3/2)/3 - 2*d**9*(d + e*x)**(5/2) + 45*d**8*(d + e*x)**(7/2)/7 - 40*d**7*(d + e*x)**(9/2)/3 + 210*d**6*(d + e*x)**(11/2)/11 - 252*d**5*(d + e*x)**(13/2)/13 + 14*d**4*(d + e*x)**(15/2) - 120*d**3*(d + e*x)**(17/2)/17 + 45*d**2*(d + e*x)**(19/2)/19 - 10*d*(d + e*x)**(21/2)/21 + (d + e*x)**(23/2)/23)/e**8","A",0
1801,1,3728,0,113.731987," ","integrate((B*x+A)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","A a^{6} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 A a^{6} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 A a^{6} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{12 A a^{5} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{24 A a^{5} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{12 A a^{5} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{30 A a^{4} b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{60 A a^{4} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{30 A a^{4} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{40 A a^{3} b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{80 A a^{3} b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{40 A a^{3} b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{30 A a^{2} b^{4} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{60 A a^{2} b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{30 A a^{2} b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{12 A a b^{5} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{24 A a b^{5} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{12 A a b^{5} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{2 A b^{6} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{4 A b^{6} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 A b^{6} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{2 B a^{6} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{4 B a^{6} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 B a^{6} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{12 B a^{5} b d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{24 B a^{5} b d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{12 B a^{5} b \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{30 B a^{4} b^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{60 B a^{4} b^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{30 B a^{4} b^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{40 B a^{3} b^{3} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{80 B a^{3} b^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{40 B a^{3} b^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{30 B a^{2} b^{4} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{60 B a^{2} b^{4} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{30 B a^{2} b^{4} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{12 B a b^{5} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{24 B a b^{5} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{12 B a b^{5} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{2 B b^{6} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{4 B b^{6} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}} + \frac{2 B b^{6} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{8}}"," ",0,"A*a**6*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*A*a**6*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*A*a**6*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 12*A*a**5*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 24*A*a**5*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 12*A*a**5*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 30*A*a**4*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 60*A*a**4*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 30*A*a**4*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 40*A*a**3*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 80*A*a**3*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 40*A*a**3*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 30*A*a**2*b**4*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 60*A*a**2*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 30*A*a**2*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 12*A*a*b**5*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 24*A*a*b**5*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 12*A*a*b**5*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 2*A*b**6*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 4*A*b**6*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*A*b**6*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*B*a**6*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 4*B*a**6*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*B*a**6*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*B*a**5*b*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 24*B*a**5*b*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 12*B*a**5*b*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 30*B*a**4*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 60*B*a**4*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 30*B*a**4*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 40*B*a**3*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 80*B*a**3*b**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 40*B*a**3*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 30*B*a**2*b**4*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 60*B*a**2*b**4*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 30*B*a**2*b**4*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 12*B*a*b**5*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 24*B*a*b**5*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 12*B*a*b**5*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*B*b**6*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 4*B*b**6*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8 + 2*B*b**6*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**8","A",0
1802,1,2252,0,69.776825," ","integrate((B*x+A)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","A a^{6} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 A a^{6} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{12 A a^{5} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{12 A a^{5} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{30 A a^{4} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{30 A a^{4} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{40 A a^{3} b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{40 A a^{3} b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{30 A a^{2} b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{30 A a^{2} b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{12 A a b^{5} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{12 A a b^{5} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 A b^{6} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{2 A b^{6} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 B a^{6} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 B a^{6} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{12 B a^{5} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{12 B a^{5} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{30 B a^{4} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{30 B a^{4} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{40 B a^{3} b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{40 B a^{3} b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{30 B a^{2} b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{30 B a^{2} b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{12 B a b^{5} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{12 B a b^{5} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 B b^{6} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{2 B b^{6} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}}"," ",0,"A*a**6*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*A*a**6*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 12*A*a**5*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 12*A*a**5*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 30*A*a**4*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 30*A*a**4*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 40*A*a**3*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 40*A*a**3*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 30*A*a**2*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 30*A*a**2*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 12*A*a*b**5*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 12*A*a*b**5*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*A*b**6*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 2*A*b**6*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*B*a**6*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*B*a**6*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 12*B*a**5*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 12*B*a**5*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 30*B*a**4*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 30*B*a**4*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 40*B*a**3*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 40*B*a**3*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 30*B*a**2*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 30*B*a**2*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 12*B*a*b**5*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 12*B*a*b**5*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*B*b**6*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 2*B*b**6*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8","A",0
1803,1,969,0,13.350304," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{B b^{6} \left(d + e x\right)^{\frac{17}{2}}}{17 e^{7}} + \frac{\left(d + e x\right)^{\frac{15}{2}} \left(A b^{6} e + 6 B a b^{5} e - 7 B b^{6} d\right)}{15 e^{7}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(6 A a b^{5} e^{2} - 6 A b^{6} d e + 15 B a^{2} b^{4} e^{2} - 36 B a b^{5} d e + 21 B b^{6} d^{2}\right)}{13 e^{7}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(15 A a^{2} b^{4} e^{3} - 30 A a b^{5} d e^{2} + 15 A b^{6} d^{2} e + 20 B a^{3} b^{3} e^{3} - 75 B a^{2} b^{4} d e^{2} + 90 B a b^{5} d^{2} e - 35 B b^{6} d^{3}\right)}{11 e^{7}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(20 A a^{3} b^{3} e^{4} - 60 A a^{2} b^{4} d e^{3} + 60 A a b^{5} d^{2} e^{2} - 20 A b^{6} d^{3} e + 15 B a^{4} b^{2} e^{4} - 80 B a^{3} b^{3} d e^{3} + 150 B a^{2} b^{4} d^{2} e^{2} - 120 B a b^{5} d^{3} e + 35 B b^{6} d^{4}\right)}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(15 A a^{4} b^{2} e^{5} - 60 A a^{3} b^{3} d e^{4} + 90 A a^{2} b^{4} d^{2} e^{3} - 60 A a b^{5} d^{3} e^{2} + 15 A b^{6} d^{4} e + 6 B a^{5} b e^{5} - 45 B a^{4} b^{2} d e^{4} + 120 B a^{3} b^{3} d^{2} e^{3} - 150 B a^{2} b^{4} d^{3} e^{2} + 90 B a b^{5} d^{4} e - 21 B b^{6} d^{5}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(6 A a^{5} b e^{6} - 30 A a^{4} b^{2} d e^{5} + 60 A a^{3} b^{3} d^{2} e^{4} - 60 A a^{2} b^{4} d^{3} e^{3} + 30 A a b^{5} d^{4} e^{2} - 6 A b^{6} d^{5} e + B a^{6} e^{6} - 12 B a^{5} b d e^{5} + 45 B a^{4} b^{2} d^{2} e^{4} - 80 B a^{3} b^{3} d^{3} e^{3} + 75 B a^{2} b^{4} d^{4} e^{2} - 36 B a b^{5} d^{5} e + 7 B b^{6} d^{6}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A a^{6} e^{7} - 6 A a^{5} b d e^{6} + 15 A a^{4} b^{2} d^{2} e^{5} - 20 A a^{3} b^{3} d^{3} e^{4} + 15 A a^{2} b^{4} d^{4} e^{3} - 6 A a b^{5} d^{5} e^{2} + A b^{6} d^{6} e - B a^{6} d e^{6} + 6 B a^{5} b d^{2} e^{5} - 15 B a^{4} b^{2} d^{3} e^{4} + 20 B a^{3} b^{3} d^{4} e^{3} - 15 B a^{2} b^{4} d^{5} e^{2} + 6 B a b^{5} d^{6} e - B b^{6} d^{7}\right)}{3 e^{7}}\right)}{e}"," ",0,"2*(B*b**6*(d + e*x)**(17/2)/(17*e**7) + (d + e*x)**(15/2)*(A*b**6*e + 6*B*a*b**5*e - 7*B*b**6*d)/(15*e**7) + (d + e*x)**(13/2)*(6*A*a*b**5*e**2 - 6*A*b**6*d*e + 15*B*a**2*b**4*e**2 - 36*B*a*b**5*d*e + 21*B*b**6*d**2)/(13*e**7) + (d + e*x)**(11/2)*(15*A*a**2*b**4*e**3 - 30*A*a*b**5*d*e**2 + 15*A*b**6*d**2*e + 20*B*a**3*b**3*e**3 - 75*B*a**2*b**4*d*e**2 + 90*B*a*b**5*d**2*e - 35*B*b**6*d**3)/(11*e**7) + (d + e*x)**(9/2)*(20*A*a**3*b**3*e**4 - 60*A*a**2*b**4*d*e**3 + 60*A*a*b**5*d**2*e**2 - 20*A*b**6*d**3*e + 15*B*a**4*b**2*e**4 - 80*B*a**3*b**3*d*e**3 + 150*B*a**2*b**4*d**2*e**2 - 120*B*a*b**5*d**3*e + 35*B*b**6*d**4)/(9*e**7) + (d + e*x)**(7/2)*(15*A*a**4*b**2*e**5 - 60*A*a**3*b**3*d*e**4 + 90*A*a**2*b**4*d**2*e**3 - 60*A*a*b**5*d**3*e**2 + 15*A*b**6*d**4*e + 6*B*a**5*b*e**5 - 45*B*a**4*b**2*d*e**4 + 120*B*a**3*b**3*d**2*e**3 - 150*B*a**2*b**4*d**3*e**2 + 90*B*a*b**5*d**4*e - 21*B*b**6*d**5)/(7*e**7) + (d + e*x)**(5/2)*(6*A*a**5*b*e**6 - 30*A*a**4*b**2*d*e**5 + 60*A*a**3*b**3*d**2*e**4 - 60*A*a**2*b**4*d**3*e**3 + 30*A*a*b**5*d**4*e**2 - 6*A*b**6*d**5*e + B*a**6*e**6 - 12*B*a**5*b*d*e**5 + 45*B*a**4*b**2*d**2*e**4 - 80*B*a**3*b**3*d**3*e**3 + 75*B*a**2*b**4*d**4*e**2 - 36*B*a*b**5*d**5*e + 7*B*b**6*d**6)/(5*e**7) + (d + e*x)**(3/2)*(A*a**6*e**7 - 6*A*a**5*b*d*e**6 + 15*A*a**4*b**2*d**2*e**5 - 20*A*a**3*b**3*d**3*e**4 + 15*A*a**2*b**4*d**4*e**3 - 6*A*a*b**5*d**5*e**2 + A*b**6*d**6*e - B*a**6*d*e**6 + 6*B*a**5*b*d**2*e**5 - 15*B*a**4*b**2*d**3*e**4 + 20*B*a**3*b**3*d**4*e**3 - 15*B*a**2*b**4*d**5*e**2 + 6*B*a*b**5*d**6*e - B*b**6*d**7)/(3*e**7))/e","B",0
1804,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1805,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1806,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1807,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1808,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1809,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1810,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1811,1,1251,0,107.952013," ","integrate((B*x+A)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{2 A a e^{2} \sqrt{d + e x}}{2 a^{2} b e^{2} - 2 a b^{2} d e + 2 a b^{2} e^{2} x - 2 b^{3} d e x} + \frac{A a e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(- a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{A a e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{A d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(- a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{A d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2} + \frac{2 A d e \sqrt{d + e x}}{2 a^{2} e^{2} - 2 a b d e + 2 a b e^{2} x - 2 b^{2} d e x} + \frac{2 A e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e}{b} - d}} \right)}}{b^{2} \sqrt{\frac{a e}{b} - d}} + \frac{2 B a^{2} e^{2} \sqrt{d + e x}}{2 a^{2} b^{2} e^{2} - 2 a b^{3} d e + 2 a b^{3} e^{2} x - 2 b^{4} d e x} - \frac{B a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(- a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} + \frac{B a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b^{2}} - \frac{2 B a d e \sqrt{d + e x}}{2 a^{2} b e^{2} - 2 a b^{2} d e + 2 a b^{2} e^{2} x - 2 b^{3} d e x} + \frac{B a d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(- a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{B a d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} \log{\left(a^{2} e^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} - 2 a b d e \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + b^{2} d^{2} \sqrt{- \frac{1}{b \left(a e - b d\right)^{3}}} + \sqrt{d + e x} \right)}}{2 b} - \frac{4 B a e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e}{b} - d}} \right)}}{b^{3} \sqrt{\frac{a e}{b} - d}} + \frac{2 B d \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e}{b} - d}} \right)}}{b^{2} \sqrt{\frac{a e}{b} - d}} + \frac{2 B \sqrt{d + e x}}{b^{2}}"," ",0,"-2*A*a*e**2*sqrt(d + e*x)/(2*a**2*b*e**2 - 2*a*b**2*d*e + 2*a*b**2*e**2*x - 2*b**3*d*e*x) + A*a*e**2*sqrt(-1/(b*(a*e - b*d)**3))*log(-a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) + 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) - b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b) - A*a*e**2*sqrt(-1/(b*(a*e - b*d)**3))*log(a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) - 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) + b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b) - A*d*e*sqrt(-1/(b*(a*e - b*d)**3))*log(-a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) + 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) - b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/2 + A*d*e*sqrt(-1/(b*(a*e - b*d)**3))*log(a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) - 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) + b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/2 + 2*A*d*e*sqrt(d + e*x)/(2*a**2*e**2 - 2*a*b*d*e + 2*a*b*e**2*x - 2*b**2*d*e*x) + 2*A*e*atan(sqrt(d + e*x)/sqrt(a*e/b - d))/(b**2*sqrt(a*e/b - d)) + 2*B*a**2*e**2*sqrt(d + e*x)/(2*a**2*b**2*e**2 - 2*a*b**3*d*e + 2*a*b**3*e**2*x - 2*b**4*d*e*x) - B*a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3))*log(-a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) + 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) - b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b**2) + B*a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3))*log(a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) - 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) + b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b**2) - 2*B*a*d*e*sqrt(d + e*x)/(2*a**2*b*e**2 - 2*a*b**2*d*e + 2*a*b**2*e**2*x - 2*b**3*d*e*x) + B*a*d*e*sqrt(-1/(b*(a*e - b*d)**3))*log(-a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) + 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) - b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b) - B*a*d*e*sqrt(-1/(b*(a*e - b*d)**3))*log(a**2*e**2*sqrt(-1/(b*(a*e - b*d)**3)) - 2*a*b*d*e*sqrt(-1/(b*(a*e - b*d)**3)) + b**2*d**2*sqrt(-1/(b*(a*e - b*d)**3)) + sqrt(d + e*x))/(2*b) - 4*B*a*e*atan(sqrt(d + e*x)/sqrt(a*e/b - d))/(b**3*sqrt(a*e/b - d)) + 2*B*d*atan(sqrt(d + e*x)/sqrt(a*e/b - d))/(b**2*sqrt(a*e/b - d)) + 2*B*sqrt(d + e*x)/b**2","B",0
1812,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1813,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1814,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1815,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1816,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1817,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1818,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1819,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1820,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1821,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1822,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1823,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1824,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1825,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(11/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1826,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1827,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1828,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1829,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1830,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1831,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1832,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1833,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1834,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1835,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1836,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1837,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1838,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)*((b*x+a)**2)**(1/2),x)","\int \left(A + B x\right) \sqrt{d + e x} \sqrt{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)*sqrt((a + b*x)**2), x)","F",0
1839,0,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{\left(a + b x\right)^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((A + B*x)*sqrt((a + b*x)**2)/sqrt(d + e*x), x)","F",0
1840,0,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{\left(a + b x\right)^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt((a + b*x)**2)/(d + e*x)**(3/2), x)","F",0
1841,-1,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1842,-1,0,0,0.000000," ","integrate((B*x+A)*((b*x+a)**2)**(1/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1843,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1844,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1845,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1846,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)*(e*x+d)**(1/2),x)","\int \left(A + B x\right) \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)*((a + b*x)**2)**(3/2), x)","F",0
1847,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1848,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1849,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1850,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1851,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1852,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1853,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1854,0,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)*(e*x+d)**(1/2),x)","\int \left(A + B x\right) \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)*((a + b*x)**2)**(5/2), x)","F",0
1855,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1856,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1857,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1858,-1,0,0,0.000000," ","integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1859,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1860,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{\frac{3}{2}}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**(3/2)/sqrt((a + b*x)**2), x)","F",0
1861,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/sqrt((a + b*x)**2), x)","F",0
1862,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{A + B x}{\sqrt{d + e x} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(d + e*x)*sqrt((a + b*x)**2)), x)","F",0
1863,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**(3/2)*sqrt((a + b*x)**2)), x)","F",0
1864,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1865,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1866,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1867,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1868,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1869,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/((a + b*x)**2)**(3/2), x)","F",0
1870,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1871,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1872,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1873,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1874,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(11/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1875,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1876,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1877,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1878,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1879,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1880,-1,0,0,0.000000," ","integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1881,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1882,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1883,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1884,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1885,1,6186,0,6.647561," ","integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} d^{m} \left(A a^{2} x + A a b x^{2} + \frac{A b^{2} x^{3}}{3} + \frac{B a^{2} x^{2}}{2} + \frac{2 B a b x^{3}}{3} + \frac{B b^{2} x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{2 A a^{2} e^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 A a b d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A a b e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 A b^{2} d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A b^{2} d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A b^{2} e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{B a^{2} d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 B a^{2} e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{4 B a b d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{12 B a b d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{12 B a b e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B b^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 B b^{2} d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B b^{2} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 B b^{2} d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B b^{2} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B b^{2} d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B b^{2} e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{A a^{2} e^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 A a b d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{4 A a b e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A b^{2} d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 A b^{2} d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A b^{2} d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A b^{2} d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A b^{2} e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{B a^{2} d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 B a^{2} e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 B a b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 B a b d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{8 B a b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{8 B a b d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 B a b e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B b^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 B b^{2} d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B b^{2} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B b^{2} d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B b^{2} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B b^{2} e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\- \frac{2 A a^{2} e^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{4 A a b d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{4 A a b d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{4 A a b e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A b^{2} d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A b^{2} d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 A b^{2} d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A b^{2} e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a^{2} d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a^{2} d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a^{2} e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{8 B a b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{8 B a b d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{8 B a b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{4 B a b e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B b^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B b^{2} d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B b^{2} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 B b^{2} d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{B b^{2} e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\\frac{A a^{2} \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{2 A a b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{2 A a b x}{e} + \frac{A b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{A b^{2} d x}{e^{2}} + \frac{A b^{2} x^{2}}{2 e} - \frac{B a^{2} d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{B a^{2} x}{e} + \frac{2 B a b d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{2 B a b d x}{e^{2}} + \frac{B a b x^{2}}{e} - \frac{B b^{2} d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{B b^{2} d^{2} x}{e^{3}} - \frac{B b^{2} d x^{2}}{2 e^{2}} + \frac{B b^{2} x^{3}}{3 e} & \text{for}\: m = -1 \\\frac{A a^{2} d e^{3} m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 A a^{2} d e^{3} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 A a^{2} d e^{3} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a^{2} d e^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A a^{2} e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 A a^{2} e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 A a^{2} e^{4} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a^{2} e^{4} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 A a b d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{14 A a b d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{24 A a b d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 A a b d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 A a b d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a b d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 A a b e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{16 A a b e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{38 A a b e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a b e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 A b^{2} d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A b^{2} d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 A b^{2} d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 A b^{2} d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A b^{2} d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 A b^{2} d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 A b^{2} d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A b^{2} e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 A b^{2} e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 A b^{2} e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A b^{2} e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{B a^{2} d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 B a^{2} d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 B a^{2} d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B a^{2} d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 B a^{2} d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 B a^{2} d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B a^{2} e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B a^{2} e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 B a^{2} e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 B a^{2} e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 B a b d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{16 B a b d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{4 B a b d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{16 B a b d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B a b d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{10 B a b d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B a b d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B a b e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 B a b e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{28 B a b e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{16 B a b e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 B b^{2} d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B b^{2} d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B b^{2} d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B b^{2} d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B b^{2} d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 B b^{2} d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B b^{2} d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B b^{2} e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B b^{2} e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 B b^{2} e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B b^{2} e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(A*a**2*x + A*a*b*x**2 + A*b**2*x**3/3 + B*a**2*x**2/2 + 2*B*a*b*x**3/3 + B*b**2*x**4/4), Eq(e, 0)), (-2*A*a**2*e**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*A*a*b*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*a*b*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*A*b**2*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*b**2*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*b**2*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - B*a**2*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*B*a**2*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 4*B*a*b*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 12*B*a*b*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 12*B*a*b*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*b**2*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*B*b**2*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*b**2*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*B*b**2*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*b**2*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*b**2*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*b**2*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-A*a**2*e**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*A*a*b*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 4*A*a*b*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*b**2*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*A*b**2*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*b**2*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*b**2*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*b**2*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - B*a**2*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*B*a**2*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*B*a*b*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*B*a*b*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 8*B*a*b*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 8*B*a*b*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*B*a*b*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*b**2*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*B*b**2*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*b**2*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*b**2*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*b**2*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*b**2*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (-2*A*a**2*e**3/(2*d*e**4 + 2*e**5*x) + 4*A*a*b*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 4*A*a*b*d*e**2/(2*d*e**4 + 2*e**5*x) + 4*A*a*b*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*b**2*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*b**2*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*A*b**2*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*A*b**2*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 2*B*a**2*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*B*a**2*d*e**2/(2*d*e**4 + 2*e**5*x) + 2*B*a**2*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 8*B*a*b*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 8*B*a*b*d**2*e/(2*d*e**4 + 2*e**5*x) - 8*B*a*b*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 4*B*a*b*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 6*B*b**2*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*B*b**2*d**3/(2*d*e**4 + 2*e**5*x) + 6*B*b**2*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*B*b**2*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + B*b**2*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (A*a**2*log(d/e + x)/e - 2*A*a*b*d*log(d/e + x)/e**2 + 2*A*a*b*x/e + A*b**2*d**2*log(d/e + x)/e**3 - A*b**2*d*x/e**2 + A*b**2*x**2/(2*e) - B*a**2*d*log(d/e + x)/e**2 + B*a**2*x/e + 2*B*a*b*d**2*log(d/e + x)/e**3 - 2*B*a*b*d*x/e**2 + B*a*b*x**2/e - B*b**2*d**3*log(d/e + x)/e**4 + B*b**2*d**2*x/e**3 - B*b**2*d*x**2/(2*e**2) + B*b**2*x**3/(3*e), Eq(m, -1)), (A*a**2*d*e**3*m**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*A*a**2*d*e**3*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*A*a**2*d*e**3*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a**2*d*e**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*a**2*e**4*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*A*a**2*e**4*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*A*a**2*e**4*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a**2*e**4*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*A*a*b*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 14*A*a*b*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 24*A*a*b*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*A*a*b*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*A*a*b*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a*b*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*A*a*b*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 16*A*a*b*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 38*A*a*b*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a*b*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*A*b**2*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*b**2*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*A*b**2*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*A*b**2*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*b**2*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*A*b**2*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*A*b**2*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*b**2*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*A*b**2*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*A*b**2*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*b**2*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - B*a**2*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*B*a**2*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*B*a**2*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*a**2*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*B*a**2*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*B*a**2*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*a**2*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*a**2*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*B*a**2*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*B*a**2*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*B*a*b*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 16*B*a*b*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 4*B*a*b*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 16*B*a*b*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*a*b*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 10*B*a*b*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*a*b*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*a*b*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*B*a*b*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 28*B*a*b*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 16*B*a*b*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*B*b**2*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*b**2*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*b**2*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*b**2*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*b**2*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*B*b**2*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*b**2*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*b**2*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*b**2*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*B*b**2*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*b**2*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
1886,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{m}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m/(a + b*x)**2, x)","F",0
1887,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**2,x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{m}}{\left(a + b x\right)^{4}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m/(a + b*x)**4, x)","F",0
1888,-2,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1889,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{m} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m*((a + b*x)**2)**(3/2), x)","F",0
1890,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(1/2),x)","\int \left(A + B x\right) \left(d + e x\right)^{m} \sqrt{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m*sqrt((a + b*x)**2), x)","F",0
1891,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{m}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m/sqrt((a + b*x)**2), x)","F",0
1892,-2,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1893,-2,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1894,-2,0,0,0.000000," ","integrate((e*x+d)**(-3-2*p)*(g*x+f)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1895,1,308,0,0.128115," ","integrate((b*x+a)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} d^{5} x + \frac{b^{3} e^{5} x^{9}}{9} + x^{8} \left(\frac{3 a b^{2} e^{5}}{8} + \frac{5 b^{3} d e^{4}}{8}\right) + x^{7} \left(\frac{3 a^{2} b e^{5}}{7} + \frac{15 a b^{2} d e^{4}}{7} + \frac{10 b^{3} d^{2} e^{3}}{7}\right) + x^{6} \left(\frac{a^{3} e^{5}}{6} + \frac{5 a^{2} b d e^{4}}{2} + 5 a b^{2} d^{2} e^{3} + \frac{5 b^{3} d^{3} e^{2}}{3}\right) + x^{5} \left(a^{3} d e^{4} + 6 a^{2} b d^{2} e^{3} + 6 a b^{2} d^{3} e^{2} + b^{3} d^{4} e\right) + x^{4} \left(\frac{5 a^{3} d^{2} e^{3}}{2} + \frac{15 a^{2} b d^{3} e^{2}}{2} + \frac{15 a b^{2} d^{4} e}{4} + \frac{b^{3} d^{5}}{4}\right) + x^{3} \left(\frac{10 a^{3} d^{3} e^{2}}{3} + 5 a^{2} b d^{4} e + a b^{2} d^{5}\right) + x^{2} \left(\frac{5 a^{3} d^{4} e}{2} + \frac{3 a^{2} b d^{5}}{2}\right)"," ",0,"a**3*d**5*x + b**3*e**5*x**9/9 + x**8*(3*a*b**2*e**5/8 + 5*b**3*d*e**4/8) + x**7*(3*a**2*b*e**5/7 + 15*a*b**2*d*e**4/7 + 10*b**3*d**2*e**3/7) + x**6*(a**3*e**5/6 + 5*a**2*b*d*e**4/2 + 5*a*b**2*d**2*e**3 + 5*b**3*d**3*e**2/3) + x**5*(a**3*d*e**4 + 6*a**2*b*d**2*e**3 + 6*a*b**2*d**3*e**2 + b**3*d**4*e) + x**4*(5*a**3*d**2*e**3/2 + 15*a**2*b*d**3*e**2/2 + 15*a*b**2*d**4*e/4 + b**3*d**5/4) + x**3*(10*a**3*d**3*e**2/3 + 5*a**2*b*d**4*e + a*b**2*d**5) + x**2*(5*a**3*d**4*e/2 + 3*a**2*b*d**5/2)","B",0
1896,1,243,0,0.109776," ","integrate((b*x+a)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} d^{4} x + \frac{b^{3} e^{4} x^{8}}{8} + x^{7} \left(\frac{3 a b^{2} e^{4}}{7} + \frac{4 b^{3} d e^{3}}{7}\right) + x^{6} \left(\frac{a^{2} b e^{4}}{2} + 2 a b^{2} d e^{3} + b^{3} d^{2} e^{2}\right) + x^{5} \left(\frac{a^{3} e^{4}}{5} + \frac{12 a^{2} b d e^{3}}{5} + \frac{18 a b^{2} d^{2} e^{2}}{5} + \frac{4 b^{3} d^{3} e}{5}\right) + x^{4} \left(a^{3} d e^{3} + \frac{9 a^{2} b d^{2} e^{2}}{2} + 3 a b^{2} d^{3} e + \frac{b^{3} d^{4}}{4}\right) + x^{3} \left(2 a^{3} d^{2} e^{2} + 4 a^{2} b d^{3} e + a b^{2} d^{4}\right) + x^{2} \left(2 a^{3} d^{3} e + \frac{3 a^{2} b d^{4}}{2}\right)"," ",0,"a**3*d**4*x + b**3*e**4*x**8/8 + x**7*(3*a*b**2*e**4/7 + 4*b**3*d*e**3/7) + x**6*(a**2*b*e**4/2 + 2*a*b**2*d*e**3 + b**3*d**2*e**2) + x**5*(a**3*e**4/5 + 12*a**2*b*d*e**3/5 + 18*a*b**2*d**2*e**2/5 + 4*b**3*d**3*e/5) + x**4*(a**3*d*e**3 + 9*a**2*b*d**2*e**2/2 + 3*a*b**2*d**3*e + b**3*d**4/4) + x**3*(2*a**3*d**2*e**2 + 4*a**2*b*d**3*e + a*b**2*d**4) + x**2*(2*a**3*d**3*e + 3*a**2*b*d**4/2)","B",0
1897,1,190,0,0.099673," ","integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} d^{3} x + \frac{b^{3} e^{3} x^{7}}{7} + x^{6} \left(\frac{a b^{2} e^{3}}{2} + \frac{b^{3} d e^{2}}{2}\right) + x^{5} \left(\frac{3 a^{2} b e^{3}}{5} + \frac{9 a b^{2} d e^{2}}{5} + \frac{3 b^{3} d^{2} e}{5}\right) + x^{4} \left(\frac{a^{3} e^{3}}{4} + \frac{9 a^{2} b d e^{2}}{4} + \frac{9 a b^{2} d^{2} e}{4} + \frac{b^{3} d^{3}}{4}\right) + x^{3} \left(a^{3} d e^{2} + 3 a^{2} b d^{2} e + a b^{2} d^{3}\right) + x^{2} \left(\frac{3 a^{3} d^{2} e}{2} + \frac{3 a^{2} b d^{3}}{2}\right)"," ",0,"a**3*d**3*x + b**3*e**3*x**7/7 + x**6*(a*b**2*e**3/2 + b**3*d*e**2/2) + x**5*(3*a**2*b*e**3/5 + 9*a*b**2*d*e**2/5 + 3*b**3*d**2*e/5) + x**4*(a**3*e**3/4 + 9*a**2*b*d*e**2/4 + 9*a*b**2*d**2*e/4 + b**3*d**3/4) + x**3*(a**3*d*e**2 + 3*a**2*b*d**2*e + a*b**2*d**3) + x**2*(3*a**3*d**2*e/2 + 3*a**2*b*d**3/2)","B",0
1898,1,133,0,0.088947," ","integrate((b*x+a)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} d^{2} x + \frac{b^{3} e^{2} x^{6}}{6} + x^{5} \left(\frac{3 a b^{2} e^{2}}{5} + \frac{2 b^{3} d e}{5}\right) + x^{4} \left(\frac{3 a^{2} b e^{2}}{4} + \frac{3 a b^{2} d e}{2} + \frac{b^{3} d^{2}}{4}\right) + x^{3} \left(\frac{a^{3} e^{2}}{3} + 2 a^{2} b d e + a b^{2} d^{2}\right) + x^{2} \left(a^{3} d e + \frac{3 a^{2} b d^{2}}{2}\right)"," ",0,"a**3*d**2*x + b**3*e**2*x**6/6 + x**5*(3*a*b**2*e**2/5 + 2*b**3*d*e/5) + x**4*(3*a**2*b*e**2/4 + 3*a*b**2*d*e/2 + b**3*d**2/4) + x**3*(a**3*e**2/3 + 2*a**2*b*d*e + a*b**2*d**2) + x**2*(a**3*d*e + 3*a**2*b*d**2/2)","B",0
1899,1,73,0,0.076372," ","integrate((b*x+a)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} d x + \frac{b^{3} e x^{5}}{5} + x^{4} \left(\frac{3 a b^{2} e}{4} + \frac{b^{3} d}{4}\right) + x^{3} \left(a^{2} b e + a b^{2} d\right) + x^{2} \left(\frac{a^{3} e}{2} + \frac{3 a^{2} b d}{2}\right)"," ",0,"a**3*d*x + b**3*e*x**5/5 + x**4*(3*a*b**2*e/4 + b**3*d/4) + x**3*(a**2*b*e + a*b**2*d) + x**2*(a**3*e/2 + 3*a**2*b*d/2)","B",0
1900,1,32,0,0.067893," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}"," ",0,"a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4","B",0
1901,1,83,0,0.316212," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d),x)","\frac{b^{3} x^{3}}{3 e} + x^{2} \left(\frac{3 a b^{2}}{2 e} - \frac{b^{3} d}{2 e^{2}}\right) + x \left(\frac{3 a^{2} b}{e} - \frac{3 a b^{2} d}{e^{2}} + \frac{b^{3} d^{2}}{e^{3}}\right) + \frac{\left(a e - b d\right)^{3} \log{\left(d + e x \right)}}{e^{4}}"," ",0,"b**3*x**3/(3*e) + x**2*(3*a*b**2/(2*e) - b**3*d/(2*e**2)) + x*(3*a**2*b/e - 3*a*b**2*d/e**2 + b**3*d**2/e**3) + (a*e - b*d)**3*log(d + e*x)/e**4","A",0
1902,1,102,0,0.658338," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**2,x)","\frac{b^{3} x^{2}}{2 e^{2}} + \frac{3 b \left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{4}} + x \left(\frac{3 a b^{2}}{e^{2}} - \frac{2 b^{3} d}{e^{3}}\right) + \frac{- a^{3} e^{3} + 3 a^{2} b d e^{2} - 3 a b^{2} d^{2} e + b^{3} d^{3}}{d e^{4} + e^{5} x}"," ",0,"b**3*x**2/(2*e**2) + 3*b*(a*e - b*d)**2*log(d + e*x)/e**4 + x*(3*a*b**2/e**2 - 2*b**3*d/e**3) + (-a**3*e**3 + 3*a**2*b*d*e**2 - 3*a*b**2*d**2*e + b**3*d**3)/(d*e**4 + e**5*x)","A",0
1903,1,128,0,0.830955," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**3,x)","\frac{b^{3} x}{e^{3}} + \frac{3 b^{2} \left(a e - b d\right) \log{\left(d + e x \right)}}{e^{4}} + \frac{- a^{3} e^{3} - 3 a^{2} b d e^{2} + 9 a b^{2} d^{2} e - 5 b^{3} d^{3} + x \left(- 6 a^{2} b e^{3} + 12 a b^{2} d e^{2} - 6 b^{3} d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}}"," ",0,"b**3*x/e**3 + 3*b**2*(a*e - b*d)*log(d + e*x)/e**4 + (-a**3*e**3 - 3*a**2*b*d*e**2 + 9*a*b**2*d**2*e - 5*b**3*d**3 + x*(-6*a**2*b*e**3 + 12*a*b**2*d*e**2 - 6*b**3*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2)","A",0
1904,1,148,0,1.183708," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**4,x)","\frac{b^{3} \log{\left(d + e x \right)}}{e^{4}} + \frac{- 2 a^{3} e^{3} - 3 a^{2} b d e^{2} - 6 a b^{2} d^{2} e + 11 b^{3} d^{3} + x^{2} \left(- 18 a b^{2} e^{3} + 18 b^{3} d e^{2}\right) + x \left(- 9 a^{2} b e^{3} - 18 a b^{2} d e^{2} + 27 b^{3} d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"b**3*log(d + e*x)/e**4 + (-2*a**3*e**3 - 3*a**2*b*d*e**2 - 6*a*b**2*d**2*e + 11*b**3*d**3 + x**2*(-18*a*b**2*e**3 + 18*b**3*d*e**2) + x*(-9*a**2*b*e**3 - 18*a*b**2*d*e**2 + 27*b**3*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
1905,1,580,0,0.162934," ","integrate((b*x+a)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d^{6} x + \frac{b^{5} e^{6} x^{12}}{12} + x^{11} \left(\frac{5 a b^{4} e^{6}}{11} + \frac{6 b^{5} d e^{5}}{11}\right) + x^{10} \left(a^{2} b^{3} e^{6} + 3 a b^{4} d e^{5} + \frac{3 b^{5} d^{2} e^{4}}{2}\right) + x^{9} \left(\frac{10 a^{3} b^{2} e^{6}}{9} + \frac{20 a^{2} b^{3} d e^{5}}{3} + \frac{25 a b^{4} d^{2} e^{4}}{3} + \frac{20 b^{5} d^{3} e^{3}}{9}\right) + x^{8} \left(\frac{5 a^{4} b e^{6}}{8} + \frac{15 a^{3} b^{2} d e^{5}}{2} + \frac{75 a^{2} b^{3} d^{2} e^{4}}{4} + \frac{25 a b^{4} d^{3} e^{3}}{2} + \frac{15 b^{5} d^{4} e^{2}}{8}\right) + x^{7} \left(\frac{a^{5} e^{6}}{7} + \frac{30 a^{4} b d e^{5}}{7} + \frac{150 a^{3} b^{2} d^{2} e^{4}}{7} + \frac{200 a^{2} b^{3} d^{3} e^{3}}{7} + \frac{75 a b^{4} d^{4} e^{2}}{7} + \frac{6 b^{5} d^{5} e}{7}\right) + x^{6} \left(a^{5} d e^{5} + \frac{25 a^{4} b d^{2} e^{4}}{2} + \frac{100 a^{3} b^{2} d^{3} e^{3}}{3} + 25 a^{2} b^{3} d^{4} e^{2} + 5 a b^{4} d^{5} e + \frac{b^{5} d^{6}}{6}\right) + x^{5} \left(3 a^{5} d^{2} e^{4} + 20 a^{4} b d^{3} e^{3} + 30 a^{3} b^{2} d^{4} e^{2} + 12 a^{2} b^{3} d^{5} e + a b^{4} d^{6}\right) + x^{4} \left(5 a^{5} d^{3} e^{3} + \frac{75 a^{4} b d^{4} e^{2}}{4} + 15 a^{3} b^{2} d^{5} e + \frac{5 a^{2} b^{3} d^{6}}{2}\right) + x^{3} \left(5 a^{5} d^{4} e^{2} + 10 a^{4} b d^{5} e + \frac{10 a^{3} b^{2} d^{6}}{3}\right) + x^{2} \left(3 a^{5} d^{5} e + \frac{5 a^{4} b d^{6}}{2}\right)"," ",0,"a**5*d**6*x + b**5*e**6*x**12/12 + x**11*(5*a*b**4*e**6/11 + 6*b**5*d*e**5/11) + x**10*(a**2*b**3*e**6 + 3*a*b**4*d*e**5 + 3*b**5*d**2*e**4/2) + x**9*(10*a**3*b**2*e**6/9 + 20*a**2*b**3*d*e**5/3 + 25*a*b**4*d**2*e**4/3 + 20*b**5*d**3*e**3/9) + x**8*(5*a**4*b*e**6/8 + 15*a**3*b**2*d*e**5/2 + 75*a**2*b**3*d**2*e**4/4 + 25*a*b**4*d**3*e**3/2 + 15*b**5*d**4*e**2/8) + x**7*(a**5*e**6/7 + 30*a**4*b*d*e**5/7 + 150*a**3*b**2*d**2*e**4/7 + 200*a**2*b**3*d**3*e**3/7 + 75*a*b**4*d**4*e**2/7 + 6*b**5*d**5*e/7) + x**6*(a**5*d*e**5 + 25*a**4*b*d**2*e**4/2 + 100*a**3*b**2*d**3*e**3/3 + 25*a**2*b**3*d**4*e**2 + 5*a*b**4*d**5*e + b**5*d**6/6) + x**5*(3*a**5*d**2*e**4 + 20*a**4*b*d**3*e**3 + 30*a**3*b**2*d**4*e**2 + 12*a**2*b**3*d**5*e + a*b**4*d**6) + x**4*(5*a**5*d**3*e**3 + 75*a**4*b*d**4*e**2/4 + 15*a**3*b**2*d**5*e + 5*a**2*b**3*d**6/2) + x**3*(5*a**5*d**4*e**2 + 10*a**4*b*d**5*e + 10*a**3*b**2*d**6/3) + x**2*(3*a**5*d**5*e + 5*a**4*b*d**6/2)","B",0
1906,1,500,0,0.148694," ","integrate((b*x+a)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d^{5} x + \frac{b^{5} e^{5} x^{11}}{11} + x^{10} \left(\frac{a b^{4} e^{5}}{2} + \frac{b^{5} d e^{4}}{2}\right) + x^{9} \left(\frac{10 a^{2} b^{3} e^{5}}{9} + \frac{25 a b^{4} d e^{4}}{9} + \frac{10 b^{5} d^{2} e^{3}}{9}\right) + x^{8} \left(\frac{5 a^{3} b^{2} e^{5}}{4} + \frac{25 a^{2} b^{3} d e^{4}}{4} + \frac{25 a b^{4} d^{2} e^{3}}{4} + \frac{5 b^{5} d^{3} e^{2}}{4}\right) + x^{7} \left(\frac{5 a^{4} b e^{5}}{7} + \frac{50 a^{3} b^{2} d e^{4}}{7} + \frac{100 a^{2} b^{3} d^{2} e^{3}}{7} + \frac{50 a b^{4} d^{3} e^{2}}{7} + \frac{5 b^{5} d^{4} e}{7}\right) + x^{6} \left(\frac{a^{5} e^{5}}{6} + \frac{25 a^{4} b d e^{4}}{6} + \frac{50 a^{3} b^{2} d^{2} e^{3}}{3} + \frac{50 a^{2} b^{3} d^{3} e^{2}}{3} + \frac{25 a b^{4} d^{4} e}{6} + \frac{b^{5} d^{5}}{6}\right) + x^{5} \left(a^{5} d e^{4} + 10 a^{4} b d^{2} e^{3} + 20 a^{3} b^{2} d^{3} e^{2} + 10 a^{2} b^{3} d^{4} e + a b^{4} d^{5}\right) + x^{4} \left(\frac{5 a^{5} d^{2} e^{3}}{2} + \frac{25 a^{4} b d^{3} e^{2}}{2} + \frac{25 a^{3} b^{2} d^{4} e}{2} + \frac{5 a^{2} b^{3} d^{5}}{2}\right) + x^{3} \left(\frac{10 a^{5} d^{3} e^{2}}{3} + \frac{25 a^{4} b d^{4} e}{3} + \frac{10 a^{3} b^{2} d^{5}}{3}\right) + x^{2} \left(\frac{5 a^{5} d^{4} e}{2} + \frac{5 a^{4} b d^{5}}{2}\right)"," ",0,"a**5*d**5*x + b**5*e**5*x**11/11 + x**10*(a*b**4*e**5/2 + b**5*d*e**4/2) + x**9*(10*a**2*b**3*e**5/9 + 25*a*b**4*d*e**4/9 + 10*b**5*d**2*e**3/9) + x**8*(5*a**3*b**2*e**5/4 + 25*a**2*b**3*d*e**4/4 + 25*a*b**4*d**2*e**3/4 + 5*b**5*d**3*e**2/4) + x**7*(5*a**4*b*e**5/7 + 50*a**3*b**2*d*e**4/7 + 100*a**2*b**3*d**2*e**3/7 + 50*a*b**4*d**3*e**2/7 + 5*b**5*d**4*e/7) + x**6*(a**5*e**5/6 + 25*a**4*b*d*e**4/6 + 50*a**3*b**2*d**2*e**3/3 + 50*a**2*b**3*d**3*e**2/3 + 25*a*b**4*d**4*e/6 + b**5*d**5/6) + x**5*(a**5*d*e**4 + 10*a**4*b*d**2*e**3 + 20*a**3*b**2*d**3*e**2 + 10*a**2*b**3*d**4*e + a*b**4*d**5) + x**4*(5*a**5*d**2*e**3/2 + 25*a**4*b*d**3*e**2/2 + 25*a**3*b**2*d**4*e/2 + 5*a**2*b**3*d**5/2) + x**3*(10*a**5*d**3*e**2/3 + 25*a**4*b*d**4*e/3 + 10*a**3*b**2*d**5/3) + x**2*(5*a**5*d**4*e/2 + 5*a**4*b*d**5/2)","B",0
1907,1,401,0,0.137262," ","integrate((b*x+a)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d^{4} x + \frac{b^{5} e^{4} x^{10}}{10} + x^{9} \left(\frac{5 a b^{4} e^{4}}{9} + \frac{4 b^{5} d e^{3}}{9}\right) + x^{8} \left(\frac{5 a^{2} b^{3} e^{4}}{4} + \frac{5 a b^{4} d e^{3}}{2} + \frac{3 b^{5} d^{2} e^{2}}{4}\right) + x^{7} \left(\frac{10 a^{3} b^{2} e^{4}}{7} + \frac{40 a^{2} b^{3} d e^{3}}{7} + \frac{30 a b^{4} d^{2} e^{2}}{7} + \frac{4 b^{5} d^{3} e}{7}\right) + x^{6} \left(\frac{5 a^{4} b e^{4}}{6} + \frac{20 a^{3} b^{2} d e^{3}}{3} + 10 a^{2} b^{3} d^{2} e^{2} + \frac{10 a b^{4} d^{3} e}{3} + \frac{b^{5} d^{4}}{6}\right) + x^{5} \left(\frac{a^{5} e^{4}}{5} + 4 a^{4} b d e^{3} + 12 a^{3} b^{2} d^{2} e^{2} + 8 a^{2} b^{3} d^{3} e + a b^{4} d^{4}\right) + x^{4} \left(a^{5} d e^{3} + \frac{15 a^{4} b d^{2} e^{2}}{2} + 10 a^{3} b^{2} d^{3} e + \frac{5 a^{2} b^{3} d^{4}}{2}\right) + x^{3} \left(2 a^{5} d^{2} e^{2} + \frac{20 a^{4} b d^{3} e}{3} + \frac{10 a^{3} b^{2} d^{4}}{3}\right) + x^{2} \left(2 a^{5} d^{3} e + \frac{5 a^{4} b d^{4}}{2}\right)"," ",0,"a**5*d**4*x + b**5*e**4*x**10/10 + x**9*(5*a*b**4*e**4/9 + 4*b**5*d*e**3/9) + x**8*(5*a**2*b**3*e**4/4 + 5*a*b**4*d*e**3/2 + 3*b**5*d**2*e**2/4) + x**7*(10*a**3*b**2*e**4/7 + 40*a**2*b**3*d*e**3/7 + 30*a*b**4*d**2*e**2/7 + 4*b**5*d**3*e/7) + x**6*(5*a**4*b*e**4/6 + 20*a**3*b**2*d*e**3/3 + 10*a**2*b**3*d**2*e**2 + 10*a*b**4*d**3*e/3 + b**5*d**4/6) + x**5*(a**5*e**4/5 + 4*a**4*b*d*e**3 + 12*a**3*b**2*d**2*e**2 + 8*a**2*b**3*d**3*e + a*b**4*d**4) + x**4*(a**5*d*e**3 + 15*a**4*b*d**2*e**2/2 + 10*a**3*b**2*d**3*e + 5*a**2*b**3*d**4/2) + x**3*(2*a**5*d**2*e**2 + 20*a**4*b*d**3*e/3 + 10*a**3*b**2*d**4/3) + x**2*(2*a**5*d**3*e + 5*a**4*b*d**4/2)","B",0
1908,1,308,0,0.124859," ","integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d^{3} x + \frac{b^{5} e^{3} x^{9}}{9} + x^{8} \left(\frac{5 a b^{4} e^{3}}{8} + \frac{3 b^{5} d e^{2}}{8}\right) + x^{7} \left(\frac{10 a^{2} b^{3} e^{3}}{7} + \frac{15 a b^{4} d e^{2}}{7} + \frac{3 b^{5} d^{2} e}{7}\right) + x^{6} \left(\frac{5 a^{3} b^{2} e^{3}}{3} + 5 a^{2} b^{3} d e^{2} + \frac{5 a b^{4} d^{2} e}{2} + \frac{b^{5} d^{3}}{6}\right) + x^{5} \left(a^{4} b e^{3} + 6 a^{3} b^{2} d e^{2} + 6 a^{2} b^{3} d^{2} e + a b^{4} d^{3}\right) + x^{4} \left(\frac{a^{5} e^{3}}{4} + \frac{15 a^{4} b d e^{2}}{4} + \frac{15 a^{3} b^{2} d^{2} e}{2} + \frac{5 a^{2} b^{3} d^{3}}{2}\right) + x^{3} \left(a^{5} d e^{2} + 5 a^{4} b d^{2} e + \frac{10 a^{3} b^{2} d^{3}}{3}\right) + x^{2} \left(\frac{3 a^{5} d^{2} e}{2} + \frac{5 a^{4} b d^{3}}{2}\right)"," ",0,"a**5*d**3*x + b**5*e**3*x**9/9 + x**8*(5*a*b**4*e**3/8 + 3*b**5*d*e**2/8) + x**7*(10*a**2*b**3*e**3/7 + 15*a*b**4*d*e**2/7 + 3*b**5*d**2*e/7) + x**6*(5*a**3*b**2*e**3/3 + 5*a**2*b**3*d*e**2 + 5*a*b**4*d**2*e/2 + b**5*d**3/6) + x**5*(a**4*b*e**3 + 6*a**3*b**2*d*e**2 + 6*a**2*b**3*d**2*e + a*b**4*d**3) + x**4*(a**5*e**3/4 + 15*a**4*b*d*e**2/4 + 15*a**3*b**2*d**2*e/2 + 5*a**2*b**3*d**3/2) + x**3*(a**5*d*e**2 + 5*a**4*b*d**2*e + 10*a**3*b**2*d**3/3) + x**2*(3*a**5*d**2*e/2 + 5*a**4*b*d**3/2)","B",0
1909,1,218,0,0.108537," ","integrate((b*x+a)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d^{2} x + \frac{b^{5} e^{2} x^{8}}{8} + x^{7} \left(\frac{5 a b^{4} e^{2}}{7} + \frac{2 b^{5} d e}{7}\right) + x^{6} \left(\frac{5 a^{2} b^{3} e^{2}}{3} + \frac{5 a b^{4} d e}{3} + \frac{b^{5} d^{2}}{6}\right) + x^{5} \left(2 a^{3} b^{2} e^{2} + 4 a^{2} b^{3} d e + a b^{4} d^{2}\right) + x^{4} \left(\frac{5 a^{4} b e^{2}}{4} + 5 a^{3} b^{2} d e + \frac{5 a^{2} b^{3} d^{2}}{2}\right) + x^{3} \left(\frac{a^{5} e^{2}}{3} + \frac{10 a^{4} b d e}{3} + \frac{10 a^{3} b^{2} d^{2}}{3}\right) + x^{2} \left(a^{5} d e + \frac{5 a^{4} b d^{2}}{2}\right)"," ",0,"a**5*d**2*x + b**5*e**2*x**8/8 + x**7*(5*a*b**4*e**2/7 + 2*b**5*d*e/7) + x**6*(5*a**2*b**3*e**2/3 + 5*a*b**4*d*e/3 + b**5*d**2/6) + x**5*(2*a**3*b**2*e**2 + 4*a**2*b**3*d*e + a*b**4*d**2) + x**4*(5*a**4*b*e**2/4 + 5*a**3*b**2*d*e + 5*a**2*b**3*d**2/2) + x**3*(a**5*e**2/3 + 10*a**4*b*d*e/3 + 10*a**3*b**2*d**2/3) + x**2*(a**5*d*e + 5*a**4*b*d**2/2)","B",0
1910,1,129,0,0.096305," ","integrate((b*x+a)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d x + \frac{b^{5} e x^{7}}{7} + x^{6} \left(\frac{5 a b^{4} e}{6} + \frac{b^{5} d}{6}\right) + x^{5} \left(2 a^{2} b^{3} e + a b^{4} d\right) + x^{4} \left(\frac{5 a^{3} b^{2} e}{2} + \frac{5 a^{2} b^{3} d}{2}\right) + x^{3} \left(\frac{5 a^{4} b e}{3} + \frac{10 a^{3} b^{2} d}{3}\right) + x^{2} \left(\frac{a^{5} e}{2} + \frac{5 a^{4} b d}{2}\right)"," ",0,"a**5*d*x + b**5*e*x**7/7 + x**6*(5*a*b**4*e/6 + b**5*d/6) + x**5*(2*a**2*b**3*e + a*b**4*d) + x**4*(5*a**3*b**2*e/2 + 5*a**2*b**3*d/2) + x**3*(5*a**4*b*e/3 + 10*a**3*b**2*d/3) + x**2*(a**5*e/2 + 5*a**4*b*d/2)","B",0
1911,1,60,0,0.076605," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6}"," ",0,"a**5*x + 5*a**4*b*x**2/2 + 10*a**3*b**2*x**3/3 + 5*a**2*b**3*x**4/2 + a*b**4*x**5 + b**5*x**6/6","B",0
1912,1,209,0,0.505569," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d),x)","\frac{b^{5} x^{5}}{5 e} + x^{4} \left(\frac{5 a b^{4}}{4 e} - \frac{b^{5} d}{4 e^{2}}\right) + x^{3} \left(\frac{10 a^{2} b^{3}}{3 e} - \frac{5 a b^{4} d}{3 e^{2}} + \frac{b^{5} d^{2}}{3 e^{3}}\right) + x^{2} \left(\frac{5 a^{3} b^{2}}{e} - \frac{5 a^{2} b^{3} d}{e^{2}} + \frac{5 a b^{4} d^{2}}{2 e^{3}} - \frac{b^{5} d^{3}}{2 e^{4}}\right) + x \left(\frac{5 a^{4} b}{e} - \frac{10 a^{3} b^{2} d}{e^{2}} + \frac{10 a^{2} b^{3} d^{2}}{e^{3}} - \frac{5 a b^{4} d^{3}}{e^{4}} + \frac{b^{5} d^{4}}{e^{5}}\right) + \frac{\left(a e - b d\right)^{5} \log{\left(d + e x \right)}}{e^{6}}"," ",0,"b**5*x**5/(5*e) + x**4*(5*a*b**4/(4*e) - b**5*d/(4*e**2)) + x**3*(10*a**2*b**3/(3*e) - 5*a*b**4*d/(3*e**2) + b**5*d**2/(3*e**3)) + x**2*(5*a**3*b**2/e - 5*a**2*b**3*d/e**2 + 5*a*b**4*d**2/(2*e**3) - b**5*d**3/(2*e**4)) + x*(5*a**4*b/e - 10*a**3*b**2*d/e**2 + 10*a**2*b**3*d**2/e**3 - 5*a*b**4*d**3/e**4 + b**5*d**4/e**5) + (a*e - b*d)**5*log(d + e*x)/e**6","B",0
1913,1,231,0,0.904287," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**2,x)","\frac{b^{5} x^{4}}{4 e^{2}} + \frac{5 b \left(a e - b d\right)^{4} \log{\left(d + e x \right)}}{e^{6}} + x^{3} \left(\frac{5 a b^{4}}{3 e^{2}} - \frac{2 b^{5} d}{3 e^{3}}\right) + x^{2} \left(\frac{5 a^{2} b^{3}}{e^{2}} - \frac{5 a b^{4} d}{e^{3}} + \frac{3 b^{5} d^{2}}{2 e^{4}}\right) + x \left(\frac{10 a^{3} b^{2}}{e^{2}} - \frac{20 a^{2} b^{3} d}{e^{3}} + \frac{15 a b^{4} d^{2}}{e^{4}} - \frac{4 b^{5} d^{3}}{e^{5}}\right) + \frac{- a^{5} e^{5} + 5 a^{4} b d e^{4} - 10 a^{3} b^{2} d^{2} e^{3} + 10 a^{2} b^{3} d^{3} e^{2} - 5 a b^{4} d^{4} e + b^{5} d^{5}}{d e^{6} + e^{7} x}"," ",0,"b**5*x**4/(4*e**2) + 5*b*(a*e - b*d)**4*log(d + e*x)/e**6 + x**3*(5*a*b**4/(3*e**2) - 2*b**5*d/(3*e**3)) + x**2*(5*a**2*b**3/e**2 - 5*a*b**4*d/e**3 + 3*b**5*d**2/(2*e**4)) + x*(10*a**3*b**2/e**2 - 20*a**2*b**3*d/e**3 + 15*a*b**4*d**2/e**4 - 4*b**5*d**3/e**5) + (-a**5*e**5 + 5*a**4*b*d*e**4 - 10*a**3*b**2*d**2*e**3 + 10*a**2*b**3*d**3*e**2 - 5*a*b**4*d**4*e + b**5*d**5)/(d*e**6 + e**7*x)","A",0
1914,1,258,0,1.648203," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**3,x)","\frac{b^{5} x^{3}}{3 e^{3}} + \frac{10 b^{2} \left(a e - b d\right)^{3} \log{\left(d + e x \right)}}{e^{6}} + x^{2} \left(\frac{5 a b^{4}}{2 e^{3}} - \frac{3 b^{5} d}{2 e^{4}}\right) + x \left(\frac{10 a^{2} b^{3}}{e^{3}} - \frac{15 a b^{4} d}{e^{4}} + \frac{6 b^{5} d^{2}}{e^{5}}\right) + \frac{- a^{5} e^{5} - 5 a^{4} b d e^{4} + 30 a^{3} b^{2} d^{2} e^{3} - 50 a^{2} b^{3} d^{3} e^{2} + 35 a b^{4} d^{4} e - 9 b^{5} d^{5} + x \left(- 10 a^{4} b e^{5} + 40 a^{3} b^{2} d e^{4} - 60 a^{2} b^{3} d^{2} e^{3} + 40 a b^{4} d^{3} e^{2} - 10 b^{5} d^{4} e\right)}{2 d^{2} e^{6} + 4 d e^{7} x + 2 e^{8} x^{2}}"," ",0,"b**5*x**3/(3*e**3) + 10*b**2*(a*e - b*d)**3*log(d + e*x)/e**6 + x**2*(5*a*b**4/(2*e**3) - 3*b**5*d/(2*e**4)) + x*(10*a**2*b**3/e**3 - 15*a*b**4*d/e**4 + 6*b**5*d**2/e**5) + (-a**5*e**5 - 5*a**4*b*d*e**4 + 30*a**3*b**2*d**2*e**3 - 50*a**2*b**3*d**3*e**2 + 35*a*b**4*d**4*e - 9*b**5*d**5 + x*(-10*a**4*b*e**5 + 40*a**3*b**2*d*e**4 - 60*a**2*b**3*d**2*e**3 + 40*a*b**4*d**3*e**2 - 10*b**5*d**4*e))/(2*d**2*e**6 + 4*d*e**7*x + 2*e**8*x**2)","B",0
1915,1,284,0,3.058802," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**4,x)","\frac{b^{5} x^{2}}{2 e^{4}} + \frac{10 b^{3} \left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{6}} + x \left(\frac{5 a b^{4}}{e^{4}} - \frac{4 b^{5} d}{e^{5}}\right) + \frac{- 2 a^{5} e^{5} - 5 a^{4} b d e^{4} - 20 a^{3} b^{2} d^{2} e^{3} + 110 a^{2} b^{3} d^{3} e^{2} - 130 a b^{4} d^{4} e + 47 b^{5} d^{5} + x^{2} \left(- 60 a^{3} b^{2} e^{5} + 180 a^{2} b^{3} d e^{4} - 180 a b^{4} d^{2} e^{3} + 60 b^{5} d^{3} e^{2}\right) + x \left(- 15 a^{4} b e^{5} - 60 a^{3} b^{2} d e^{4} + 270 a^{2} b^{3} d^{2} e^{3} - 300 a b^{4} d^{3} e^{2} + 105 b^{5} d^{4} e\right)}{6 d^{3} e^{6} + 18 d^{2} e^{7} x + 18 d e^{8} x^{2} + 6 e^{9} x^{3}}"," ",0,"b**5*x**2/(2*e**4) + 10*b**3*(a*e - b*d)**2*log(d + e*x)/e**6 + x*(5*a*b**4/e**4 - 4*b**5*d/e**5) + (-2*a**5*e**5 - 5*a**4*b*d*e**4 - 20*a**3*b**2*d**2*e**3 + 110*a**2*b**3*d**3*e**2 - 130*a*b**4*d**4*e + 47*b**5*d**5 + x**2*(-60*a**3*b**2*e**5 + 180*a**2*b**3*d*e**4 - 180*a*b**4*d**2*e**3 + 60*b**5*d**3*e**2) + x*(-15*a**4*b*e**5 - 60*a**3*b**2*d*e**4 + 270*a**2*b**3*d**2*e**3 - 300*a*b**4*d**3*e**2 + 105*b**5*d**4*e))/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3)","B",0
1916,1,796,0,0.194930," ","integrate((b*x+a)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{6} x + \frac{b^{7} e^{6} x^{14}}{14} + x^{13} \left(\frac{7 a b^{6} e^{6}}{13} + \frac{6 b^{7} d e^{5}}{13}\right) + x^{12} \left(\frac{7 a^{2} b^{5} e^{6}}{4} + \frac{7 a b^{6} d e^{5}}{2} + \frac{5 b^{7} d^{2} e^{4}}{4}\right) + x^{11} \left(\frac{35 a^{3} b^{4} e^{6}}{11} + \frac{126 a^{2} b^{5} d e^{5}}{11} + \frac{105 a b^{6} d^{2} e^{4}}{11} + \frac{20 b^{7} d^{3} e^{3}}{11}\right) + x^{10} \left(\frac{7 a^{4} b^{3} e^{6}}{2} + 21 a^{3} b^{4} d e^{5} + \frac{63 a^{2} b^{5} d^{2} e^{4}}{2} + 14 a b^{6} d^{3} e^{3} + \frac{3 b^{7} d^{4} e^{2}}{2}\right) + x^{9} \left(\frac{7 a^{5} b^{2} e^{6}}{3} + \frac{70 a^{4} b^{3} d e^{5}}{3} + \frac{175 a^{3} b^{4} d^{2} e^{4}}{3} + \frac{140 a^{2} b^{5} d^{3} e^{3}}{3} + \frac{35 a b^{6} d^{4} e^{2}}{3} + \frac{2 b^{7} d^{5} e}{3}\right) + x^{8} \left(\frac{7 a^{6} b e^{6}}{8} + \frac{63 a^{5} b^{2} d e^{5}}{4} + \frac{525 a^{4} b^{3} d^{2} e^{4}}{8} + \frac{175 a^{3} b^{4} d^{3} e^{3}}{2} + \frac{315 a^{2} b^{5} d^{4} e^{2}}{8} + \frac{21 a b^{6} d^{5} e}{4} + \frac{b^{7} d^{6}}{8}\right) + x^{7} \left(\frac{a^{7} e^{6}}{7} + 6 a^{6} b d e^{5} + 45 a^{5} b^{2} d^{2} e^{4} + 100 a^{4} b^{3} d^{3} e^{3} + 75 a^{3} b^{4} d^{4} e^{2} + 18 a^{2} b^{5} d^{5} e + a b^{6} d^{6}\right) + x^{6} \left(a^{7} d e^{5} + \frac{35 a^{6} b d^{2} e^{4}}{2} + 70 a^{5} b^{2} d^{3} e^{3} + \frac{175 a^{4} b^{3} d^{4} e^{2}}{2} + 35 a^{3} b^{4} d^{5} e + \frac{7 a^{2} b^{5} d^{6}}{2}\right) + x^{5} \left(3 a^{7} d^{2} e^{4} + 28 a^{6} b d^{3} e^{3} + 63 a^{5} b^{2} d^{4} e^{2} + 42 a^{4} b^{3} d^{5} e + 7 a^{3} b^{4} d^{6}\right) + x^{4} \left(5 a^{7} d^{3} e^{3} + \frac{105 a^{6} b d^{4} e^{2}}{4} + \frac{63 a^{5} b^{2} d^{5} e}{2} + \frac{35 a^{4} b^{3} d^{6}}{4}\right) + x^{3} \left(5 a^{7} d^{4} e^{2} + 14 a^{6} b d^{5} e + 7 a^{5} b^{2} d^{6}\right) + x^{2} \left(3 a^{7} d^{5} e + \frac{7 a^{6} b d^{6}}{2}\right)"," ",0,"a**7*d**6*x + b**7*e**6*x**14/14 + x**13*(7*a*b**6*e**6/13 + 6*b**7*d*e**5/13) + x**12*(7*a**2*b**5*e**6/4 + 7*a*b**6*d*e**5/2 + 5*b**7*d**2*e**4/4) + x**11*(35*a**3*b**4*e**6/11 + 126*a**2*b**5*d*e**5/11 + 105*a*b**6*d**2*e**4/11 + 20*b**7*d**3*e**3/11) + x**10*(7*a**4*b**3*e**6/2 + 21*a**3*b**4*d*e**5 + 63*a**2*b**5*d**2*e**4/2 + 14*a*b**6*d**3*e**3 + 3*b**7*d**4*e**2/2) + x**9*(7*a**5*b**2*e**6/3 + 70*a**4*b**3*d*e**5/3 + 175*a**3*b**4*d**2*e**4/3 + 140*a**2*b**5*d**3*e**3/3 + 35*a*b**6*d**4*e**2/3 + 2*b**7*d**5*e/3) + x**8*(7*a**6*b*e**6/8 + 63*a**5*b**2*d*e**5/4 + 525*a**4*b**3*d**2*e**4/8 + 175*a**3*b**4*d**3*e**3/2 + 315*a**2*b**5*d**4*e**2/8 + 21*a*b**6*d**5*e/4 + b**7*d**6/8) + x**7*(a**7*e**6/7 + 6*a**6*b*d*e**5 + 45*a**5*b**2*d**2*e**4 + 100*a**4*b**3*d**3*e**3 + 75*a**3*b**4*d**4*e**2 + 18*a**2*b**5*d**5*e + a*b**6*d**6) + x**6*(a**7*d*e**5 + 35*a**6*b*d**2*e**4/2 + 70*a**5*b**2*d**3*e**3 + 175*a**4*b**3*d**4*e**2/2 + 35*a**3*b**4*d**5*e + 7*a**2*b**5*d**6/2) + x**5*(3*a**7*d**2*e**4 + 28*a**6*b*d**3*e**3 + 63*a**5*b**2*d**4*e**2 + 42*a**4*b**3*d**5*e + 7*a**3*b**4*d**6) + x**4*(5*a**7*d**3*e**3 + 105*a**6*b*d**4*e**2/4 + 63*a**5*b**2*d**5*e/2 + 35*a**4*b**3*d**6/4) + x**3*(5*a**7*d**4*e**2 + 14*a**6*b*d**5*e + 7*a**5*b**2*d**6) + x**2*(3*a**7*d**5*e + 7*a**6*b*d**6/2)","B",0
1917,1,673,0,0.176696," ","integrate((b*x+a)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{5} x + \frac{b^{7} e^{5} x^{13}}{13} + x^{12} \left(\frac{7 a b^{6} e^{5}}{12} + \frac{5 b^{7} d e^{4}}{12}\right) + x^{11} \left(\frac{21 a^{2} b^{5} e^{5}}{11} + \frac{35 a b^{6} d e^{4}}{11} + \frac{10 b^{7} d^{2} e^{3}}{11}\right) + x^{10} \left(\frac{7 a^{3} b^{4} e^{5}}{2} + \frac{21 a^{2} b^{5} d e^{4}}{2} + 7 a b^{6} d^{2} e^{3} + b^{7} d^{3} e^{2}\right) + x^{9} \left(\frac{35 a^{4} b^{3} e^{5}}{9} + \frac{175 a^{3} b^{4} d e^{4}}{9} + \frac{70 a^{2} b^{5} d^{2} e^{3}}{3} + \frac{70 a b^{6} d^{3} e^{2}}{9} + \frac{5 b^{7} d^{4} e}{9}\right) + x^{8} \left(\frac{21 a^{5} b^{2} e^{5}}{8} + \frac{175 a^{4} b^{3} d e^{4}}{8} + \frac{175 a^{3} b^{4} d^{2} e^{3}}{4} + \frac{105 a^{2} b^{5} d^{3} e^{2}}{4} + \frac{35 a b^{6} d^{4} e}{8} + \frac{b^{7} d^{5}}{8}\right) + x^{7} \left(a^{6} b e^{5} + 15 a^{5} b^{2} d e^{4} + 50 a^{4} b^{3} d^{2} e^{3} + 50 a^{3} b^{4} d^{3} e^{2} + 15 a^{2} b^{5} d^{4} e + a b^{6} d^{5}\right) + x^{6} \left(\frac{a^{7} e^{5}}{6} + \frac{35 a^{6} b d e^{4}}{6} + 35 a^{5} b^{2} d^{2} e^{3} + \frac{175 a^{4} b^{3} d^{3} e^{2}}{3} + \frac{175 a^{3} b^{4} d^{4} e}{6} + \frac{7 a^{2} b^{5} d^{5}}{2}\right) + x^{5} \left(a^{7} d e^{4} + 14 a^{6} b d^{2} e^{3} + 42 a^{5} b^{2} d^{3} e^{2} + 35 a^{4} b^{3} d^{4} e + 7 a^{3} b^{4} d^{5}\right) + x^{4} \left(\frac{5 a^{7} d^{2} e^{3}}{2} + \frac{35 a^{6} b d^{3} e^{2}}{2} + \frac{105 a^{5} b^{2} d^{4} e}{4} + \frac{35 a^{4} b^{3} d^{5}}{4}\right) + x^{3} \left(\frac{10 a^{7} d^{3} e^{2}}{3} + \frac{35 a^{6} b d^{4} e}{3} + 7 a^{5} b^{2} d^{5}\right) + x^{2} \left(\frac{5 a^{7} d^{4} e}{2} + \frac{7 a^{6} b d^{5}}{2}\right)"," ",0,"a**7*d**5*x + b**7*e**5*x**13/13 + x**12*(7*a*b**6*e**5/12 + 5*b**7*d*e**4/12) + x**11*(21*a**2*b**5*e**5/11 + 35*a*b**6*d*e**4/11 + 10*b**7*d**2*e**3/11) + x**10*(7*a**3*b**4*e**5/2 + 21*a**2*b**5*d*e**4/2 + 7*a*b**6*d**2*e**3 + b**7*d**3*e**2) + x**9*(35*a**4*b**3*e**5/9 + 175*a**3*b**4*d*e**4/9 + 70*a**2*b**5*d**2*e**3/3 + 70*a*b**6*d**3*e**2/9 + 5*b**7*d**4*e/9) + x**8*(21*a**5*b**2*e**5/8 + 175*a**4*b**3*d*e**4/8 + 175*a**3*b**4*d**2*e**3/4 + 105*a**2*b**5*d**3*e**2/4 + 35*a*b**6*d**4*e/8 + b**7*d**5/8) + x**7*(a**6*b*e**5 + 15*a**5*b**2*d*e**4 + 50*a**4*b**3*d**2*e**3 + 50*a**3*b**4*d**3*e**2 + 15*a**2*b**5*d**4*e + a*b**6*d**5) + x**6*(a**7*e**5/6 + 35*a**6*b*d*e**4/6 + 35*a**5*b**2*d**2*e**3 + 175*a**4*b**3*d**3*e**2/3 + 175*a**3*b**4*d**4*e/6 + 7*a**2*b**5*d**5/2) + x**5*(a**7*d*e**4 + 14*a**6*b*d**2*e**3 + 42*a**5*b**2*d**3*e**2 + 35*a**4*b**3*d**4*e + 7*a**3*b**4*d**5) + x**4*(5*a**7*d**2*e**3/2 + 35*a**6*b*d**3*e**2/2 + 105*a**5*b**2*d**4*e/4 + 35*a**4*b**3*d**5/4) + x**3*(10*a**7*d**3*e**2/3 + 35*a**6*b*d**4*e/3 + 7*a**5*b**2*d**5) + x**2*(5*a**7*d**4*e/2 + 7*a**6*b*d**5/2)","B",0
1918,1,549,0,0.160002," ","integrate((b*x+a)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{4} x + \frac{b^{7} e^{4} x^{12}}{12} + x^{11} \left(\frac{7 a b^{6} e^{4}}{11} + \frac{4 b^{7} d e^{3}}{11}\right) + x^{10} \left(\frac{21 a^{2} b^{5} e^{4}}{10} + \frac{14 a b^{6} d e^{3}}{5} + \frac{3 b^{7} d^{2} e^{2}}{5}\right) + x^{9} \left(\frac{35 a^{3} b^{4} e^{4}}{9} + \frac{28 a^{2} b^{5} d e^{3}}{3} + \frac{14 a b^{6} d^{2} e^{2}}{3} + \frac{4 b^{7} d^{3} e}{9}\right) + x^{8} \left(\frac{35 a^{4} b^{3} e^{4}}{8} + \frac{35 a^{3} b^{4} d e^{3}}{2} + \frac{63 a^{2} b^{5} d^{2} e^{2}}{4} + \frac{7 a b^{6} d^{3} e}{2} + \frac{b^{7} d^{4}}{8}\right) + x^{7} \left(3 a^{5} b^{2} e^{4} + 20 a^{4} b^{3} d e^{3} + 30 a^{3} b^{4} d^{2} e^{2} + 12 a^{2} b^{5} d^{3} e + a b^{6} d^{4}\right) + x^{6} \left(\frac{7 a^{6} b e^{4}}{6} + 14 a^{5} b^{2} d e^{3} + 35 a^{4} b^{3} d^{2} e^{2} + \frac{70 a^{3} b^{4} d^{3} e}{3} + \frac{7 a^{2} b^{5} d^{4}}{2}\right) + x^{5} \left(\frac{a^{7} e^{4}}{5} + \frac{28 a^{6} b d e^{3}}{5} + \frac{126 a^{5} b^{2} d^{2} e^{2}}{5} + 28 a^{4} b^{3} d^{3} e + 7 a^{3} b^{4} d^{4}\right) + x^{4} \left(a^{7} d e^{3} + \frac{21 a^{6} b d^{2} e^{2}}{2} + 21 a^{5} b^{2} d^{3} e + \frac{35 a^{4} b^{3} d^{4}}{4}\right) + x^{3} \left(2 a^{7} d^{2} e^{2} + \frac{28 a^{6} b d^{3} e}{3} + 7 a^{5} b^{2} d^{4}\right) + x^{2} \left(2 a^{7} d^{3} e + \frac{7 a^{6} b d^{4}}{2}\right)"," ",0,"a**7*d**4*x + b**7*e**4*x**12/12 + x**11*(7*a*b**6*e**4/11 + 4*b**7*d*e**3/11) + x**10*(21*a**2*b**5*e**4/10 + 14*a*b**6*d*e**3/5 + 3*b**7*d**2*e**2/5) + x**9*(35*a**3*b**4*e**4/9 + 28*a**2*b**5*d*e**3/3 + 14*a*b**6*d**2*e**2/3 + 4*b**7*d**3*e/9) + x**8*(35*a**4*b**3*e**4/8 + 35*a**3*b**4*d*e**3/2 + 63*a**2*b**5*d**2*e**2/4 + 7*a*b**6*d**3*e/2 + b**7*d**4/8) + x**7*(3*a**5*b**2*e**4 + 20*a**4*b**3*d*e**3 + 30*a**3*b**4*d**2*e**2 + 12*a**2*b**5*d**3*e + a*b**6*d**4) + x**6*(7*a**6*b*e**4/6 + 14*a**5*b**2*d*e**3 + 35*a**4*b**3*d**2*e**2 + 70*a**3*b**4*d**3*e/3 + 7*a**2*b**5*d**4/2) + x**5*(a**7*e**4/5 + 28*a**6*b*d*e**3/5 + 126*a**5*b**2*d**2*e**2/5 + 28*a**4*b**3*d**3*e + 7*a**3*b**4*d**4) + x**4*(a**7*d*e**3 + 21*a**6*b*d**2*e**2/2 + 21*a**5*b**2*d**3*e + 35*a**4*b**3*d**4/4) + x**3*(2*a**7*d**2*e**2 + 28*a**6*b*d**3*e/3 + 7*a**5*b**2*d**4) + x**2*(2*a**7*d**3*e + 7*a**6*b*d**4/2)","B",0
1919,1,427,0,0.141590," ","integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{3} x + \frac{b^{7} e^{3} x^{11}}{11} + x^{10} \left(\frac{7 a b^{6} e^{3}}{10} + \frac{3 b^{7} d e^{2}}{10}\right) + x^{9} \left(\frac{7 a^{2} b^{5} e^{3}}{3} + \frac{7 a b^{6} d e^{2}}{3} + \frac{b^{7} d^{2} e}{3}\right) + x^{8} \left(\frac{35 a^{3} b^{4} e^{3}}{8} + \frac{63 a^{2} b^{5} d e^{2}}{8} + \frac{21 a b^{6} d^{2} e}{8} + \frac{b^{7} d^{3}}{8}\right) + x^{7} \left(5 a^{4} b^{3} e^{3} + 15 a^{3} b^{4} d e^{2} + 9 a^{2} b^{5} d^{2} e + a b^{6} d^{3}\right) + x^{6} \left(\frac{7 a^{5} b^{2} e^{3}}{2} + \frac{35 a^{4} b^{3} d e^{2}}{2} + \frac{35 a^{3} b^{4} d^{2} e}{2} + \frac{7 a^{2} b^{5} d^{3}}{2}\right) + x^{5} \left(\frac{7 a^{6} b e^{3}}{5} + \frac{63 a^{5} b^{2} d e^{2}}{5} + 21 a^{4} b^{3} d^{2} e + 7 a^{3} b^{4} d^{3}\right) + x^{4} \left(\frac{a^{7} e^{3}}{4} + \frac{21 a^{6} b d e^{2}}{4} + \frac{63 a^{5} b^{2} d^{2} e}{4} + \frac{35 a^{4} b^{3} d^{3}}{4}\right) + x^{3} \left(a^{7} d e^{2} + 7 a^{6} b d^{2} e + 7 a^{5} b^{2} d^{3}\right) + x^{2} \left(\frac{3 a^{7} d^{2} e}{2} + \frac{7 a^{6} b d^{3}}{2}\right)"," ",0,"a**7*d**3*x + b**7*e**3*x**11/11 + x**10*(7*a*b**6*e**3/10 + 3*b**7*d*e**2/10) + x**9*(7*a**2*b**5*e**3/3 + 7*a*b**6*d*e**2/3 + b**7*d**2*e/3) + x**8*(35*a**3*b**4*e**3/8 + 63*a**2*b**5*d*e**2/8 + 21*a*b**6*d**2*e/8 + b**7*d**3/8) + x**7*(5*a**4*b**3*e**3 + 15*a**3*b**4*d*e**2 + 9*a**2*b**5*d**2*e + a*b**6*d**3) + x**6*(7*a**5*b**2*e**3/2 + 35*a**4*b**3*d*e**2/2 + 35*a**3*b**4*d**2*e/2 + 7*a**2*b**5*d**3/2) + x**5*(7*a**6*b*e**3/5 + 63*a**5*b**2*d*e**2/5 + 21*a**4*b**3*d**2*e + 7*a**3*b**4*d**3) + x**4*(a**7*e**3/4 + 21*a**6*b*d*e**2/4 + 63*a**5*b**2*d**2*e/4 + 35*a**4*b**3*d**3/4) + x**3*(a**7*d*e**2 + 7*a**6*b*d**2*e + 7*a**5*b**2*d**3) + x**2*(3*a**7*d**2*e/2 + 7*a**6*b*d**3/2)","B",0
1920,1,303,0,0.124187," ","integrate((b*x+a)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{2} x + \frac{b^{7} e^{2} x^{10}}{10} + x^{9} \left(\frac{7 a b^{6} e^{2}}{9} + \frac{2 b^{7} d e}{9}\right) + x^{8} \left(\frac{21 a^{2} b^{5} e^{2}}{8} + \frac{7 a b^{6} d e}{4} + \frac{b^{7} d^{2}}{8}\right) + x^{7} \left(5 a^{3} b^{4} e^{2} + 6 a^{2} b^{5} d e + a b^{6} d^{2}\right) + x^{6} \left(\frac{35 a^{4} b^{3} e^{2}}{6} + \frac{35 a^{3} b^{4} d e}{3} + \frac{7 a^{2} b^{5} d^{2}}{2}\right) + x^{5} \left(\frac{21 a^{5} b^{2} e^{2}}{5} + 14 a^{4} b^{3} d e + 7 a^{3} b^{4} d^{2}\right) + x^{4} \left(\frac{7 a^{6} b e^{2}}{4} + \frac{21 a^{5} b^{2} d e}{2} + \frac{35 a^{4} b^{3} d^{2}}{4}\right) + x^{3} \left(\frac{a^{7} e^{2}}{3} + \frac{14 a^{6} b d e}{3} + 7 a^{5} b^{2} d^{2}\right) + x^{2} \left(a^{7} d e + \frac{7 a^{6} b d^{2}}{2}\right)"," ",0,"a**7*d**2*x + b**7*e**2*x**10/10 + x**9*(7*a*b**6*e**2/9 + 2*b**7*d*e/9) + x**8*(21*a**2*b**5*e**2/8 + 7*a*b**6*d*e/4 + b**7*d**2/8) + x**7*(5*a**3*b**4*e**2 + 6*a**2*b**5*d*e + a*b**6*d**2) + x**6*(35*a**4*b**3*e**2/6 + 35*a**3*b**4*d*e/3 + 7*a**2*b**5*d**2/2) + x**5*(21*a**5*b**2*e**2/5 + 14*a**4*b**3*d*e + 7*a**3*b**4*d**2) + x**4*(7*a**6*b*e**2/4 + 21*a**5*b**2*d*e/2 + 35*a**4*b**3*d**2/4) + x**3*(a**7*e**2/3 + 14*a**6*b*d*e/3 + 7*a**5*b**2*d**2) + x**2*(a**7*d*e + 7*a**6*b*d**2/2)","B",0
1921,1,178,0,0.104175," ","integrate((b*x+a)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d x + \frac{b^{7} e x^{9}}{9} + x^{8} \left(\frac{7 a b^{6} e}{8} + \frac{b^{7} d}{8}\right) + x^{7} \left(3 a^{2} b^{5} e + a b^{6} d\right) + x^{6} \left(\frac{35 a^{3} b^{4} e}{6} + \frac{7 a^{2} b^{5} d}{2}\right) + x^{5} \left(7 a^{4} b^{3} e + 7 a^{3} b^{4} d\right) + x^{4} \left(\frac{21 a^{5} b^{2} e}{4} + \frac{35 a^{4} b^{3} d}{4}\right) + x^{3} \left(\frac{7 a^{6} b e}{3} + 7 a^{5} b^{2} d\right) + x^{2} \left(\frac{a^{7} e}{2} + \frac{7 a^{6} b d}{2}\right)"," ",0,"a**7*d*x + b**7*e*x**9/9 + x**8*(7*a*b**6*e/8 + b**7*d/8) + x**7*(3*a**2*b**5*e + a*b**6*d) + x**6*(35*a**3*b**4*e/6 + 7*a**2*b**5*d/2) + x**5*(7*a**4*b**3*e + 7*a**3*b**4*d) + x**4*(21*a**5*b**2*e/4 + 35*a**4*b**3*d/4) + x**3*(7*a**6*b*e/3 + 7*a**5*b**2*d) + x**2*(a**7*e/2 + 7*a**6*b*d/2)","B",0
1922,1,83,0,0.084136," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} x + \frac{7 a^{6} b x^{2}}{2} + 7 a^{5} b^{2} x^{3} + \frac{35 a^{4} b^{3} x^{4}}{4} + 7 a^{3} b^{4} x^{5} + \frac{7 a^{2} b^{5} x^{6}}{2} + a b^{6} x^{7} + \frac{b^{7} x^{8}}{8}"," ",0,"a**7*x + 7*a**6*b*x**2/2 + 7*a**5*b**2*x**3 + 35*a**4*b**3*x**4/4 + 7*a**3*b**4*x**5 + 7*a**2*b**5*x**6/2 + a*b**6*x**7 + b**7*x**8/8","B",0
1923,1,408,0,0.825721," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d),x)","\frac{b^{7} x^{7}}{7 e} + x^{6} \left(\frac{7 a b^{6}}{6 e} - \frac{b^{7} d}{6 e^{2}}\right) + x^{5} \left(\frac{21 a^{2} b^{5}}{5 e} - \frac{7 a b^{6} d}{5 e^{2}} + \frac{b^{7} d^{2}}{5 e^{3}}\right) + x^{4} \left(\frac{35 a^{3} b^{4}}{4 e} - \frac{21 a^{2} b^{5} d}{4 e^{2}} + \frac{7 a b^{6} d^{2}}{4 e^{3}} - \frac{b^{7} d^{3}}{4 e^{4}}\right) + x^{3} \left(\frac{35 a^{4} b^{3}}{3 e} - \frac{35 a^{3} b^{4} d}{3 e^{2}} + \frac{7 a^{2} b^{5} d^{2}}{e^{3}} - \frac{7 a b^{6} d^{3}}{3 e^{4}} + \frac{b^{7} d^{4}}{3 e^{5}}\right) + x^{2} \left(\frac{21 a^{5} b^{2}}{2 e} - \frac{35 a^{4} b^{3} d}{2 e^{2}} + \frac{35 a^{3} b^{4} d^{2}}{2 e^{3}} - \frac{21 a^{2} b^{5} d^{3}}{2 e^{4}} + \frac{7 a b^{6} d^{4}}{2 e^{5}} - \frac{b^{7} d^{5}}{2 e^{6}}\right) + x \left(\frac{7 a^{6} b}{e} - \frac{21 a^{5} b^{2} d}{e^{2}} + \frac{35 a^{4} b^{3} d^{2}}{e^{3}} - \frac{35 a^{3} b^{4} d^{3}}{e^{4}} + \frac{21 a^{2} b^{5} d^{4}}{e^{5}} - \frac{7 a b^{6} d^{5}}{e^{6}} + \frac{b^{7} d^{6}}{e^{7}}\right) + \frac{\left(a e - b d\right)^{7} \log{\left(d + e x \right)}}{e^{8}}"," ",0,"b**7*x**7/(7*e) + x**6*(7*a*b**6/(6*e) - b**7*d/(6*e**2)) + x**5*(21*a**2*b**5/(5*e) - 7*a*b**6*d/(5*e**2) + b**7*d**2/(5*e**3)) + x**4*(35*a**3*b**4/(4*e) - 21*a**2*b**5*d/(4*e**2) + 7*a*b**6*d**2/(4*e**3) - b**7*d**3/(4*e**4)) + x**3*(35*a**4*b**3/(3*e) - 35*a**3*b**4*d/(3*e**2) + 7*a**2*b**5*d**2/e**3 - 7*a*b**6*d**3/(3*e**4) + b**7*d**4/(3*e**5)) + x**2*(21*a**5*b**2/(2*e) - 35*a**4*b**3*d/(2*e**2) + 35*a**3*b**4*d**2/(2*e**3) - 21*a**2*b**5*d**3/(2*e**4) + 7*a*b**6*d**4/(2*e**5) - b**7*d**5/(2*e**6)) + x*(7*a**6*b/e - 21*a**5*b**2*d/e**2 + 35*a**4*b**3*d**2/e**3 - 35*a**3*b**4*d**3/e**4 + 21*a**2*b**5*d**4/e**5 - 7*a*b**6*d**5/e**6 + b**7*d**6/e**7) + (a*e - b*d)**7*log(d + e*x)/e**8","B",0
1924,1,428,0,1.500719," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**2,x)","\frac{b^{7} x^{6}}{6 e^{2}} + \frac{7 b \left(a e - b d\right)^{6} \log{\left(d + e x \right)}}{e^{8}} + x^{5} \left(\frac{7 a b^{6}}{5 e^{2}} - \frac{2 b^{7} d}{5 e^{3}}\right) + x^{4} \left(\frac{21 a^{2} b^{5}}{4 e^{2}} - \frac{7 a b^{6} d}{2 e^{3}} + \frac{3 b^{7} d^{2}}{4 e^{4}}\right) + x^{3} \left(\frac{35 a^{3} b^{4}}{3 e^{2}} - \frac{14 a^{2} b^{5} d}{e^{3}} + \frac{7 a b^{6} d^{2}}{e^{4}} - \frac{4 b^{7} d^{3}}{3 e^{5}}\right) + x^{2} \left(\frac{35 a^{4} b^{3}}{2 e^{2}} - \frac{35 a^{3} b^{4} d}{e^{3}} + \frac{63 a^{2} b^{5} d^{2}}{2 e^{4}} - \frac{14 a b^{6} d^{3}}{e^{5}} + \frac{5 b^{7} d^{4}}{2 e^{6}}\right) + x \left(\frac{21 a^{5} b^{2}}{e^{2}} - \frac{70 a^{4} b^{3} d}{e^{3}} + \frac{105 a^{3} b^{4} d^{2}}{e^{4}} - \frac{84 a^{2} b^{5} d^{3}}{e^{5}} + \frac{35 a b^{6} d^{4}}{e^{6}} - \frac{6 b^{7} d^{5}}{e^{7}}\right) + \frac{- a^{7} e^{7} + 7 a^{6} b d e^{6} - 21 a^{5} b^{2} d^{2} e^{5} + 35 a^{4} b^{3} d^{3} e^{4} - 35 a^{3} b^{4} d^{4} e^{3} + 21 a^{2} b^{5} d^{5} e^{2} - 7 a b^{6} d^{6} e + b^{7} d^{7}}{d e^{8} + e^{9} x}"," ",0,"b**7*x**6/(6*e**2) + 7*b*(a*e - b*d)**6*log(d + e*x)/e**8 + x**5*(7*a*b**6/(5*e**2) - 2*b**7*d/(5*e**3)) + x**4*(21*a**2*b**5/(4*e**2) - 7*a*b**6*d/(2*e**3) + 3*b**7*d**2/(4*e**4)) + x**3*(35*a**3*b**4/(3*e**2) - 14*a**2*b**5*d/e**3 + 7*a*b**6*d**2/e**4 - 4*b**7*d**3/(3*e**5)) + x**2*(35*a**4*b**3/(2*e**2) - 35*a**3*b**4*d/e**3 + 63*a**2*b**5*d**2/(2*e**4) - 14*a*b**6*d**3/e**5 + 5*b**7*d**4/(2*e**6)) + x*(21*a**5*b**2/e**2 - 70*a**4*b**3*d/e**3 + 105*a**3*b**4*d**2/e**4 - 84*a**2*b**5*d**3/e**5 + 35*a*b**6*d**4/e**6 - 6*b**7*d**5/e**7) + (-a**7*e**7 + 7*a**6*b*d*e**6 - 21*a**5*b**2*d**2*e**5 + 35*a**4*b**3*d**3*e**4 - 35*a**3*b**4*d**4*e**3 + 21*a**2*b**5*d**5*e**2 - 7*a*b**6*d**6*e + b**7*d**7)/(d*e**8 + e**9*x)","B",0
1925,1,447,0,3.018697," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**3,x)","\frac{b^{7} x^{5}}{5 e^{3}} + \frac{21 b^{2} \left(a e - b d\right)^{5} \log{\left(d + e x \right)}}{e^{8}} + x^{4} \left(\frac{7 a b^{6}}{4 e^{3}} - \frac{3 b^{7} d}{4 e^{4}}\right) + x^{3} \left(\frac{7 a^{2} b^{5}}{e^{3}} - \frac{7 a b^{6} d}{e^{4}} + \frac{2 b^{7} d^{2}}{e^{5}}\right) + x^{2} \left(\frac{35 a^{3} b^{4}}{2 e^{3}} - \frac{63 a^{2} b^{5} d}{2 e^{4}} + \frac{21 a b^{6} d^{2}}{e^{5}} - \frac{5 b^{7} d^{3}}{e^{6}}\right) + x \left(\frac{35 a^{4} b^{3}}{e^{3}} - \frac{105 a^{3} b^{4} d}{e^{4}} + \frac{126 a^{2} b^{5} d^{2}}{e^{5}} - \frac{70 a b^{6} d^{3}}{e^{6}} + \frac{15 b^{7} d^{4}}{e^{7}}\right) + \frac{- a^{7} e^{7} - 7 a^{6} b d e^{6} + 63 a^{5} b^{2} d^{2} e^{5} - 175 a^{4} b^{3} d^{3} e^{4} + 245 a^{3} b^{4} d^{4} e^{3} - 189 a^{2} b^{5} d^{5} e^{2} + 77 a b^{6} d^{6} e - 13 b^{7} d^{7} + x \left(- 14 a^{6} b e^{7} + 84 a^{5} b^{2} d e^{6} - 210 a^{4} b^{3} d^{2} e^{5} + 280 a^{3} b^{4} d^{3} e^{4} - 210 a^{2} b^{5} d^{4} e^{3} + 84 a b^{6} d^{5} e^{2} - 14 b^{7} d^{6} e\right)}{2 d^{2} e^{8} + 4 d e^{9} x + 2 e^{10} x^{2}}"," ",0,"b**7*x**5/(5*e**3) + 21*b**2*(a*e - b*d)**5*log(d + e*x)/e**8 + x**4*(7*a*b**6/(4*e**3) - 3*b**7*d/(4*e**4)) + x**3*(7*a**2*b**5/e**3 - 7*a*b**6*d/e**4 + 2*b**7*d**2/e**5) + x**2*(35*a**3*b**4/(2*e**3) - 63*a**2*b**5*d/(2*e**4) + 21*a*b**6*d**2/e**5 - 5*b**7*d**3/e**6) + x*(35*a**4*b**3/e**3 - 105*a**3*b**4*d/e**4 + 126*a**2*b**5*d**2/e**5 - 70*a*b**6*d**3/e**6 + 15*b**7*d**4/e**7) + (-a**7*e**7 - 7*a**6*b*d*e**6 + 63*a**5*b**2*d**2*e**5 - 175*a**4*b**3*d**3*e**4 + 245*a**3*b**4*d**4*e**3 - 189*a**2*b**5*d**5*e**2 + 77*a*b**6*d**6*e - 13*b**7*d**7 + x*(-14*a**6*b*e**7 + 84*a**5*b**2*d*e**6 - 210*a**4*b**3*d**2*e**5 + 280*a**3*b**4*d**3*e**4 - 210*a**2*b**5*d**4*e**3 + 84*a*b**6*d**5*e**2 - 14*b**7*d**6*e))/(2*d**2*e**8 + 4*d*e**9*x + 2*e**10*x**2)","B",0
1926,1,474,0,6.271990," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**4,x)","\frac{b^{7} x^{4}}{4 e^{4}} + \frac{35 b^{3} \left(a e - b d\right)^{4} \log{\left(d + e x \right)}}{e^{8}} + x^{3} \left(\frac{7 a b^{6}}{3 e^{4}} - \frac{4 b^{7} d}{3 e^{5}}\right) + x^{2} \left(\frac{21 a^{2} b^{5}}{2 e^{4}} - \frac{14 a b^{6} d}{e^{5}} + \frac{5 b^{7} d^{2}}{e^{6}}\right) + x \left(\frac{35 a^{3} b^{4}}{e^{4}} - \frac{84 a^{2} b^{5} d}{e^{5}} + \frac{70 a b^{6} d^{2}}{e^{6}} - \frac{20 b^{7} d^{3}}{e^{7}}\right) + \frac{- 2 a^{7} e^{7} - 7 a^{6} b d e^{6} - 42 a^{5} b^{2} d^{2} e^{5} + 385 a^{4} b^{3} d^{3} e^{4} - 910 a^{3} b^{4} d^{4} e^{3} + 987 a^{2} b^{5} d^{5} e^{2} - 518 a b^{6} d^{6} e + 107 b^{7} d^{7} + x^{2} \left(- 126 a^{5} b^{2} e^{7} + 630 a^{4} b^{3} d e^{6} - 1260 a^{3} b^{4} d^{2} e^{5} + 1260 a^{2} b^{5} d^{3} e^{4} - 630 a b^{6} d^{4} e^{3} + 126 b^{7} d^{5} e^{2}\right) + x \left(- 21 a^{6} b e^{7} - 126 a^{5} b^{2} d e^{6} + 945 a^{4} b^{3} d^{2} e^{5} - 2100 a^{3} b^{4} d^{3} e^{4} + 2205 a^{2} b^{5} d^{4} e^{3} - 1134 a b^{6} d^{5} e^{2} + 231 b^{7} d^{6} e\right)}{6 d^{3} e^{8} + 18 d^{2} e^{9} x + 18 d e^{10} x^{2} + 6 e^{11} x^{3}}"," ",0,"b**7*x**4/(4*e**4) + 35*b**3*(a*e - b*d)**4*log(d + e*x)/e**8 + x**3*(7*a*b**6/(3*e**4) - 4*b**7*d/(3*e**5)) + x**2*(21*a**2*b**5/(2*e**4) - 14*a*b**6*d/e**5 + 5*b**7*d**2/e**6) + x*(35*a**3*b**4/e**4 - 84*a**2*b**5*d/e**5 + 70*a*b**6*d**2/e**6 - 20*b**7*d**3/e**7) + (-2*a**7*e**7 - 7*a**6*b*d*e**6 - 42*a**5*b**2*d**2*e**5 + 385*a**4*b**3*d**3*e**4 - 910*a**3*b**4*d**4*e**3 + 987*a**2*b**5*d**5*e**2 - 518*a*b**6*d**6*e + 107*b**7*d**7 + x**2*(-126*a**5*b**2*e**7 + 630*a**4*b**3*d*e**6 - 1260*a**3*b**4*d**2*e**5 + 1260*a**2*b**5*d**3*e**4 - 630*a*b**6*d**4*e**3 + 126*b**7*d**5*e**2) + x*(-21*a**6*b*e**7 - 126*a**5*b**2*d*e**6 + 945*a**4*b**3*d**2*e**5 - 2100*a**3*b**4*d**3*e**4 + 2205*a**2*b**5*d**4*e**3 - 1134*a*b**6*d**5*e**2 + 231*b**7*d**6*e))/(6*d**3*e**8 + 18*d**2*e**9*x + 18*d*e**10*x**2 + 6*e**11*x**3)","B",0
1927,1,136,0,0.442481," ","integrate((b*x+a)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2),x)","x^{3} \left(- \frac{a e^{4}}{3 b^{2}} + \frac{4 d e^{3}}{3 b}\right) + x^{2} \left(\frac{a^{2} e^{4}}{2 b^{3}} - \frac{2 a d e^{3}}{b^{2}} + \frac{3 d^{2} e^{2}}{b}\right) + x \left(- \frac{a^{3} e^{4}}{b^{4}} + \frac{4 a^{2} d e^{3}}{b^{3}} - \frac{6 a d^{2} e^{2}}{b^{2}} + \frac{4 d^{3} e}{b}\right) + \frac{e^{4} x^{4}}{4 b} + \frac{\left(a e - b d\right)^{4} \log{\left(a + b x \right)}}{b^{5}}"," ",0,"x**3*(-a*e**4/(3*b**2) + 4*d*e**3/(3*b)) + x**2*(a**2*e**4/(2*b**3) - 2*a*d*e**3/b**2 + 3*d**2*e**2/b) + x*(-a**3*e**4/b**4 + 4*a**2*d*e**3/b**3 - 6*a*d**2*e**2/b**2 + 4*d**3*e/b) + e**4*x**4/(4*b) + (a*e - b*d)**4*log(a + b*x)/b**5","A",0
1928,1,83,0,0.330028," ","integrate((b*x+a)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2),x)","x^{2} \left(- \frac{a e^{3}}{2 b^{2}} + \frac{3 d e^{2}}{2 b}\right) + x \left(\frac{a^{2} e^{3}}{b^{3}} - \frac{3 a d e^{2}}{b^{2}} + \frac{3 d^{2} e}{b}\right) + \frac{e^{3} x^{3}}{3 b} - \frac{\left(a e - b d\right)^{3} \log{\left(a + b x \right)}}{b^{4}}"," ",0,"x**2*(-a*e**3/(2*b**2) + 3*d*e**2/(2*b)) + x*(a**2*e**3/b**3 - 3*a*d*e**2/b**2 + 3*d**2*e/b) + e**3*x**3/(3*b) - (a*e - b*d)**3*log(a + b*x)/b**4","A",0
1929,1,44,0,0.258013," ","integrate((b*x+a)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2),x)","x \left(- \frac{a e^{2}}{b^{2}} + \frac{2 d e}{b}\right) + \frac{e^{2} x^{2}}{2 b} + \frac{\left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{3}}"," ",0,"x*(-a*e**2/b**2 + 2*d*e/b) + e**2*x**2/(2*b) + (a*e - b*d)**2*log(a + b*x)/b**3","A",0
1930,1,20,0,0.190430," ","integrate((b*x+a)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{e x}{b} - \frac{\left(a e - b d\right) \log{\left(a + b x \right)}}{b^{2}}"," ",0,"e*x/b - (a*e - b*d)*log(a + b*x)/b**2","A",0
1931,1,7,0,0.093779," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{\log{\left(a + b x \right)}}{b}"," ",0,"log(a + b*x)/b","A",0
1932,1,128,0,0.380126," ","integrate((b*x+a)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{\log{\left(x + \frac{- \frac{a^{2} e^{2}}{a e - b d} + \frac{2 a b d e}{a e - b d} + a e - \frac{b^{2} d^{2}}{a e - b d} + b d}{2 b e} \right)}}{a e - b d} - \frac{\log{\left(x + \frac{\frac{a^{2} e^{2}}{a e - b d} - \frac{2 a b d e}{a e - b d} + a e + \frac{b^{2} d^{2}}{a e - b d} + b d}{2 b e} \right)}}{a e - b d}"," ",0,"log(x + (-a**2*e**2/(a*e - b*d) + 2*a*b*d*e/(a*e - b*d) + a*e - b**2*d**2/(a*e - b*d) + b*d)/(2*b*e))/(a*e - b*d) - log(x + (a**2*e**2/(a*e - b*d) - 2*a*b*d*e/(a*e - b*d) + a*e + b**2*d**2/(a*e - b*d) + b*d)/(2*b*e))/(a*e - b*d)","B",0
1933,1,233,0,0.707796," ","integrate((b*x+a)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{b \log{\left(x + \frac{- \frac{a^{3} b e^{3}}{\left(a e - b d\right)^{2}} + \frac{3 a^{2} b^{2} d e^{2}}{\left(a e - b d\right)^{2}} - \frac{3 a b^{3} d^{2} e}{\left(a e - b d\right)^{2}} + a b e + \frac{b^{4} d^{3}}{\left(a e - b d\right)^{2}} + b^{2} d}{2 b^{2} e} \right)}}{\left(a e - b d\right)^{2}} + \frac{b \log{\left(x + \frac{\frac{a^{3} b e^{3}}{\left(a e - b d\right)^{2}} - \frac{3 a^{2} b^{2} d e^{2}}{\left(a e - b d\right)^{2}} + \frac{3 a b^{3} d^{2} e}{\left(a e - b d\right)^{2}} + a b e - \frac{b^{4} d^{3}}{\left(a e - b d\right)^{2}} + b^{2} d}{2 b^{2} e} \right)}}{\left(a e - b d\right)^{2}} - \frac{1}{a d e - b d^{2} + x \left(a e^{2} - b d e\right)}"," ",0,"-b*log(x + (-a**3*b*e**3/(a*e - b*d)**2 + 3*a**2*b**2*d*e**2/(a*e - b*d)**2 - 3*a*b**3*d**2*e/(a*e - b*d)**2 + a*b*e + b**4*d**3/(a*e - b*d)**2 + b**2*d)/(2*b**2*e))/(a*e - b*d)**2 + b*log(x + (a**3*b*e**3/(a*e - b*d)**2 - 3*a**2*b**2*d*e**2/(a*e - b*d)**2 + 3*a*b**3*d**2*e/(a*e - b*d)**2 + a*b*e - b**4*d**3/(a*e - b*d)**2 + b**2*d)/(2*b**2*e))/(a*e - b*d)**2 - 1/(a*d*e - b*d**2 + x*(a*e**2 - b*d*e))","B",0
1934,1,381,0,1.079650," ","integrate((b*x+a)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2),x)","\frac{b^{2} \log{\left(x + \frac{- \frac{a^{4} b^{2} e^{4}}{\left(a e - b d\right)^{3}} + \frac{4 a^{3} b^{3} d e^{3}}{\left(a e - b d\right)^{3}} - \frac{6 a^{2} b^{4} d^{2} e^{2}}{\left(a e - b d\right)^{3}} + \frac{4 a b^{5} d^{3} e}{\left(a e - b d\right)^{3}} + a b^{2} e - \frac{b^{6} d^{4}}{\left(a e - b d\right)^{3}} + b^{3} d}{2 b^{3} e} \right)}}{\left(a e - b d\right)^{3}} - \frac{b^{2} \log{\left(x + \frac{\frac{a^{4} b^{2} e^{4}}{\left(a e - b d\right)^{3}} - \frac{4 a^{3} b^{3} d e^{3}}{\left(a e - b d\right)^{3}} + \frac{6 a^{2} b^{4} d^{2} e^{2}}{\left(a e - b d\right)^{3}} - \frac{4 a b^{5} d^{3} e}{\left(a e - b d\right)^{3}} + a b^{2} e + \frac{b^{6} d^{4}}{\left(a e - b d\right)^{3}} + b^{3} d}{2 b^{3} e} \right)}}{\left(a e - b d\right)^{3}} + \frac{- a e + 3 b d + 2 b e x}{2 a^{2} d^{2} e^{2} - 4 a b d^{3} e + 2 b^{2} d^{4} + x^{2} \left(2 a^{2} e^{4} - 4 a b d e^{3} + 2 b^{2} d^{2} e^{2}\right) + x \left(4 a^{2} d e^{3} - 8 a b d^{2} e^{2} + 4 b^{2} d^{3} e\right)}"," ",0,"b**2*log(x + (-a**4*b**2*e**4/(a*e - b*d)**3 + 4*a**3*b**3*d*e**3/(a*e - b*d)**3 - 6*a**2*b**4*d**2*e**2/(a*e - b*d)**3 + 4*a*b**5*d**3*e/(a*e - b*d)**3 + a*b**2*e - b**6*d**4/(a*e - b*d)**3 + b**3*d)/(2*b**3*e))/(a*e - b*d)**3 - b**2*log(x + (a**4*b**2*e**4/(a*e - b*d)**3 - 4*a**3*b**3*d*e**3/(a*e - b*d)**3 + 6*a**2*b**4*d**2*e**2/(a*e - b*d)**3 - 4*a*b**5*d**3*e/(a*e - b*d)**3 + a*b**2*e + b**6*d**4/(a*e - b*d)**3 + b**3*d)/(2*b**3*e))/(a*e - b*d)**3 + (-a*e + 3*b*d + 2*b*e*x)/(2*a**2*d**2*e**2 - 4*a*b*d**3*e + 2*b**2*d**4 + x**2*(2*a**2*e**4 - 4*a*b*d*e**3 + 2*b**2*d**2*e**2) + x*(4*a**2*d*e**3 - 8*a*b*d**2*e**2 + 4*b**2*d**3*e))","B",0
1935,1,570,0,1.533025," ","integrate((b*x+a)/(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{b^{3} \log{\left(x + \frac{- \frac{a^{5} b^{3} e^{5}}{\left(a e - b d\right)^{4}} + \frac{5 a^{4} b^{4} d e^{4}}{\left(a e - b d\right)^{4}} - \frac{10 a^{3} b^{5} d^{2} e^{3}}{\left(a e - b d\right)^{4}} + \frac{10 a^{2} b^{6} d^{3} e^{2}}{\left(a e - b d\right)^{4}} - \frac{5 a b^{7} d^{4} e}{\left(a e - b d\right)^{4}} + a b^{3} e + \frac{b^{8} d^{5}}{\left(a e - b d\right)^{4}} + b^{4} d}{2 b^{4} e} \right)}}{\left(a e - b d\right)^{4}} + \frac{b^{3} \log{\left(x + \frac{\frac{a^{5} b^{3} e^{5}}{\left(a e - b d\right)^{4}} - \frac{5 a^{4} b^{4} d e^{4}}{\left(a e - b d\right)^{4}} + \frac{10 a^{3} b^{5} d^{2} e^{3}}{\left(a e - b d\right)^{4}} - \frac{10 a^{2} b^{6} d^{3} e^{2}}{\left(a e - b d\right)^{4}} + \frac{5 a b^{7} d^{4} e}{\left(a e - b d\right)^{4}} + a b^{3} e - \frac{b^{8} d^{5}}{\left(a e - b d\right)^{4}} + b^{4} d}{2 b^{4} e} \right)}}{\left(a e - b d\right)^{4}} + \frac{- 2 a^{2} e^{2} + 7 a b d e - 11 b^{2} d^{2} - 6 b^{2} e^{2} x^{2} + x \left(3 a b e^{2} - 15 b^{2} d e\right)}{6 a^{3} d^{3} e^{3} - 18 a^{2} b d^{4} e^{2} + 18 a b^{2} d^{5} e - 6 b^{3} d^{6} + x^{3} \left(6 a^{3} e^{6} - 18 a^{2} b d e^{5} + 18 a b^{2} d^{2} e^{4} - 6 b^{3} d^{3} e^{3}\right) + x^{2} \left(18 a^{3} d e^{5} - 54 a^{2} b d^{2} e^{4} + 54 a b^{2} d^{3} e^{3} - 18 b^{3} d^{4} e^{2}\right) + x \left(18 a^{3} d^{2} e^{4} - 54 a^{2} b d^{3} e^{3} + 54 a b^{2} d^{4} e^{2} - 18 b^{3} d^{5} e\right)}"," ",0,"-b**3*log(x + (-a**5*b**3*e**5/(a*e - b*d)**4 + 5*a**4*b**4*d*e**4/(a*e - b*d)**4 - 10*a**3*b**5*d**2*e**3/(a*e - b*d)**4 + 10*a**2*b**6*d**3*e**2/(a*e - b*d)**4 - 5*a*b**7*d**4*e/(a*e - b*d)**4 + a*b**3*e + b**8*d**5/(a*e - b*d)**4 + b**4*d)/(2*b**4*e))/(a*e - b*d)**4 + b**3*log(x + (a**5*b**3*e**5/(a*e - b*d)**4 - 5*a**4*b**4*d*e**4/(a*e - b*d)**4 + 10*a**3*b**5*d**2*e**3/(a*e - b*d)**4 - 10*a**2*b**6*d**3*e**2/(a*e - b*d)**4 + 5*a*b**7*d**4*e/(a*e - b*d)**4 + a*b**3*e - b**8*d**5/(a*e - b*d)**4 + b**4*d)/(2*b**4*e))/(a*e - b*d)**4 + (-2*a**2*e**2 + 7*a*b*d*e - 11*b**2*d**2 - 6*b**2*e**2*x**2 + x*(3*a*b*e**2 - 15*b**2*d*e))/(6*a**3*d**3*e**3 - 18*a**2*b*d**4*e**2 + 18*a*b**2*d**5*e - 6*b**3*d**6 + x**3*(6*a**3*e**6 - 18*a**2*b*d*e**5 + 18*a*b**2*d**2*e**4 - 6*b**3*d**3*e**3) + x**2*(18*a**3*d*e**5 - 54*a**2*b*d**2*e**4 + 54*a*b**2*d**3*e**3 - 18*b**3*d**4*e**2) + x*(18*a**3*d**2*e**4 - 54*a**2*b*d**3*e**3 + 54*a*b**2*d**4*e**2 - 18*b**3*d**5*e))","B",0
1936,1,185,0,1.243492," ","integrate((b*x+a)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**2,x)","x \left(- \frac{3 a e^{4}}{b^{4}} + \frac{4 d e^{3}}{b^{3}}\right) + \frac{7 a^{4} e^{4} - 20 a^{3} b d e^{3} + 18 a^{2} b^{2} d^{2} e^{2} - 4 a b^{3} d^{3} e - b^{4} d^{4} + x \left(8 a^{3} b e^{4} - 24 a^{2} b^{2} d e^{3} + 24 a b^{3} d^{2} e^{2} - 8 b^{4} d^{3} e\right)}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{e^{4} x^{2}}{2 b^{3}} + \frac{6 e^{2} \left(a e - b d\right)^{2} \log{\left(a + b x \right)}}{b^{5}}"," ",0,"x*(-3*a*e**4/b**4 + 4*d*e**3/b**3) + (7*a**4*e**4 - 20*a**3*b*d*e**3 + 18*a**2*b**2*d**2*e**2 - 4*a*b**3*d**3*e - b**4*d**4 + x*(8*a**3*b*e**4 - 24*a**2*b**2*d*e**3 + 24*a*b**3*d**2*e**2 - 8*b**4*d**3*e))/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + e**4*x**2/(2*b**3) + 6*e**2*(a*e - b*d)**2*log(a + b*x)/b**5","A",0
1937,1,128,0,0.854327," ","integrate((b*x+a)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- 5 a^{3} e^{3} + 9 a^{2} b d e^{2} - 3 a b^{2} d^{2} e - b^{3} d^{3} + x \left(- 6 a^{2} b e^{3} + 12 a b^{2} d e^{2} - 6 b^{3} d^{2} e\right)}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{e^{3} x}{b^{3}} - \frac{3 e^{2} \left(a e - b d\right) \log{\left(a + b x \right)}}{b^{4}}"," ",0,"(-5*a**3*e**3 + 9*a**2*b*d*e**2 - 3*a*b**2*d**2*e - b**3*d**3 + x*(-6*a**2*b*e**3 + 12*a*b**2*d*e**2 - 6*b**3*d**2*e))/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + e**3*x/b**3 - 3*e**2*(a*e - b*d)*log(a + b*x)/b**4","A",0
1938,1,80,0,0.475554," ","integrate((b*x+a)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{3 a^{2} e^{2} - 2 a b d e - b^{2} d^{2} + x \left(4 a b e^{2} - 4 b^{2} d e\right)}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{e^{2} \log{\left(a + b x \right)}}{b^{3}}"," ",0,"(3*a**2*e**2 - 2*a*b*d*e - b**2*d**2 + x*(4*a*b*e**2 - 4*b**2*d*e))/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + e**2*log(a + b*x)/b**3","A",0
1939,1,39,0,0.278466," ","integrate((b*x+a)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{- a e - b d - 2 b e x}{2 a^{2} b^{2} + 4 a b^{3} x + 2 b^{4} x^{2}}"," ",0,"(-a*e - b*d - 2*b*e*x)/(2*a**2*b**2 + 4*a*b**3*x + 2*b**4*x**2)","A",0
1940,1,26,0,0.190532," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**2,x)","- \frac{1}{2 a^{2} b + 4 a b^{2} x + 2 b^{3} x^{2}}"," ",0,"-1/(2*a**2*b + 4*a*b**2*x + 2*b**3*x**2)","B",0
1941,1,381,0,1.092296," ","integrate((b*x+a)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{e^{2} \log{\left(x + \frac{- \frac{a^{4} e^{6}}{\left(a e - b d\right)^{3}} + \frac{4 a^{3} b d e^{5}}{\left(a e - b d\right)^{3}} - \frac{6 a^{2} b^{2} d^{2} e^{4}}{\left(a e - b d\right)^{3}} + \frac{4 a b^{3} d^{3} e^{3}}{\left(a e - b d\right)^{3}} + a e^{3} - \frac{b^{4} d^{4} e^{2}}{\left(a e - b d\right)^{3}} + b d e^{2}}{2 b e^{3}} \right)}}{\left(a e - b d\right)^{3}} - \frac{e^{2} \log{\left(x + \frac{\frac{a^{4} e^{6}}{\left(a e - b d\right)^{3}} - \frac{4 a^{3} b d e^{5}}{\left(a e - b d\right)^{3}} + \frac{6 a^{2} b^{2} d^{2} e^{4}}{\left(a e - b d\right)^{3}} - \frac{4 a b^{3} d^{3} e^{3}}{\left(a e - b d\right)^{3}} + a e^{3} + \frac{b^{4} d^{4} e^{2}}{\left(a e - b d\right)^{3}} + b d e^{2}}{2 b e^{3}} \right)}}{\left(a e - b d\right)^{3}} + \frac{3 a e - b d + 2 b e x}{2 a^{4} e^{2} - 4 a^{3} b d e + 2 a^{2} b^{2} d^{2} + x^{2} \left(2 a^{2} b^{2} e^{2} - 4 a b^{3} d e + 2 b^{4} d^{2}\right) + x \left(4 a^{3} b e^{2} - 8 a^{2} b^{2} d e + 4 a b^{3} d^{2}\right)}"," ",0,"e**2*log(x + (-a**4*e**6/(a*e - b*d)**3 + 4*a**3*b*d*e**5/(a*e - b*d)**3 - 6*a**2*b**2*d**2*e**4/(a*e - b*d)**3 + 4*a*b**3*d**3*e**3/(a*e - b*d)**3 + a*e**3 - b**4*d**4*e**2/(a*e - b*d)**3 + b*d*e**2)/(2*b*e**3))/(a*e - b*d)**3 - e**2*log(x + (a**4*e**6/(a*e - b*d)**3 - 4*a**3*b*d*e**5/(a*e - b*d)**3 + 6*a**2*b**2*d**2*e**4/(a*e - b*d)**3 - 4*a*b**3*d**3*e**3/(a*e - b*d)**3 + a*e**3 + b**4*d**4*e**2/(a*e - b*d)**3 + b*d*e**2)/(2*b*e**3))/(a*e - b*d)**3 + (3*a*e - b*d + 2*b*e*x)/(2*a**4*e**2 - 4*a**3*b*d*e + 2*a**2*b**2*d**2 + x**2*(2*a**2*b**2*e**2 - 4*a*b**3*d*e + 2*b**4*d**2) + x*(4*a**3*b*e**2 - 8*a**2*b**2*d*e + 4*a*b**3*d**2))","B",0
1942,1,634,0,1.729575," ","integrate((b*x+a)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**2,x)","- \frac{3 b e^{2} \log{\left(x + \frac{- \frac{3 a^{5} b e^{7}}{\left(a e - b d\right)^{4}} + \frac{15 a^{4} b^{2} d e^{6}}{\left(a e - b d\right)^{4}} - \frac{30 a^{3} b^{3} d^{2} e^{5}}{\left(a e - b d\right)^{4}} + \frac{30 a^{2} b^{4} d^{3} e^{4}}{\left(a e - b d\right)^{4}} - \frac{15 a b^{5} d^{4} e^{3}}{\left(a e - b d\right)^{4}} + 3 a b e^{3} + \frac{3 b^{6} d^{5} e^{2}}{\left(a e - b d\right)^{4}} + 3 b^{2} d e^{2}}{6 b^{2} e^{3}} \right)}}{\left(a e - b d\right)^{4}} + \frac{3 b e^{2} \log{\left(x + \frac{\frac{3 a^{5} b e^{7}}{\left(a e - b d\right)^{4}} - \frac{15 a^{4} b^{2} d e^{6}}{\left(a e - b d\right)^{4}} + \frac{30 a^{3} b^{3} d^{2} e^{5}}{\left(a e - b d\right)^{4}} - \frac{30 a^{2} b^{4} d^{3} e^{4}}{\left(a e - b d\right)^{4}} + \frac{15 a b^{5} d^{4} e^{3}}{\left(a e - b d\right)^{4}} + 3 a b e^{3} - \frac{3 b^{6} d^{5} e^{2}}{\left(a e - b d\right)^{4}} + 3 b^{2} d e^{2}}{6 b^{2} e^{3}} \right)}}{\left(a e - b d\right)^{4}} + \frac{- 2 a^{2} e^{2} - 5 a b d e + b^{2} d^{2} - 6 b^{2} e^{2} x^{2} + x \left(- 9 a b e^{2} - 3 b^{2} d e\right)}{2 a^{5} d e^{3} - 6 a^{4} b d^{2} e^{2} + 6 a^{3} b^{2} d^{3} e - 2 a^{2} b^{3} d^{4} + x^{3} \left(2 a^{3} b^{2} e^{4} - 6 a^{2} b^{3} d e^{3} + 6 a b^{4} d^{2} e^{2} - 2 b^{5} d^{3} e\right) + x^{2} \left(4 a^{4} b e^{4} - 10 a^{3} b^{2} d e^{3} + 6 a^{2} b^{3} d^{2} e^{2} + 2 a b^{4} d^{3} e - 2 b^{5} d^{4}\right) + x \left(2 a^{5} e^{4} - 2 a^{4} b d e^{3} - 6 a^{3} b^{2} d^{2} e^{2} + 10 a^{2} b^{3} d^{3} e - 4 a b^{4} d^{4}\right)}"," ",0,"-3*b*e**2*log(x + (-3*a**5*b*e**7/(a*e - b*d)**4 + 15*a**4*b**2*d*e**6/(a*e - b*d)**4 - 30*a**3*b**3*d**2*e**5/(a*e - b*d)**4 + 30*a**2*b**4*d**3*e**4/(a*e - b*d)**4 - 15*a*b**5*d**4*e**3/(a*e - b*d)**4 + 3*a*b*e**3 + 3*b**6*d**5*e**2/(a*e - b*d)**4 + 3*b**2*d*e**2)/(6*b**2*e**3))/(a*e - b*d)**4 + 3*b*e**2*log(x + (3*a**5*b*e**7/(a*e - b*d)**4 - 15*a**4*b**2*d*e**6/(a*e - b*d)**4 + 30*a**3*b**3*d**2*e**5/(a*e - b*d)**4 - 30*a**2*b**4*d**3*e**4/(a*e - b*d)**4 + 15*a*b**5*d**4*e**3/(a*e - b*d)**4 + 3*a*b*e**3 - 3*b**6*d**5*e**2/(a*e - b*d)**4 + 3*b**2*d*e**2)/(6*b**2*e**3))/(a*e - b*d)**4 + (-2*a**2*e**2 - 5*a*b*d*e + b**2*d**2 - 6*b**2*e**2*x**2 + x*(-9*a*b*e**2 - 3*b**2*d*e))/(2*a**5*d*e**3 - 6*a**4*b*d**2*e**2 + 6*a**3*b**2*d**3*e - 2*a**2*b**3*d**4 + x**3*(2*a**3*b**2*e**4 - 6*a**2*b**3*d*e**3 + 6*a*b**4*d**2*e**2 - 2*b**5*d**3*e) + x**2*(4*a**4*b*e**4 - 10*a**3*b**2*d*e**3 + 6*a**2*b**3*d**2*e**2 + 2*a*b**4*d**3*e - 2*b**5*d**4) + x*(2*a**5*e**4 - 2*a**4*b*d*e**3 - 6*a**3*b**2*d**2*e**2 + 10*a**2*b**3*d**3*e - 4*a*b**4*d**4))","B",0
1943,1,881,0,2.421996," ","integrate((b*x+a)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**2,x)","\frac{6 b^{2} e^{2} \log{\left(x + \frac{- \frac{6 a^{6} b^{2} e^{8}}{\left(a e - b d\right)^{5}} + \frac{36 a^{5} b^{3} d e^{7}}{\left(a e - b d\right)^{5}} - \frac{90 a^{4} b^{4} d^{2} e^{6}}{\left(a e - b d\right)^{5}} + \frac{120 a^{3} b^{5} d^{3} e^{5}}{\left(a e - b d\right)^{5}} - \frac{90 a^{2} b^{6} d^{4} e^{4}}{\left(a e - b d\right)^{5}} + \frac{36 a b^{7} d^{5} e^{3}}{\left(a e - b d\right)^{5}} + 6 a b^{2} e^{3} - \frac{6 b^{8} d^{6} e^{2}}{\left(a e - b d\right)^{5}} + 6 b^{3} d e^{2}}{12 b^{3} e^{3}} \right)}}{\left(a e - b d\right)^{5}} - \frac{6 b^{2} e^{2} \log{\left(x + \frac{\frac{6 a^{6} b^{2} e^{8}}{\left(a e - b d\right)^{5}} - \frac{36 a^{5} b^{3} d e^{7}}{\left(a e - b d\right)^{5}} + \frac{90 a^{4} b^{4} d^{2} e^{6}}{\left(a e - b d\right)^{5}} - \frac{120 a^{3} b^{5} d^{3} e^{5}}{\left(a e - b d\right)^{5}} + \frac{90 a^{2} b^{6} d^{4} e^{4}}{\left(a e - b d\right)^{5}} - \frac{36 a b^{7} d^{5} e^{3}}{\left(a e - b d\right)^{5}} + 6 a b^{2} e^{3} + \frac{6 b^{8} d^{6} e^{2}}{\left(a e - b d\right)^{5}} + 6 b^{3} d e^{2}}{12 b^{3} e^{3}} \right)}}{\left(a e - b d\right)^{5}} + \frac{- a^{3} e^{3} + 7 a^{2} b d e^{2} + 7 a b^{2} d^{2} e - b^{3} d^{3} + 12 b^{3} e^{3} x^{3} + x^{2} \left(18 a b^{2} e^{3} + 18 b^{3} d e^{2}\right) + x \left(4 a^{2} b e^{3} + 28 a b^{2} d e^{2} + 4 b^{3} d^{2} e\right)}{2 a^{6} d^{2} e^{4} - 8 a^{5} b d^{3} e^{3} + 12 a^{4} b^{2} d^{4} e^{2} - 8 a^{3} b^{3} d^{5} e + 2 a^{2} b^{4} d^{6} + x^{4} \left(2 a^{4} b^{2} e^{6} - 8 a^{3} b^{3} d e^{5} + 12 a^{2} b^{4} d^{2} e^{4} - 8 a b^{5} d^{3} e^{3} + 2 b^{6} d^{4} e^{2}\right) + x^{3} \left(4 a^{5} b e^{6} - 12 a^{4} b^{2} d e^{5} + 8 a^{3} b^{3} d^{2} e^{4} + 8 a^{2} b^{4} d^{3} e^{3} - 12 a b^{5} d^{4} e^{2} + 4 b^{6} d^{5} e\right) + x^{2} \left(2 a^{6} e^{6} - 18 a^{4} b^{2} d^{2} e^{4} + 32 a^{3} b^{3} d^{3} e^{3} - 18 a^{2} b^{4} d^{4} e^{2} + 2 b^{6} d^{6}\right) + x \left(4 a^{6} d e^{5} - 12 a^{5} b d^{2} e^{4} + 8 a^{4} b^{2} d^{3} e^{3} + 8 a^{3} b^{3} d^{4} e^{2} - 12 a^{2} b^{4} d^{5} e + 4 a b^{5} d^{6}\right)}"," ",0,"6*b**2*e**2*log(x + (-6*a**6*b**2*e**8/(a*e - b*d)**5 + 36*a**5*b**3*d*e**7/(a*e - b*d)**5 - 90*a**4*b**4*d**2*e**6/(a*e - b*d)**5 + 120*a**3*b**5*d**3*e**5/(a*e - b*d)**5 - 90*a**2*b**6*d**4*e**4/(a*e - b*d)**5 + 36*a*b**7*d**5*e**3/(a*e - b*d)**5 + 6*a*b**2*e**3 - 6*b**8*d**6*e**2/(a*e - b*d)**5 + 6*b**3*d*e**2)/(12*b**3*e**3))/(a*e - b*d)**5 - 6*b**2*e**2*log(x + (6*a**6*b**2*e**8/(a*e - b*d)**5 - 36*a**5*b**3*d*e**7/(a*e - b*d)**5 + 90*a**4*b**4*d**2*e**6/(a*e - b*d)**5 - 120*a**3*b**5*d**3*e**5/(a*e - b*d)**5 + 90*a**2*b**6*d**4*e**4/(a*e - b*d)**5 - 36*a*b**7*d**5*e**3/(a*e - b*d)**5 + 6*a*b**2*e**3 + 6*b**8*d**6*e**2/(a*e - b*d)**5 + 6*b**3*d*e**2)/(12*b**3*e**3))/(a*e - b*d)**5 + (-a**3*e**3 + 7*a**2*b*d*e**2 + 7*a*b**2*d**2*e - b**3*d**3 + 12*b**3*e**3*x**3 + x**2*(18*a*b**2*e**3 + 18*b**3*d*e**2) + x*(4*a**2*b*e**3 + 28*a*b**2*d*e**2 + 4*b**3*d**2*e))/(2*a**6*d**2*e**4 - 8*a**5*b*d**3*e**3 + 12*a**4*b**2*d**4*e**2 - 8*a**3*b**3*d**5*e + 2*a**2*b**4*d**6 + x**4*(2*a**4*b**2*e**6 - 8*a**3*b**3*d*e**5 + 12*a**2*b**4*d**2*e**4 - 8*a*b**5*d**3*e**3 + 2*b**6*d**4*e**2) + x**3*(4*a**5*b*e**6 - 12*a**4*b**2*d*e**5 + 8*a**3*b**3*d**2*e**4 + 8*a**2*b**4*d**3*e**3 - 12*a*b**5*d**4*e**2 + 4*b**6*d**5*e) + x**2*(2*a**6*e**6 - 18*a**4*b**2*d**2*e**4 + 32*a**3*b**3*d**3*e**3 - 18*a**2*b**4*d**4*e**2 + 2*b**6*d**6) + x*(4*a**6*d*e**5 - 12*a**5*b*d**2*e**4 + 8*a**4*b**2*d**3*e**3 + 8*a**3*b**3*d**4*e**2 - 12*a**2*b**4*d**5*e + 4*a*b**5*d**6))","B",0
1944,1,1221,0,3.362826," ","integrate((b*x+a)/(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**2,x)","- \frac{10 b^{3} e^{2} \log{\left(x + \frac{- \frac{10 a^{7} b^{3} e^{9}}{\left(a e - b d\right)^{6}} + \frac{70 a^{6} b^{4} d e^{8}}{\left(a e - b d\right)^{6}} - \frac{210 a^{5} b^{5} d^{2} e^{7}}{\left(a e - b d\right)^{6}} + \frac{350 a^{4} b^{6} d^{3} e^{6}}{\left(a e - b d\right)^{6}} - \frac{350 a^{3} b^{7} d^{4} e^{5}}{\left(a e - b d\right)^{6}} + \frac{210 a^{2} b^{8} d^{5} e^{4}}{\left(a e - b d\right)^{6}} - \frac{70 a b^{9} d^{6} e^{3}}{\left(a e - b d\right)^{6}} + 10 a b^{3} e^{3} + \frac{10 b^{10} d^{7} e^{2}}{\left(a e - b d\right)^{6}} + 10 b^{4} d e^{2}}{20 b^{4} e^{3}} \right)}}{\left(a e - b d\right)^{6}} + \frac{10 b^{3} e^{2} \log{\left(x + \frac{\frac{10 a^{7} b^{3} e^{9}}{\left(a e - b d\right)^{6}} - \frac{70 a^{6} b^{4} d e^{8}}{\left(a e - b d\right)^{6}} + \frac{210 a^{5} b^{5} d^{2} e^{7}}{\left(a e - b d\right)^{6}} - \frac{350 a^{4} b^{6} d^{3} e^{6}}{\left(a e - b d\right)^{6}} + \frac{350 a^{3} b^{7} d^{4} e^{5}}{\left(a e - b d\right)^{6}} - \frac{210 a^{2} b^{8} d^{5} e^{4}}{\left(a e - b d\right)^{6}} + \frac{70 a b^{9} d^{6} e^{3}}{\left(a e - b d\right)^{6}} + 10 a b^{3} e^{3} - \frac{10 b^{10} d^{7} e^{2}}{\left(a e - b d\right)^{6}} + 10 b^{4} d e^{2}}{20 b^{4} e^{3}} \right)}}{\left(a e - b d\right)^{6}} + \frac{- 2 a^{4} e^{4} + 13 a^{3} b d e^{3} - 47 a^{2} b^{2} d^{2} e^{2} - 27 a b^{3} d^{3} e + 3 b^{4} d^{4} - 60 b^{4} e^{4} x^{4} + x^{3} \left(- 90 a b^{3} e^{4} - 150 b^{4} d e^{3}\right) + x^{2} \left(- 20 a^{2} b^{2} e^{4} - 230 a b^{3} d e^{3} - 110 b^{4} d^{2} e^{2}\right) + x \left(5 a^{3} b e^{4} - 55 a^{2} b^{2} d e^{3} - 175 a b^{3} d^{2} e^{2} - 15 b^{4} d^{3} e\right)}{6 a^{7} d^{3} e^{5} - 30 a^{6} b d^{4} e^{4} + 60 a^{5} b^{2} d^{5} e^{3} - 60 a^{4} b^{3} d^{6} e^{2} + 30 a^{3} b^{4} d^{7} e - 6 a^{2} b^{5} d^{8} + x^{5} \left(6 a^{5} b^{2} e^{8} - 30 a^{4} b^{3} d e^{7} + 60 a^{3} b^{4} d^{2} e^{6} - 60 a^{2} b^{5} d^{3} e^{5} + 30 a b^{6} d^{4} e^{4} - 6 b^{7} d^{5} e^{3}\right) + x^{4} \left(12 a^{6} b e^{8} - 42 a^{5} b^{2} d e^{7} + 30 a^{4} b^{3} d^{2} e^{6} + 60 a^{3} b^{4} d^{3} e^{5} - 120 a^{2} b^{5} d^{4} e^{4} + 78 a b^{6} d^{5} e^{3} - 18 b^{7} d^{6} e^{2}\right) + x^{3} \left(6 a^{7} e^{8} + 6 a^{6} b d e^{7} - 102 a^{5} b^{2} d^{2} e^{6} + 210 a^{4} b^{3} d^{3} e^{5} - 150 a^{3} b^{4} d^{4} e^{4} - 6 a^{2} b^{5} d^{5} e^{3} + 54 a b^{6} d^{6} e^{2} - 18 b^{7} d^{7} e\right) + x^{2} \left(18 a^{7} d e^{7} - 54 a^{6} b d^{2} e^{6} + 6 a^{5} b^{2} d^{3} e^{5} + 150 a^{4} b^{3} d^{4} e^{4} - 210 a^{3} b^{4} d^{5} e^{3} + 102 a^{2} b^{5} d^{6} e^{2} - 6 a b^{6} d^{7} e - 6 b^{7} d^{8}\right) + x \left(18 a^{7} d^{2} e^{6} - 78 a^{6} b d^{3} e^{5} + 120 a^{5} b^{2} d^{4} e^{4} - 60 a^{4} b^{3} d^{5} e^{3} - 30 a^{3} b^{4} d^{6} e^{2} + 42 a^{2} b^{5} d^{7} e - 12 a b^{6} d^{8}\right)}"," ",0,"-10*b**3*e**2*log(x + (-10*a**7*b**3*e**9/(a*e - b*d)**6 + 70*a**6*b**4*d*e**8/(a*e - b*d)**6 - 210*a**5*b**5*d**2*e**7/(a*e - b*d)**6 + 350*a**4*b**6*d**3*e**6/(a*e - b*d)**6 - 350*a**3*b**7*d**4*e**5/(a*e - b*d)**6 + 210*a**2*b**8*d**5*e**4/(a*e - b*d)**6 - 70*a*b**9*d**6*e**3/(a*e - b*d)**6 + 10*a*b**3*e**3 + 10*b**10*d**7*e**2/(a*e - b*d)**6 + 10*b**4*d*e**2)/(20*b**4*e**3))/(a*e - b*d)**6 + 10*b**3*e**2*log(x + (10*a**7*b**3*e**9/(a*e - b*d)**6 - 70*a**6*b**4*d*e**8/(a*e - b*d)**6 + 210*a**5*b**5*d**2*e**7/(a*e - b*d)**6 - 350*a**4*b**6*d**3*e**6/(a*e - b*d)**6 + 350*a**3*b**7*d**4*e**5/(a*e - b*d)**6 - 210*a**2*b**8*d**5*e**4/(a*e - b*d)**6 + 70*a*b**9*d**6*e**3/(a*e - b*d)**6 + 10*a*b**3*e**3 - 10*b**10*d**7*e**2/(a*e - b*d)**6 + 10*b**4*d*e**2)/(20*b**4*e**3))/(a*e - b*d)**6 + (-2*a**4*e**4 + 13*a**3*b*d*e**3 - 47*a**2*b**2*d**2*e**2 - 27*a*b**3*d**3*e + 3*b**4*d**4 - 60*b**4*e**4*x**4 + x**3*(-90*a*b**3*e**4 - 150*b**4*d*e**3) + x**2*(-20*a**2*b**2*e**4 - 230*a*b**3*d*e**3 - 110*b**4*d**2*e**2) + x*(5*a**3*b*e**4 - 55*a**2*b**2*d*e**3 - 175*a*b**3*d**2*e**2 - 15*b**4*d**3*e))/(6*a**7*d**3*e**5 - 30*a**6*b*d**4*e**4 + 60*a**5*b**2*d**5*e**3 - 60*a**4*b**3*d**6*e**2 + 30*a**3*b**4*d**7*e - 6*a**2*b**5*d**8 + x**5*(6*a**5*b**2*e**8 - 30*a**4*b**3*d*e**7 + 60*a**3*b**4*d**2*e**6 - 60*a**2*b**5*d**3*e**5 + 30*a*b**6*d**4*e**4 - 6*b**7*d**5*e**3) + x**4*(12*a**6*b*e**8 - 42*a**5*b**2*d*e**7 + 30*a**4*b**3*d**2*e**6 + 60*a**3*b**4*d**3*e**5 - 120*a**2*b**5*d**4*e**4 + 78*a*b**6*d**5*e**3 - 18*b**7*d**6*e**2) + x**3*(6*a**7*e**8 + 6*a**6*b*d*e**7 - 102*a**5*b**2*d**2*e**6 + 210*a**4*b**3*d**3*e**5 - 150*a**3*b**4*d**4*e**4 - 6*a**2*b**5*d**5*e**3 + 54*a*b**6*d**6*e**2 - 18*b**7*d**7*e) + x**2*(18*a**7*d*e**7 - 54*a**6*b*d**2*e**6 + 6*a**5*b**2*d**3*e**5 + 150*a**4*b**3*d**4*e**4 - 210*a**3*b**4*d**5*e**3 + 102*a**2*b**5*d**6*e**2 - 6*a*b**6*d**7*e - 6*b**7*d**8) + x*(18*a**7*d**2*e**6 - 78*a**6*b*d**3*e**5 + 120*a**5*b**2*d**4*e**4 - 60*a**4*b**3*d**5*e**3 - 30*a**3*b**4*d**6*e**2 + 42*a**2*b**5*d**7*e - 12*a*b**6*d**8))","B",0
1945,1,230,0,3.339731," ","integrate((b*x+a)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{25 a^{4} e^{4} - 12 a^{3} b d e^{3} - 6 a^{2} b^{2} d^{2} e^{2} - 4 a b^{3} d^{3} e - 3 b^{4} d^{4} + x^{3} \left(48 a b^{3} e^{4} - 48 b^{4} d e^{3}\right) + x^{2} \left(108 a^{2} b^{2} e^{4} - 72 a b^{3} d e^{3} - 36 b^{4} d^{2} e^{2}\right) + x \left(88 a^{3} b e^{4} - 48 a^{2} b^{2} d e^{3} - 24 a b^{3} d^{2} e^{2} - 16 b^{4} d^{3} e\right)}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{e^{4} \log{\left(a + b x \right)}}{b^{5}}"," ",0,"(25*a**4*e**4 - 12*a**3*b*d*e**3 - 6*a**2*b**2*d**2*e**2 - 4*a*b**3*d**3*e - 3*b**4*d**4 + x**3*(48*a*b**3*e**4 - 48*b**4*d*e**3) + x**2*(108*a**2*b**2*e**4 - 72*a*b**3*d*e**3 - 36*b**4*d**2*e**2) + x*(88*a**3*b*e**4 - 48*a**2*b**2*d*e**3 - 24*a*b**3*d**2*e**2 - 16*b**4*d**3*e))/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + e**4*log(a + b*x)/b**5","B",0
1946,1,155,0,1.831880," ","integrate((b*x+a)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a^{3} e^{3} - a^{2} b d e^{2} - a b^{2} d^{2} e - b^{3} d^{3} - 4 b^{3} e^{3} x^{3} + x^{2} \left(- 6 a b^{2} e^{3} - 6 b^{3} d e^{2}\right) + x \left(- 4 a^{2} b e^{3} - 4 a b^{2} d e^{2} - 4 b^{3} d^{2} e\right)}{4 a^{4} b^{4} + 16 a^{3} b^{5} x + 24 a^{2} b^{6} x^{2} + 16 a b^{7} x^{3} + 4 b^{8} x^{4}}"," ",0,"(-a**3*e**3 - a**2*b*d*e**2 - a*b**2*d**2*e - b**3*d**3 - 4*b**3*e**3*x**3 + x**2*(-6*a*b**2*e**3 - 6*b**3*d*e**2) + x*(-4*a**2*b*e**3 - 4*a*b**2*d*e**2 - 4*b**3*d**2*e))/(4*a**4*b**4 + 16*a**3*b**5*x + 24*a**2*b**6*x**2 + 16*a*b**7*x**3 + 4*b**8*x**4)","B",0
1947,1,104,0,0.798891," ","integrate((b*x+a)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a^{2} e^{2} - 2 a b d e - 3 b^{2} d^{2} - 6 b^{2} e^{2} x^{2} + x \left(- 4 a b e^{2} - 8 b^{2} d e\right)}{12 a^{4} b^{3} + 48 a^{3} b^{4} x + 72 a^{2} b^{5} x^{2} + 48 a b^{6} x^{3} + 12 b^{7} x^{4}}"," ",0,"(-a**2*e**2 - 2*a*b*d*e - 3*b**2*d**2 - 6*b**2*e**2*x**2 + x*(-4*a*b*e**2 - 8*b**2*d*e))/(12*a**4*b**3 + 48*a**3*b**4*x + 72*a**2*b**5*x**2 + 48*a*b**6*x**3 + 12*b**7*x**4)","A",0
1948,1,65,0,0.455273," ","integrate((b*x+a)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{- a e - 3 b d - 4 b e x}{12 a^{4} b^{2} + 48 a^{3} b^{3} x + 72 a^{2} b^{4} x^{2} + 48 a b^{5} x^{3} + 12 b^{6} x^{4}}"," ",0,"(-a*e - 3*b*d - 4*b*e*x)/(12*a**4*b**2 + 48*a**3*b**3*x + 72*a**2*b**4*x**2 + 48*a*b**5*x**3 + 12*b**6*x**4)","B",0
1949,1,49,0,0.319995," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**3,x)","- \frac{1}{4 a^{4} b + 16 a^{3} b^{2} x + 24 a^{2} b^{3} x^{2} + 16 a b^{4} x^{3} + 4 b^{5} x^{4}}"," ",0,"-1/(4*a**4*b + 16*a**3*b**2*x + 24*a**2*b**3*x**2 + 16*a*b**4*x**3 + 4*b**5*x**4)","B",0
1950,1,802,0,2.140689," ","integrate((b*x+a)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{e^{4} \log{\left(x + \frac{- \frac{a^{6} e^{10}}{\left(a e - b d\right)^{5}} + \frac{6 a^{5} b d e^{9}}{\left(a e - b d\right)^{5}} - \frac{15 a^{4} b^{2} d^{2} e^{8}}{\left(a e - b d\right)^{5}} + \frac{20 a^{3} b^{3} d^{3} e^{7}}{\left(a e - b d\right)^{5}} - \frac{15 a^{2} b^{4} d^{4} e^{6}}{\left(a e - b d\right)^{5}} + \frac{6 a b^{5} d^{5} e^{5}}{\left(a e - b d\right)^{5}} + a e^{5} - \frac{b^{6} d^{6} e^{4}}{\left(a e - b d\right)^{5}} + b d e^{4}}{2 b e^{5}} \right)}}{\left(a e - b d\right)^{5}} - \frac{e^{4} \log{\left(x + \frac{\frac{a^{6} e^{10}}{\left(a e - b d\right)^{5}} - \frac{6 a^{5} b d e^{9}}{\left(a e - b d\right)^{5}} + \frac{15 a^{4} b^{2} d^{2} e^{8}}{\left(a e - b d\right)^{5}} - \frac{20 a^{3} b^{3} d^{3} e^{7}}{\left(a e - b d\right)^{5}} + \frac{15 a^{2} b^{4} d^{4} e^{6}}{\left(a e - b d\right)^{5}} - \frac{6 a b^{5} d^{5} e^{5}}{\left(a e - b d\right)^{5}} + a e^{5} + \frac{b^{6} d^{6} e^{4}}{\left(a e - b d\right)^{5}} + b d e^{4}}{2 b e^{5}} \right)}}{\left(a e - b d\right)^{5}} + \frac{25 a^{3} e^{3} - 23 a^{2} b d e^{2} + 13 a b^{2} d^{2} e - 3 b^{3} d^{3} + 12 b^{3} e^{3} x^{3} + x^{2} \left(42 a b^{2} e^{3} - 6 b^{3} d e^{2}\right) + x \left(52 a^{2} b e^{3} - 20 a b^{2} d e^{2} + 4 b^{3} d^{2} e\right)}{12 a^{8} e^{4} - 48 a^{7} b d e^{3} + 72 a^{6} b^{2} d^{2} e^{2} - 48 a^{5} b^{3} d^{3} e + 12 a^{4} b^{4} d^{4} + x^{4} \left(12 a^{4} b^{4} e^{4} - 48 a^{3} b^{5} d e^{3} + 72 a^{2} b^{6} d^{2} e^{2} - 48 a b^{7} d^{3} e + 12 b^{8} d^{4}\right) + x^{3} \left(48 a^{5} b^{3} e^{4} - 192 a^{4} b^{4} d e^{3} + 288 a^{3} b^{5} d^{2} e^{2} - 192 a^{2} b^{6} d^{3} e + 48 a b^{7} d^{4}\right) + x^{2} \left(72 a^{6} b^{2} e^{4} - 288 a^{5} b^{3} d e^{3} + 432 a^{4} b^{4} d^{2} e^{2} - 288 a^{3} b^{5} d^{3} e + 72 a^{2} b^{6} d^{4}\right) + x \left(48 a^{7} b e^{4} - 192 a^{6} b^{2} d e^{3} + 288 a^{5} b^{3} d^{2} e^{2} - 192 a^{4} b^{4} d^{3} e + 48 a^{3} b^{5} d^{4}\right)}"," ",0,"e**4*log(x + (-a**6*e**10/(a*e - b*d)**5 + 6*a**5*b*d*e**9/(a*e - b*d)**5 - 15*a**4*b**2*d**2*e**8/(a*e - b*d)**5 + 20*a**3*b**3*d**3*e**7/(a*e - b*d)**5 - 15*a**2*b**4*d**4*e**6/(a*e - b*d)**5 + 6*a*b**5*d**5*e**5/(a*e - b*d)**5 + a*e**5 - b**6*d**6*e**4/(a*e - b*d)**5 + b*d*e**4)/(2*b*e**5))/(a*e - b*d)**5 - e**4*log(x + (a**6*e**10/(a*e - b*d)**5 - 6*a**5*b*d*e**9/(a*e - b*d)**5 + 15*a**4*b**2*d**2*e**8/(a*e - b*d)**5 - 20*a**3*b**3*d**3*e**7/(a*e - b*d)**5 + 15*a**2*b**4*d**4*e**6/(a*e - b*d)**5 - 6*a*b**5*d**5*e**5/(a*e - b*d)**5 + a*e**5 + b**6*d**6*e**4/(a*e - b*d)**5 + b*d*e**4)/(2*b*e**5))/(a*e - b*d)**5 + (25*a**3*e**3 - 23*a**2*b*d*e**2 + 13*a*b**2*d**2*e - 3*b**3*d**3 + 12*b**3*e**3*x**3 + x**2*(42*a*b**2*e**3 - 6*b**3*d*e**2) + x*(52*a**2*b*e**3 - 20*a*b**2*d*e**2 + 4*b**3*d**2*e))/(12*a**8*e**4 - 48*a**7*b*d*e**3 + 72*a**6*b**2*d**2*e**2 - 48*a**5*b**3*d**3*e + 12*a**4*b**4*d**4 + x**4*(12*a**4*b**4*e**4 - 48*a**3*b**5*d*e**3 + 72*a**2*b**6*d**2*e**2 - 48*a*b**7*d**3*e + 12*b**8*d**4) + x**3*(48*a**5*b**3*e**4 - 192*a**4*b**4*d*e**3 + 288*a**3*b**5*d**2*e**2 - 192*a**2*b**6*d**3*e + 48*a*b**7*d**4) + x**2*(72*a**6*b**2*e**4 - 288*a**5*b**3*d*e**3 + 432*a**4*b**4*d**2*e**2 - 288*a**3*b**5*d**3*e + 72*a**2*b**6*d**4) + x*(48*a**7*b*e**4 - 192*a**6*b**2*d*e**3 + 288*a**5*b**3*d**2*e**2 - 192*a**4*b**4*d**3*e + 48*a**3*b**5*d**4))","B",0
1951,1,1178,0,3.552985," ","integrate((b*x+a)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**3,x)","- \frac{5 b e^{4} \log{\left(x + \frac{- \frac{5 a^{7} b e^{11}}{\left(a e - b d\right)^{6}} + \frac{35 a^{6} b^{2} d e^{10}}{\left(a e - b d\right)^{6}} - \frac{105 a^{5} b^{3} d^{2} e^{9}}{\left(a e - b d\right)^{6}} + \frac{175 a^{4} b^{4} d^{3} e^{8}}{\left(a e - b d\right)^{6}} - \frac{175 a^{3} b^{5} d^{4} e^{7}}{\left(a e - b d\right)^{6}} + \frac{105 a^{2} b^{6} d^{5} e^{6}}{\left(a e - b d\right)^{6}} - \frac{35 a b^{7} d^{6} e^{5}}{\left(a e - b d\right)^{6}} + 5 a b e^{5} + \frac{5 b^{8} d^{7} e^{4}}{\left(a e - b d\right)^{6}} + 5 b^{2} d e^{4}}{10 b^{2} e^{5}} \right)}}{\left(a e - b d\right)^{6}} + \frac{5 b e^{4} \log{\left(x + \frac{\frac{5 a^{7} b e^{11}}{\left(a e - b d\right)^{6}} - \frac{35 a^{6} b^{2} d e^{10}}{\left(a e - b d\right)^{6}} + \frac{105 a^{5} b^{3} d^{2} e^{9}}{\left(a e - b d\right)^{6}} - \frac{175 a^{4} b^{4} d^{3} e^{8}}{\left(a e - b d\right)^{6}} + \frac{175 a^{3} b^{5} d^{4} e^{7}}{\left(a e - b d\right)^{6}} - \frac{105 a^{2} b^{6} d^{5} e^{6}}{\left(a e - b d\right)^{6}} + \frac{35 a b^{7} d^{6} e^{5}}{\left(a e - b d\right)^{6}} + 5 a b e^{5} - \frac{5 b^{8} d^{7} e^{4}}{\left(a e - b d\right)^{6}} + 5 b^{2} d e^{4}}{10 b^{2} e^{5}} \right)}}{\left(a e - b d\right)^{6}} + \frac{- 12 a^{4} e^{4} - 77 a^{3} b d e^{3} + 43 a^{2} b^{2} d^{2} e^{2} - 17 a b^{3} d^{3} e + 3 b^{4} d^{4} - 60 b^{4} e^{4} x^{4} + x^{3} \left(- 210 a b^{3} e^{4} - 30 b^{4} d e^{3}\right) + x^{2} \left(- 260 a^{2} b^{2} e^{4} - 110 a b^{3} d e^{3} + 10 b^{4} d^{2} e^{2}\right) + x \left(- 125 a^{3} b e^{4} - 145 a^{2} b^{2} d e^{3} + 35 a b^{3} d^{2} e^{2} - 5 b^{4} d^{3} e\right)}{12 a^{9} d e^{5} - 60 a^{8} b d^{2} e^{4} + 120 a^{7} b^{2} d^{3} e^{3} - 120 a^{6} b^{3} d^{4} e^{2} + 60 a^{5} b^{4} d^{5} e - 12 a^{4} b^{5} d^{6} + x^{5} \left(12 a^{5} b^{4} e^{6} - 60 a^{4} b^{5} d e^{5} + 120 a^{3} b^{6} d^{2} e^{4} - 120 a^{2} b^{7} d^{3} e^{3} + 60 a b^{8} d^{4} e^{2} - 12 b^{9} d^{5} e\right) + x^{4} \left(48 a^{6} b^{3} e^{6} - 228 a^{5} b^{4} d e^{5} + 420 a^{4} b^{5} d^{2} e^{4} - 360 a^{3} b^{6} d^{3} e^{3} + 120 a^{2} b^{7} d^{4} e^{2} + 12 a b^{8} d^{5} e - 12 b^{9} d^{6}\right) + x^{3} \left(72 a^{7} b^{2} e^{6} - 312 a^{6} b^{3} d e^{5} + 480 a^{5} b^{4} d^{2} e^{4} - 240 a^{4} b^{5} d^{3} e^{3} - 120 a^{3} b^{6} d^{4} e^{2} + 168 a^{2} b^{7} d^{5} e - 48 a b^{8} d^{6}\right) + x^{2} \left(48 a^{8} b e^{6} - 168 a^{7} b^{2} d e^{5} + 120 a^{6} b^{3} d^{2} e^{4} + 240 a^{5} b^{4} d^{3} e^{3} - 480 a^{4} b^{5} d^{4} e^{2} + 312 a^{3} b^{6} d^{5} e - 72 a^{2} b^{7} d^{6}\right) + x \left(12 a^{9} e^{6} - 12 a^{8} b d e^{5} - 120 a^{7} b^{2} d^{2} e^{4} + 360 a^{6} b^{3} d^{3} e^{3} - 420 a^{5} b^{4} d^{4} e^{2} + 228 a^{4} b^{5} d^{5} e - 48 a^{3} b^{6} d^{6}\right)}"," ",0,"-5*b*e**4*log(x + (-5*a**7*b*e**11/(a*e - b*d)**6 + 35*a**6*b**2*d*e**10/(a*e - b*d)**6 - 105*a**5*b**3*d**2*e**9/(a*e - b*d)**6 + 175*a**4*b**4*d**3*e**8/(a*e - b*d)**6 - 175*a**3*b**5*d**4*e**7/(a*e - b*d)**6 + 105*a**2*b**6*d**5*e**6/(a*e - b*d)**6 - 35*a*b**7*d**6*e**5/(a*e - b*d)**6 + 5*a*b*e**5 + 5*b**8*d**7*e**4/(a*e - b*d)**6 + 5*b**2*d*e**4)/(10*b**2*e**5))/(a*e - b*d)**6 + 5*b*e**4*log(x + (5*a**7*b*e**11/(a*e - b*d)**6 - 35*a**6*b**2*d*e**10/(a*e - b*d)**6 + 105*a**5*b**3*d**2*e**9/(a*e - b*d)**6 - 175*a**4*b**4*d**3*e**8/(a*e - b*d)**6 + 175*a**3*b**5*d**4*e**7/(a*e - b*d)**6 - 105*a**2*b**6*d**5*e**6/(a*e - b*d)**6 + 35*a*b**7*d**6*e**5/(a*e - b*d)**6 + 5*a*b*e**5 - 5*b**8*d**7*e**4/(a*e - b*d)**6 + 5*b**2*d*e**4)/(10*b**2*e**5))/(a*e - b*d)**6 + (-12*a**4*e**4 - 77*a**3*b*d*e**3 + 43*a**2*b**2*d**2*e**2 - 17*a*b**3*d**3*e + 3*b**4*d**4 - 60*b**4*e**4*x**4 + x**3*(-210*a*b**3*e**4 - 30*b**4*d*e**3) + x**2*(-260*a**2*b**2*e**4 - 110*a*b**3*d*e**3 + 10*b**4*d**2*e**2) + x*(-125*a**3*b*e**4 - 145*a**2*b**2*d*e**3 + 35*a*b**3*d**2*e**2 - 5*b**4*d**3*e))/(12*a**9*d*e**5 - 60*a**8*b*d**2*e**4 + 120*a**7*b**2*d**3*e**3 - 120*a**6*b**3*d**4*e**2 + 60*a**5*b**4*d**5*e - 12*a**4*b**5*d**6 + x**5*(12*a**5*b**4*e**6 - 60*a**4*b**5*d*e**5 + 120*a**3*b**6*d**2*e**4 - 120*a**2*b**7*d**3*e**3 + 60*a*b**8*d**4*e**2 - 12*b**9*d**5*e) + x**4*(48*a**6*b**3*e**6 - 228*a**5*b**4*d*e**5 + 420*a**4*b**5*d**2*e**4 - 360*a**3*b**6*d**3*e**3 + 120*a**2*b**7*d**4*e**2 + 12*a*b**8*d**5*e - 12*b**9*d**6) + x**3*(72*a**7*b**2*e**6 - 312*a**6*b**3*d*e**5 + 480*a**5*b**4*d**2*e**4 - 240*a**4*b**5*d**3*e**3 - 120*a**3*b**6*d**4*e**2 + 168*a**2*b**7*d**5*e - 48*a*b**8*d**6) + x**2*(48*a**8*b*e**6 - 168*a**7*b**2*d*e**5 + 120*a**6*b**3*d**2*e**4 + 240*a**5*b**4*d**3*e**3 - 480*a**4*b**5*d**4*e**2 + 312*a**3*b**6*d**5*e - 72*a**2*b**7*d**6) + x*(12*a**9*e**6 - 12*a**8*b*d*e**5 - 120*a**7*b**2*d**2*e**4 + 360*a**6*b**3*d**3*e**3 - 420*a**5*b**4*d**4*e**2 + 228*a**4*b**5*d**5*e - 48*a**3*b**6*d**6))","B",0
1952,1,1571,0,5.063033," ","integrate((b*x+a)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**3,x)","\frac{15 b^{2} e^{4} \log{\left(x + \frac{- \frac{15 a^{8} b^{2} e^{12}}{\left(a e - b d\right)^{7}} + \frac{120 a^{7} b^{3} d e^{11}}{\left(a e - b d\right)^{7}} - \frac{420 a^{6} b^{4} d^{2} e^{10}}{\left(a e - b d\right)^{7}} + \frac{840 a^{5} b^{5} d^{3} e^{9}}{\left(a e - b d\right)^{7}} - \frac{1050 a^{4} b^{6} d^{4} e^{8}}{\left(a e - b d\right)^{7}} + \frac{840 a^{3} b^{7} d^{5} e^{7}}{\left(a e - b d\right)^{7}} - \frac{420 a^{2} b^{8} d^{6} e^{6}}{\left(a e - b d\right)^{7}} + \frac{120 a b^{9} d^{7} e^{5}}{\left(a e - b d\right)^{7}} + 15 a b^{2} e^{5} - \frac{15 b^{10} d^{8} e^{4}}{\left(a e - b d\right)^{7}} + 15 b^{3} d e^{4}}{30 b^{3} e^{5}} \right)}}{\left(a e - b d\right)^{7}} - \frac{15 b^{2} e^{4} \log{\left(x + \frac{\frac{15 a^{8} b^{2} e^{12}}{\left(a e - b d\right)^{7}} - \frac{120 a^{7} b^{3} d e^{11}}{\left(a e - b d\right)^{7}} + \frac{420 a^{6} b^{4} d^{2} e^{10}}{\left(a e - b d\right)^{7}} - \frac{840 a^{5} b^{5} d^{3} e^{9}}{\left(a e - b d\right)^{7}} + \frac{1050 a^{4} b^{6} d^{4} e^{8}}{\left(a e - b d\right)^{7}} - \frac{840 a^{3} b^{7} d^{5} e^{7}}{\left(a e - b d\right)^{7}} + \frac{420 a^{2} b^{8} d^{6} e^{6}}{\left(a e - b d\right)^{7}} - \frac{120 a b^{9} d^{7} e^{5}}{\left(a e - b d\right)^{7}} + 15 a b^{2} e^{5} + \frac{15 b^{10} d^{8} e^{4}}{\left(a e - b d\right)^{7}} + 15 b^{3} d e^{4}}{30 b^{3} e^{5}} \right)}}{\left(a e - b d\right)^{7}} + \frac{- 2 a^{5} e^{5} + 22 a^{4} b d e^{4} + 57 a^{3} b^{2} d^{2} e^{3} - 23 a^{2} b^{3} d^{3} e^{2} + 7 a b^{4} d^{4} e - b^{5} d^{5} + 60 b^{5} e^{5} x^{5} + x^{4} \left(210 a b^{4} e^{5} + 90 b^{5} d e^{4}\right) + x^{3} \left(260 a^{2} b^{3} e^{5} + 320 a b^{4} d e^{4} + 20 b^{5} d^{2} e^{3}\right) + x^{2} \left(125 a^{3} b^{2} e^{5} + 405 a^{2} b^{3} d e^{4} + 75 a b^{4} d^{2} e^{3} - 5 b^{5} d^{3} e^{2}\right) + x \left(12 a^{4} b e^{5} + 202 a^{3} b^{2} d e^{4} + 102 a^{2} b^{3} d^{2} e^{3} - 18 a b^{4} d^{3} e^{2} + 2 b^{5} d^{4} e\right)}{4 a^{10} d^{2} e^{6} - 24 a^{9} b d^{3} e^{5} + 60 a^{8} b^{2} d^{4} e^{4} - 80 a^{7} b^{3} d^{5} e^{3} + 60 a^{6} b^{4} d^{6} e^{2} - 24 a^{5} b^{5} d^{7} e + 4 a^{4} b^{6} d^{8} + x^{6} \left(4 a^{6} b^{4} e^{8} - 24 a^{5} b^{5} d e^{7} + 60 a^{4} b^{6} d^{2} e^{6} - 80 a^{3} b^{7} d^{3} e^{5} + 60 a^{2} b^{8} d^{4} e^{4} - 24 a b^{9} d^{5} e^{3} + 4 b^{10} d^{6} e^{2}\right) + x^{5} \left(16 a^{7} b^{3} e^{8} - 88 a^{6} b^{4} d e^{7} + 192 a^{5} b^{5} d^{2} e^{6} - 200 a^{4} b^{6} d^{3} e^{5} + 80 a^{3} b^{7} d^{4} e^{4} + 24 a^{2} b^{8} d^{5} e^{3} - 32 a b^{9} d^{6} e^{2} + 8 b^{10} d^{7} e\right) + x^{4} \left(24 a^{8} b^{2} e^{8} - 112 a^{7} b^{3} d e^{7} + 172 a^{6} b^{4} d^{2} e^{6} - 24 a^{5} b^{5} d^{3} e^{5} - 220 a^{4} b^{6} d^{4} e^{4} + 256 a^{3} b^{7} d^{5} e^{3} - 108 a^{2} b^{8} d^{6} e^{2} + 8 a b^{9} d^{7} e + 4 b^{10} d^{8}\right) + x^{3} \left(16 a^{9} b e^{8} - 48 a^{8} b^{2} d e^{7} - 32 a^{7} b^{3} d^{2} e^{6} + 304 a^{6} b^{4} d^{3} e^{5} - 480 a^{5} b^{5} d^{4} e^{4} + 304 a^{4} b^{6} d^{5} e^{3} - 32 a^{3} b^{7} d^{6} e^{2} - 48 a^{2} b^{8} d^{7} e + 16 a b^{9} d^{8}\right) + x^{2} \left(4 a^{10} e^{8} + 8 a^{9} b d e^{7} - 108 a^{8} b^{2} d^{2} e^{6} + 256 a^{7} b^{3} d^{3} e^{5} - 220 a^{6} b^{4} d^{4} e^{4} - 24 a^{5} b^{5} d^{5} e^{3} + 172 a^{4} b^{6} d^{6} e^{2} - 112 a^{3} b^{7} d^{7} e + 24 a^{2} b^{8} d^{8}\right) + x \left(8 a^{10} d e^{7} - 32 a^{9} b d^{2} e^{6} + 24 a^{8} b^{2} d^{3} e^{5} + 80 a^{7} b^{3} d^{4} e^{4} - 200 a^{6} b^{4} d^{5} e^{3} + 192 a^{5} b^{5} d^{6} e^{2} - 88 a^{4} b^{6} d^{7} e + 16 a^{3} b^{7} d^{8}\right)}"," ",0,"15*b**2*e**4*log(x + (-15*a**8*b**2*e**12/(a*e - b*d)**7 + 120*a**7*b**3*d*e**11/(a*e - b*d)**7 - 420*a**6*b**4*d**2*e**10/(a*e - b*d)**7 + 840*a**5*b**5*d**3*e**9/(a*e - b*d)**7 - 1050*a**4*b**6*d**4*e**8/(a*e - b*d)**7 + 840*a**3*b**7*d**5*e**7/(a*e - b*d)**7 - 420*a**2*b**8*d**6*e**6/(a*e - b*d)**7 + 120*a*b**9*d**7*e**5/(a*e - b*d)**7 + 15*a*b**2*e**5 - 15*b**10*d**8*e**4/(a*e - b*d)**7 + 15*b**3*d*e**4)/(30*b**3*e**5))/(a*e - b*d)**7 - 15*b**2*e**4*log(x + (15*a**8*b**2*e**12/(a*e - b*d)**7 - 120*a**7*b**3*d*e**11/(a*e - b*d)**7 + 420*a**6*b**4*d**2*e**10/(a*e - b*d)**7 - 840*a**5*b**5*d**3*e**9/(a*e - b*d)**7 + 1050*a**4*b**6*d**4*e**8/(a*e - b*d)**7 - 840*a**3*b**7*d**5*e**7/(a*e - b*d)**7 + 420*a**2*b**8*d**6*e**6/(a*e - b*d)**7 - 120*a*b**9*d**7*e**5/(a*e - b*d)**7 + 15*a*b**2*e**5 + 15*b**10*d**8*e**4/(a*e - b*d)**7 + 15*b**3*d*e**4)/(30*b**3*e**5))/(a*e - b*d)**7 + (-2*a**5*e**5 + 22*a**4*b*d*e**4 + 57*a**3*b**2*d**2*e**3 - 23*a**2*b**3*d**3*e**2 + 7*a*b**4*d**4*e - b**5*d**5 + 60*b**5*e**5*x**5 + x**4*(210*a*b**4*e**5 + 90*b**5*d*e**4) + x**3*(260*a**2*b**3*e**5 + 320*a*b**4*d*e**4 + 20*b**5*d**2*e**3) + x**2*(125*a**3*b**2*e**5 + 405*a**2*b**3*d*e**4 + 75*a*b**4*d**2*e**3 - 5*b**5*d**3*e**2) + x*(12*a**4*b*e**5 + 202*a**3*b**2*d*e**4 + 102*a**2*b**3*d**2*e**3 - 18*a*b**4*d**3*e**2 + 2*b**5*d**4*e))/(4*a**10*d**2*e**6 - 24*a**9*b*d**3*e**5 + 60*a**8*b**2*d**4*e**4 - 80*a**7*b**3*d**5*e**3 + 60*a**6*b**4*d**6*e**2 - 24*a**5*b**5*d**7*e + 4*a**4*b**6*d**8 + x**6*(4*a**6*b**4*e**8 - 24*a**5*b**5*d*e**7 + 60*a**4*b**6*d**2*e**6 - 80*a**3*b**7*d**3*e**5 + 60*a**2*b**8*d**4*e**4 - 24*a*b**9*d**5*e**3 + 4*b**10*d**6*e**2) + x**5*(16*a**7*b**3*e**8 - 88*a**6*b**4*d*e**7 + 192*a**5*b**5*d**2*e**6 - 200*a**4*b**6*d**3*e**5 + 80*a**3*b**7*d**4*e**4 + 24*a**2*b**8*d**5*e**3 - 32*a*b**9*d**6*e**2 + 8*b**10*d**7*e) + x**4*(24*a**8*b**2*e**8 - 112*a**7*b**3*d*e**7 + 172*a**6*b**4*d**2*e**6 - 24*a**5*b**5*d**3*e**5 - 220*a**4*b**6*d**4*e**4 + 256*a**3*b**7*d**5*e**3 - 108*a**2*b**8*d**6*e**2 + 8*a*b**9*d**7*e + 4*b**10*d**8) + x**3*(16*a**9*b*e**8 - 48*a**8*b**2*d*e**7 - 32*a**7*b**3*d**2*e**6 + 304*a**6*b**4*d**3*e**5 - 480*a**5*b**5*d**4*e**4 + 304*a**4*b**6*d**5*e**3 - 32*a**3*b**7*d**6*e**2 - 48*a**2*b**8*d**7*e + 16*a*b**9*d**8) + x**2*(4*a**10*e**8 + 8*a**9*b*d*e**7 - 108*a**8*b**2*d**2*e**6 + 256*a**7*b**3*d**3*e**5 - 220*a**6*b**4*d**4*e**4 - 24*a**5*b**5*d**5*e**3 + 172*a**4*b**6*d**6*e**2 - 112*a**3*b**7*d**7*e + 24*a**2*b**8*d**8) + x*(8*a**10*d*e**7 - 32*a**9*b*d**2*e**6 + 24*a**8*b**2*d**3*e**5 + 80*a**7*b**3*d**4*e**4 - 200*a**6*b**4*d**5*e**3 + 192*a**5*b**5*d**6*e**2 - 88*a**4*b**6*d**7*e + 16*a**3*b**7*d**8))","B",0
1953,1,2009,0,7.633052," ","integrate((b*x+a)/(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**3,x)","- \frac{35 b^{3} e^{4} \log{\left(x + \frac{- \frac{35 a^{9} b^{3} e^{13}}{\left(a e - b d\right)^{8}} + \frac{315 a^{8} b^{4} d e^{12}}{\left(a e - b d\right)^{8}} - \frac{1260 a^{7} b^{5} d^{2} e^{11}}{\left(a e - b d\right)^{8}} + \frac{2940 a^{6} b^{6} d^{3} e^{10}}{\left(a e - b d\right)^{8}} - \frac{4410 a^{5} b^{7} d^{4} e^{9}}{\left(a e - b d\right)^{8}} + \frac{4410 a^{4} b^{8} d^{5} e^{8}}{\left(a e - b d\right)^{8}} - \frac{2940 a^{3} b^{9} d^{6} e^{7}}{\left(a e - b d\right)^{8}} + \frac{1260 a^{2} b^{10} d^{7} e^{6}}{\left(a e - b d\right)^{8}} - \frac{315 a b^{11} d^{8} e^{5}}{\left(a e - b d\right)^{8}} + 35 a b^{3} e^{5} + \frac{35 b^{12} d^{9} e^{4}}{\left(a e - b d\right)^{8}} + 35 b^{4} d e^{4}}{70 b^{4} e^{5}} \right)}}{\left(a e - b d\right)^{8}} + \frac{35 b^{3} e^{4} \log{\left(x + \frac{\frac{35 a^{9} b^{3} e^{13}}{\left(a e - b d\right)^{8}} - \frac{315 a^{8} b^{4} d e^{12}}{\left(a e - b d\right)^{8}} + \frac{1260 a^{7} b^{5} d^{2} e^{11}}{\left(a e - b d\right)^{8}} - \frac{2940 a^{6} b^{6} d^{3} e^{10}}{\left(a e - b d\right)^{8}} + \frac{4410 a^{5} b^{7} d^{4} e^{9}}{\left(a e - b d\right)^{8}} - \frac{4410 a^{4} b^{8} d^{5} e^{8}}{\left(a e - b d\right)^{8}} + \frac{2940 a^{3} b^{9} d^{6} e^{7}}{\left(a e - b d\right)^{8}} - \frac{1260 a^{2} b^{10} d^{7} e^{6}}{\left(a e - b d\right)^{8}} + \frac{315 a b^{11} d^{8} e^{5}}{\left(a e - b d\right)^{8}} + 35 a b^{3} e^{5} - \frac{35 b^{12} d^{9} e^{4}}{\left(a e - b d\right)^{8}} + 35 b^{4} d e^{4}}{70 b^{4} e^{5}} \right)}}{\left(a e - b d\right)^{8}} + \frac{- 4 a^{6} e^{6} + 38 a^{5} b d e^{5} - 214 a^{4} b^{2} d^{2} e^{4} - 319 a^{3} b^{3} d^{3} e^{3} + 101 a^{2} b^{4} d^{4} e^{2} - 25 a b^{5} d^{5} e + 3 b^{6} d^{6} - 420 b^{6} e^{6} x^{6} + x^{5} \left(- 1470 a b^{5} e^{6} - 1050 b^{6} d e^{5}\right) + x^{4} \left(- 1820 a^{2} b^{4} e^{6} - 3710 a b^{5} d e^{5} - 770 b^{6} d^{2} e^{4}\right) + x^{3} \left(- 875 a^{3} b^{3} e^{6} - 4655 a^{2} b^{4} d e^{5} - 2765 a b^{5} d^{2} e^{4} - 105 b^{6} d^{3} e^{3}\right) + x^{2} \left(- 84 a^{4} b^{2} e^{6} - 2289 a^{3} b^{3} d e^{5} - 3549 a^{2} b^{4} d^{2} e^{4} - 399 a b^{5} d^{3} e^{3} + 21 b^{6} d^{4} e^{2}\right) + x \left(14 a^{5} b e^{6} - 238 a^{4} b^{2} d e^{5} - 1813 a^{3} b^{3} d^{2} e^{4} - 553 a^{2} b^{4} d^{3} e^{3} + 77 a b^{5} d^{4} e^{2} - 7 b^{6} d^{5} e\right)}{12 a^{11} d^{3} e^{7} - 84 a^{10} b d^{4} e^{6} + 252 a^{9} b^{2} d^{5} e^{5} - 420 a^{8} b^{3} d^{6} e^{4} + 420 a^{7} b^{4} d^{7} e^{3} - 252 a^{6} b^{5} d^{8} e^{2} + 84 a^{5} b^{6} d^{9} e - 12 a^{4} b^{7} d^{10} + x^{7} \left(12 a^{7} b^{4} e^{10} - 84 a^{6} b^{5} d e^{9} + 252 a^{5} b^{6} d^{2} e^{8} - 420 a^{4} b^{7} d^{3} e^{7} + 420 a^{3} b^{8} d^{4} e^{6} - 252 a^{2} b^{9} d^{5} e^{5} + 84 a b^{10} d^{6} e^{4} - 12 b^{11} d^{7} e^{3}\right) + x^{6} \left(48 a^{8} b^{3} e^{10} - 300 a^{7} b^{4} d e^{9} + 756 a^{6} b^{5} d^{2} e^{8} - 924 a^{5} b^{6} d^{3} e^{7} + 420 a^{4} b^{7} d^{4} e^{6} + 252 a^{3} b^{8} d^{5} e^{5} - 420 a^{2} b^{9} d^{6} e^{4} + 204 a b^{10} d^{7} e^{3} - 36 b^{11} d^{8} e^{2}\right) + x^{5} \left(72 a^{9} b^{2} e^{10} - 360 a^{8} b^{3} d e^{9} + 540 a^{7} b^{4} d^{2} e^{8} + 252 a^{6} b^{5} d^{3} e^{7} - 1764 a^{5} b^{6} d^{4} e^{6} + 2268 a^{4} b^{7} d^{5} e^{5} - 1260 a^{3} b^{8} d^{6} e^{4} + 180 a^{2} b^{9} d^{7} e^{3} + 108 a b^{10} d^{8} e^{2} - 36 b^{11} d^{9} e\right) + x^{4} \left(48 a^{10} b e^{10} - 120 a^{9} b^{2} d e^{9} - 360 a^{8} b^{3} d^{2} e^{8} + 1860 a^{7} b^{4} d^{3} e^{7} - 2940 a^{6} b^{5} d^{4} e^{6} + 1764 a^{5} b^{6} d^{5} e^{5} + 420 a^{4} b^{7} d^{6} e^{4} - 1140 a^{3} b^{8} d^{7} e^{3} + 540 a^{2} b^{9} d^{8} e^{2} - 60 a b^{10} d^{9} e - 12 b^{11} d^{10}\right) + x^{3} \left(12 a^{11} e^{10} + 60 a^{10} b d e^{9} - 540 a^{9} b^{2} d^{2} e^{8} + 1140 a^{8} b^{3} d^{3} e^{7} - 420 a^{7} b^{4} d^{4} e^{6} - 1764 a^{6} b^{5} d^{5} e^{5} + 2940 a^{5} b^{6} d^{6} e^{4} - 1860 a^{4} b^{7} d^{7} e^{3} + 360 a^{3} b^{8} d^{8} e^{2} + 120 a^{2} b^{9} d^{9} e - 48 a b^{10} d^{10}\right) + x^{2} \left(36 a^{11} d e^{9} - 108 a^{10} b d^{2} e^{8} - 180 a^{9} b^{2} d^{3} e^{7} + 1260 a^{8} b^{3} d^{4} e^{6} - 2268 a^{7} b^{4} d^{5} e^{5} + 1764 a^{6} b^{5} d^{6} e^{4} - 252 a^{5} b^{6} d^{7} e^{3} - 540 a^{4} b^{7} d^{8} e^{2} + 360 a^{3} b^{8} d^{9} e - 72 a^{2} b^{9} d^{10}\right) + x \left(36 a^{11} d^{2} e^{8} - 204 a^{10} b d^{3} e^{7} + 420 a^{9} b^{2} d^{4} e^{6} - 252 a^{8} b^{3} d^{5} e^{5} - 420 a^{7} b^{4} d^{6} e^{4} + 924 a^{6} b^{5} d^{7} e^{3} - 756 a^{5} b^{6} d^{8} e^{2} + 300 a^{4} b^{7} d^{9} e - 48 a^{3} b^{8} d^{10}\right)}"," ",0,"-35*b**3*e**4*log(x + (-35*a**9*b**3*e**13/(a*e - b*d)**8 + 315*a**8*b**4*d*e**12/(a*e - b*d)**8 - 1260*a**7*b**5*d**2*e**11/(a*e - b*d)**8 + 2940*a**6*b**6*d**3*e**10/(a*e - b*d)**8 - 4410*a**5*b**7*d**4*e**9/(a*e - b*d)**8 + 4410*a**4*b**8*d**5*e**8/(a*e - b*d)**8 - 2940*a**3*b**9*d**6*e**7/(a*e - b*d)**8 + 1260*a**2*b**10*d**7*e**6/(a*e - b*d)**8 - 315*a*b**11*d**8*e**5/(a*e - b*d)**8 + 35*a*b**3*e**5 + 35*b**12*d**9*e**4/(a*e - b*d)**8 + 35*b**4*d*e**4)/(70*b**4*e**5))/(a*e - b*d)**8 + 35*b**3*e**4*log(x + (35*a**9*b**3*e**13/(a*e - b*d)**8 - 315*a**8*b**4*d*e**12/(a*e - b*d)**8 + 1260*a**7*b**5*d**2*e**11/(a*e - b*d)**8 - 2940*a**6*b**6*d**3*e**10/(a*e - b*d)**8 + 4410*a**5*b**7*d**4*e**9/(a*e - b*d)**8 - 4410*a**4*b**8*d**5*e**8/(a*e - b*d)**8 + 2940*a**3*b**9*d**6*e**7/(a*e - b*d)**8 - 1260*a**2*b**10*d**7*e**6/(a*e - b*d)**8 + 315*a*b**11*d**8*e**5/(a*e - b*d)**8 + 35*a*b**3*e**5 - 35*b**12*d**9*e**4/(a*e - b*d)**8 + 35*b**4*d*e**4)/(70*b**4*e**5))/(a*e - b*d)**8 + (-4*a**6*e**6 + 38*a**5*b*d*e**5 - 214*a**4*b**2*d**2*e**4 - 319*a**3*b**3*d**3*e**3 + 101*a**2*b**4*d**4*e**2 - 25*a*b**5*d**5*e + 3*b**6*d**6 - 420*b**6*e**6*x**6 + x**5*(-1470*a*b**5*e**6 - 1050*b**6*d*e**5) + x**4*(-1820*a**2*b**4*e**6 - 3710*a*b**5*d*e**5 - 770*b**6*d**2*e**4) + x**3*(-875*a**3*b**3*e**6 - 4655*a**2*b**4*d*e**5 - 2765*a*b**5*d**2*e**4 - 105*b**6*d**3*e**3) + x**2*(-84*a**4*b**2*e**6 - 2289*a**3*b**3*d*e**5 - 3549*a**2*b**4*d**2*e**4 - 399*a*b**5*d**3*e**3 + 21*b**6*d**4*e**2) + x*(14*a**5*b*e**6 - 238*a**4*b**2*d*e**5 - 1813*a**3*b**3*d**2*e**4 - 553*a**2*b**4*d**3*e**3 + 77*a*b**5*d**4*e**2 - 7*b**6*d**5*e))/(12*a**11*d**3*e**7 - 84*a**10*b*d**4*e**6 + 252*a**9*b**2*d**5*e**5 - 420*a**8*b**3*d**6*e**4 + 420*a**7*b**4*d**7*e**3 - 252*a**6*b**5*d**8*e**2 + 84*a**5*b**6*d**9*e - 12*a**4*b**7*d**10 + x**7*(12*a**7*b**4*e**10 - 84*a**6*b**5*d*e**9 + 252*a**5*b**6*d**2*e**8 - 420*a**4*b**7*d**3*e**7 + 420*a**3*b**8*d**4*e**6 - 252*a**2*b**9*d**5*e**5 + 84*a*b**10*d**6*e**4 - 12*b**11*d**7*e**3) + x**6*(48*a**8*b**3*e**10 - 300*a**7*b**4*d*e**9 + 756*a**6*b**5*d**2*e**8 - 924*a**5*b**6*d**3*e**7 + 420*a**4*b**7*d**4*e**6 + 252*a**3*b**8*d**5*e**5 - 420*a**2*b**9*d**6*e**4 + 204*a*b**10*d**7*e**3 - 36*b**11*d**8*e**2) + x**5*(72*a**9*b**2*e**10 - 360*a**8*b**3*d*e**9 + 540*a**7*b**4*d**2*e**8 + 252*a**6*b**5*d**3*e**7 - 1764*a**5*b**6*d**4*e**6 + 2268*a**4*b**7*d**5*e**5 - 1260*a**3*b**8*d**6*e**4 + 180*a**2*b**9*d**7*e**3 + 108*a*b**10*d**8*e**2 - 36*b**11*d**9*e) + x**4*(48*a**10*b*e**10 - 120*a**9*b**2*d*e**9 - 360*a**8*b**3*d**2*e**8 + 1860*a**7*b**4*d**3*e**7 - 2940*a**6*b**5*d**4*e**6 + 1764*a**5*b**6*d**5*e**5 + 420*a**4*b**7*d**6*e**4 - 1140*a**3*b**8*d**7*e**3 + 540*a**2*b**9*d**8*e**2 - 60*a*b**10*d**9*e - 12*b**11*d**10) + x**3*(12*a**11*e**10 + 60*a**10*b*d*e**9 - 540*a**9*b**2*d**2*e**8 + 1140*a**8*b**3*d**3*e**7 - 420*a**7*b**4*d**4*e**6 - 1764*a**6*b**5*d**5*e**5 + 2940*a**5*b**6*d**6*e**4 - 1860*a**4*b**7*d**7*e**3 + 360*a**3*b**8*d**8*e**2 + 120*a**2*b**9*d**9*e - 48*a*b**10*d**10) + x**2*(36*a**11*d*e**9 - 108*a**10*b*d**2*e**8 - 180*a**9*b**2*d**3*e**7 + 1260*a**8*b**3*d**4*e**6 - 2268*a**7*b**4*d**5*e**5 + 1764*a**6*b**5*d**6*e**4 - 252*a**5*b**6*d**7*e**3 - 540*a**4*b**7*d**8*e**2 + 360*a**3*b**8*d**9*e - 72*a**2*b**9*d**10) + x*(36*a**11*d**2*e**8 - 204*a**10*b*d**3*e**7 + 420*a**9*b**2*d**4*e**6 - 252*a**8*b**3*d**5*e**5 - 420*a**7*b**4*d**6*e**4 + 924*a**6*b**5*d**7*e**3 - 756*a**5*b**6*d**8*e**2 + 300*a**4*b**7*d**9*e - 48*a**3*b**8*d**10))","B",0
1954,1,218,0,0.164676," ","integrate((b*x+a)*(e*x+d)**5*((b*x+a)**2)**(1/2),x)","a^{2} d^{5} x + \frac{b^{2} e^{5} x^{8}}{8} + x^{7} \left(\frac{2 a b e^{5}}{7} + \frac{5 b^{2} d e^{4}}{7}\right) + x^{6} \left(\frac{a^{2} e^{5}}{6} + \frac{5 a b d e^{4}}{3} + \frac{5 b^{2} d^{2} e^{3}}{3}\right) + x^{5} \left(a^{2} d e^{4} + 4 a b d^{2} e^{3} + 2 b^{2} d^{3} e^{2}\right) + x^{4} \left(\frac{5 a^{2} d^{2} e^{3}}{2} + 5 a b d^{3} e^{2} + \frac{5 b^{2} d^{4} e}{4}\right) + x^{3} \left(\frac{10 a^{2} d^{3} e^{2}}{3} + \frac{10 a b d^{4} e}{3} + \frac{b^{2} d^{5}}{3}\right) + x^{2} \left(\frac{5 a^{2} d^{4} e}{2} + a b d^{5}\right)"," ",0,"a**2*d**5*x + b**2*e**5*x**8/8 + x**7*(2*a*b*e**5/7 + 5*b**2*d*e**4/7) + x**6*(a**2*e**5/6 + 5*a*b*d*e**4/3 + 5*b**2*d**2*e**3/3) + x**5*(a**2*d*e**4 + 4*a*b*d**2*e**3 + 2*b**2*d**3*e**2) + x**4*(5*a**2*d**2*e**3/2 + 5*a*b*d**3*e**2 + 5*b**2*d**4*e/4) + x**3*(10*a**2*d**3*e**2/3 + 10*a*b*d**4*e/3 + b**2*d**5/3) + x**2*(5*a**2*d**4*e/2 + a*b*d**5)","B",0
1955,1,168,0,0.164782," ","integrate((b*x+a)*(e*x+d)**4*((b*x+a)**2)**(1/2),x)","a^{2} d^{4} x + \frac{b^{2} e^{4} x^{7}}{7} + x^{6} \left(\frac{a b e^{4}}{3} + \frac{2 b^{2} d e^{3}}{3}\right) + x^{5} \left(\frac{a^{2} e^{4}}{5} + \frac{8 a b d e^{3}}{5} + \frac{6 b^{2} d^{2} e^{2}}{5}\right) + x^{4} \left(a^{2} d e^{3} + 3 a b d^{2} e^{2} + b^{2} d^{3} e\right) + x^{3} \left(2 a^{2} d^{2} e^{2} + \frac{8 a b d^{3} e}{3} + \frac{b^{2} d^{4}}{3}\right) + x^{2} \left(2 a^{2} d^{3} e + a b d^{4}\right)"," ",0,"a**2*d**4*x + b**2*e**4*x**7/7 + x**6*(a*b*e**4/3 + 2*b**2*d*e**3/3) + x**5*(a**2*e**4/5 + 8*a*b*d*e**3/5 + 6*b**2*d**2*e**2/5) + x**4*(a**2*d*e**3 + 3*a*b*d**2*e**2 + b**2*d**3*e) + x**3*(2*a**2*d**2*e**2 + 8*a*b*d**3*e/3 + b**2*d**4/3) + x**2*(2*a**2*d**3*e + a*b*d**4)","A",0
1956,1,133,0,0.134072," ","integrate((b*x+a)*(e*x+d)**3*((b*x+a)**2)**(1/2),x)","a^{2} d^{3} x + \frac{b^{2} e^{3} x^{6}}{6} + x^{5} \left(\frac{2 a b e^{3}}{5} + \frac{3 b^{2} d e^{2}}{5}\right) + x^{4} \left(\frac{a^{2} e^{3}}{4} + \frac{3 a b d e^{2}}{2} + \frac{3 b^{2} d^{2} e}{4}\right) + x^{3} \left(a^{2} d e^{2} + 2 a b d^{2} e + \frac{b^{2} d^{3}}{3}\right) + x^{2} \left(\frac{3 a^{2} d^{2} e}{2} + a b d^{3}\right)"," ",0,"a**2*d**3*x + b**2*e**3*x**6/6 + x**5*(2*a*b*e**3/5 + 3*b**2*d*e**2/5) + x**4*(a**2*e**3/4 + 3*a*b*d*e**2/2 + 3*b**2*d**2*e/4) + x**3*(a**2*d*e**2 + 2*a*b*d**2*e + b**2*d**3/3) + x**2*(3*a**2*d**2*e/2 + a*b*d**3)","A",0
1957,1,87,0,0.124072," ","integrate((b*x+a)*(e*x+d)**2*((b*x+a)**2)**(1/2),x)","a^{2} d^{2} x + \frac{b^{2} e^{2} x^{5}}{5} + x^{4} \left(\frac{a b e^{2}}{2} + \frac{b^{2} d e}{2}\right) + x^{3} \left(\frac{a^{2} e^{2}}{3} + \frac{4 a b d e}{3} + \frac{b^{2} d^{2}}{3}\right) + x^{2} \left(a^{2} d e + a b d^{2}\right)"," ",0,"a**2*d**2*x + b**2*e**2*x**5/5 + x**4*(a*b*e**2/2 + b**2*d*e/2) + x**3*(a**2*e**2/3 + 4*a*b*d*e/3 + b**2*d**2/3) + x**2*(a**2*d*e + a*b*d**2)","A",0
1958,1,49,0,0.107719," ","integrate((b*x+a)*(e*x+d)*((b*x+a)**2)**(1/2),x)","a^{2} d x + \frac{b^{2} e x^{4}}{4} + x^{3} \left(\frac{2 a b e}{3} + \frac{b^{2} d}{3}\right) + x^{2} \left(\frac{a^{2} e}{2} + a b d\right)"," ",0,"a**2*d*x + b**2*e*x**4/4 + x**3*(2*a*b*e/3 + b**2*d/3) + x**2*(a**2*e/2 + a*b*d)","A",0
1959,1,19,0,0.088040," ","integrate((b*x+a)*((b*x+a)**2)**(1/2),x)","a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}"," ",0,"a**2*x + a*b*x**2 + b**2*x**3/3","A",0
1960,1,44,0,0.244702," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d),x)","\frac{b^{2} x^{2}}{2 e} + x \left(\frac{2 a b}{e} - \frac{b^{2} d}{e^{2}}\right) + \frac{\left(a e - b d\right)^{2} \log{\left(d + e x \right)}}{e^{3}}"," ",0,"b**2*x**2/(2*e) + x*(2*a*b/e - b**2*d/e**2) + (a*e - b*d)**2*log(d + e*x)/e**3","A",0
1961,1,60,0,0.365962," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**2,x)","\frac{b^{2} x}{e^{2}} + \frac{2 b \left(a e - b d\right) \log{\left(d + e x \right)}}{e^{3}} + \frac{- a^{2} e^{2} + 2 a b d e - b^{2} d^{2}}{d e^{3} + e^{4} x}"," ",0,"b**2*x/e**2 + 2*b*(a*e - b*d)*log(d + e*x)/e**3 + (-a**2*e**2 + 2*a*b*d*e - b**2*d**2)/(d*e**3 + e**4*x)","A",0
1962,1,80,0,0.478353," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**3,x)","\frac{b^{2} \log{\left(d + e x \right)}}{e^{3}} + \frac{- a^{2} e^{2} - 2 a b d e + 3 b^{2} d^{2} + x \left(- 4 a b e^{2} + 4 b^{2} d e\right)}{2 d^{2} e^{3} + 4 d e^{4} x + 2 e^{5} x^{2}}"," ",0,"b**2*log(d + e*x)/e**3 + (-a**2*e**2 - 2*a*b*d*e + 3*b**2*d**2 + x*(-4*a*b*e**2 + 4*b**2*d*e))/(2*d**2*e**3 + 4*d*e**4*x + 2*e**5*x**2)","A",0
1963,1,88,0,0.653631," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**4,x)","\frac{- a^{2} e^{2} - a b d e - b^{2} d^{2} - 3 b^{2} e^{2} x^{2} + x \left(- 3 a b e^{2} - 3 b^{2} d e\right)}{3 d^{3} e^{3} + 9 d^{2} e^{4} x + 9 d e^{5} x^{2} + 3 e^{6} x^{3}}"," ",0,"(-a**2*e**2 - a*b*d*e - b**2*d**2 - 3*b**2*e**2*x**2 + x*(-3*a*b*e**2 - 3*b**2*d*e))/(3*d**3*e**3 + 9*d**2*e**4*x + 9*d*e**5*x**2 + 3*e**6*x**3)","B",0
1964,1,104,0,0.987737," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**5,x)","\frac{- 3 a^{2} e^{2} - 2 a b d e - b^{2} d^{2} - 6 b^{2} e^{2} x^{2} + x \left(- 8 a b e^{2} - 4 b^{2} d e\right)}{12 d^{4} e^{3} + 48 d^{3} e^{4} x + 72 d^{2} e^{5} x^{2} + 48 d e^{6} x^{3} + 12 e^{7} x^{4}}"," ",0,"(-3*a**2*e**2 - 2*a*b*d*e - b**2*d**2 - 6*b**2*e**2*x**2 + x*(-8*a*b*e**2 - 4*b**2*d*e))/(12*d**4*e**3 + 48*d**3*e**4*x + 72*d**2*e**5*x**2 + 48*d*e**6*x**3 + 12*e**7*x**4)","A",0
1965,1,116,0,1.019377," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**6,x)","\frac{- 6 a^{2} e^{2} - 3 a b d e - b^{2} d^{2} - 10 b^{2} e^{2} x^{2} + x \left(- 15 a b e^{2} - 5 b^{2} d e\right)}{30 d^{5} e^{3} + 150 d^{4} e^{4} x + 300 d^{3} e^{5} x^{2} + 300 d^{2} e^{6} x^{3} + 150 d e^{7} x^{4} + 30 e^{8} x^{5}}"," ",0,"(-6*a**2*e**2 - 3*a*b*d*e - b**2*d**2 - 10*b**2*e**2*x**2 + x*(-15*a*b*e**2 - 5*b**2*d*e))/(30*d**5*e**3 + 150*d**4*e**4*x + 300*d**3*e**5*x**2 + 300*d**2*e**6*x**3 + 150*d*e**7*x**4 + 30*e**8*x**5)","A",0
1966,1,128,0,1.219903," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**7,x)","\frac{- 10 a^{2} e^{2} - 4 a b d e - b^{2} d^{2} - 15 b^{2} e^{2} x^{2} + x \left(- 24 a b e^{2} - 6 b^{2} d e\right)}{60 d^{6} e^{3} + 360 d^{5} e^{4} x + 900 d^{4} e^{5} x^{2} + 1200 d^{3} e^{6} x^{3} + 900 d^{2} e^{7} x^{4} + 360 d e^{8} x^{5} + 60 e^{9} x^{6}}"," ",0,"(-10*a**2*e**2 - 4*a*b*d*e - b**2*d**2 - 15*b**2*e**2*x**2 + x*(-24*a*b*e**2 - 6*b**2*d*e))/(60*d**6*e**3 + 360*d**5*e**4*x + 900*d**4*e**5*x**2 + 1200*d**3*e**6*x**3 + 900*d**2*e**7*x**4 + 360*d*e**8*x**5 + 60*e**9*x**6)","A",0
1967,1,139,0,1.427047," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**8,x)","\frac{- 15 a^{2} e^{2} - 5 a b d e - b^{2} d^{2} - 21 b^{2} e^{2} x^{2} + x \left(- 35 a b e^{2} - 7 b^{2} d e\right)}{105 d^{7} e^{3} + 735 d^{6} e^{4} x + 2205 d^{5} e^{5} x^{2} + 3675 d^{4} e^{6} x^{3} + 3675 d^{3} e^{7} x^{4} + 2205 d^{2} e^{8} x^{5} + 735 d e^{9} x^{6} + 105 e^{10} x^{7}}"," ",0,"(-15*a**2*e**2 - 5*a*b*d*e - b**2*d**2 - 21*b**2*e**2*x**2 + x*(-35*a*b*e**2 - 7*b**2*d*e))/(105*d**7*e**3 + 735*d**6*e**4*x + 2205*d**5*e**5*x**2 + 3675*d**4*e**6*x**3 + 3675*d**3*e**7*x**4 + 2205*d**2*e**8*x**5 + 735*d*e**9*x**6 + 105*e**10*x**7)","A",0
1968,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**7*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{7} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**7*((a + b*x)**2)**(3/2), x)","F",0
1969,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{6} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**6*((a + b*x)**2)**(3/2), x)","F",0
1970,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**5*((a + b*x)**2)**(3/2), x)","F",0
1971,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**4*((a + b*x)**2)**(3/2), x)","F",0
1972,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**3*((a + b*x)**2)**(3/2), x)","F",0
1973,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**2*((a + b*x)**2)**(3/2), x)","F",0
1974,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)*((a + b*x)**2)**(3/2), x)","F",0
1975,1,158,0,0.927866," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\begin{cases} \frac{a^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{5 b} + \frac{4 a^{3} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{5} + \frac{6 a^{2} b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{5} + \frac{4 a b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{5} + \frac{b^{3} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{5} & \text{for}\: b \neq 0 \\a x \left(a^{2}\right)^{\frac{3}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sqrt(a**2 + 2*a*b*x + b**2*x**2)/(5*b) + 4*a**3*x*sqrt(a**2 + 2*a*b*x + b**2*x**2)/5 + 6*a**2*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2)/5 + 4*a*b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2)/5 + b**3*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2)/5, Ne(b, 0)), (a*x*(a**2)**(3/2), True))","A",0
1976,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d),x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x), x)","F",0
1977,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**2, x)","F",0
1978,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**3, x)","F",0
1979,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**4, x)","F",0
1980,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**5, x)","F",0
1981,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**6, x)","F",0
1982,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**7, x)","F",0
1983,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**8,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**8, x)","F",0
1984,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1985,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1986,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1987,-2,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**12,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1988,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**9*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{9} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**9*((a + b*x)**2)**(5/2), x)","F",0
1989,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**8*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{8} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**8*((a + b*x)**2)**(5/2), x)","F",0
1990,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**7*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{7} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**7*((a + b*x)**2)**(5/2), x)","F",0
1991,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{6} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**6*((a + b*x)**2)**(5/2), x)","F",0
1992,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**5*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{5} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**5*((a + b*x)**2)**(5/2), x)","F",0
1993,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{4} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**4*((a + b*x)**2)**(5/2), x)","F",0
1994,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**3*((a + b*x)**2)**(5/2), x)","F",0
1995,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**2*((a + b*x)**2)**(5/2), x)","F",0
1996,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \left(a + b x\right) \left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)*((a + b*x)**2)**(5/2), x)","F",0
1997,1,226,0,5.515319," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\begin{cases} \frac{a^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7 b} + \frac{6 a^{5} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7} + \frac{15 a^{4} b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7} + \frac{20 a^{3} b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7} + \frac{15 a^{2} b^{3} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7} + \frac{6 a b^{4} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7} + \frac{b^{5} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}}{7} & \text{for}\: b \neq 0 \\a x \left(a^{2}\right)^{\frac{5}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*sqrt(a**2 + 2*a*b*x + b**2*x**2)/(7*b) + 6*a**5*x*sqrt(a**2 + 2*a*b*x + b**2*x**2)/7 + 15*a**4*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2)/7 + 20*a**3*b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2)/7 + 15*a**2*b**3*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2)/7 + 6*a*b**4*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2)/7 + b**5*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2)/7, Ne(b, 0)), (a*x*(a**2)**(5/2), True))","A",0
1998,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d),x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(5/2)/(d + e*x), x)","F",0
1999,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(5/2)/(d + e*x)**2, x)","F",0
2000,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(5/2)/(d + e*x)**3, x)","F",0
2001,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(5/2)/(d + e*x)**4, x)","F",0
2002,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(5/2)/(d + e*x)**5, x)","F",0
2003,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(5/2)/(d + e*x)**6, x)","F",0
2004,-2,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**7,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2005,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2006,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2007,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2008,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2009,-2,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2010,-2,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**13,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2011,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**14,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2012,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**15,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2013,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**16,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2014,-2,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**17,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2015,1,42,0,0.122485," ","integrate((b*x+a)*(e*x+d)**4/((b*x+a)**2)**(1/2),x)","d^{4} x + 2 d^{3} e x^{2} + 2 d^{2} e^{2} x^{3} + d e^{3} x^{4} + \frac{e^{4} x^{5}}{5}"," ",0,"d**4*x + 2*d**3*e*x**2 + 2*d**2*e**2*x**3 + d*e**3*x**4 + e**4*x**5/5","A",0
2016,1,32,0,0.110599," ","integrate((b*x+a)*(e*x+d)**3/((b*x+a)**2)**(1/2),x)","d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}"," ",0,"d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4","A",0
2017,1,19,0,0.103207," ","integrate((b*x+a)*(e*x+d)**2/((b*x+a)**2)**(1/2),x)","d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}"," ",0,"d**2*x + d*e*x**2 + e**2*x**3/3","A",0
2018,1,8,0,0.094840," ","integrate((b*x+a)*(e*x+d)/((b*x+a)**2)**(1/2),x)","d x + \frac{e x^{2}}{2}"," ",0,"d*x + e*x**2/2","A",0
2019,1,0,0,0.084125," ","integrate((b*x+a)/((b*x+a)**2)**(1/2),x)","x"," ",0,"x","A",0
2020,1,7,0,0.099339," ","integrate((b*x+a)/(e*x+d)/((b*x+a)**2)**(1/2),x)","\frac{\log{\left(d + e x \right)}}{e}"," ",0,"log(d + e*x)/e","A",0
2021,1,10,0,0.165360," ","integrate((b*x+a)/(e*x+d)**2/((b*x+a)**2)**(1/2),x)","- \frac{1}{d e + e^{2} x}"," ",0,"-1/(d*e + e**2*x)","A",0
2022,1,26,0,0.224351," ","integrate((b*x+a)/(e*x+d)**3/((b*x+a)**2)**(1/2),x)","- \frac{1}{2 d^{2} e + 4 d e^{2} x + 2 e^{3} x^{2}}"," ",0,"-1/(2*d**2*e + 4*d*e**2*x + 2*e**3*x**2)","A",0
2023,1,37,0,0.282677," ","integrate((b*x+a)/(e*x+d)**4/((b*x+a)**2)**(1/2),x)","- \frac{1}{3 d^{3} e + 9 d^{2} e^{2} x + 9 d e^{3} x^{2} + 3 e^{4} x^{3}}"," ",0,"-1/(3*d**3*e + 9*d**2*e**2*x + 9*d*e**3*x**2 + 3*e**4*x**3)","A",0
2024,1,49,0,0.342694," ","integrate((b*x+a)/(e*x+d)**5/((b*x+a)**2)**(1/2),x)","- \frac{1}{4 d^{4} e + 16 d^{3} e^{2} x + 24 d^{2} e^{3} x^{2} + 16 d e^{4} x^{3} + 4 e^{5} x^{4}}"," ",0,"-1/(4*d**4*e + 16*d**3*e**2*x + 24*d**2*e**3*x**2 + 16*d*e**4*x**3 + 4*e**5*x**4)","A",0
2025,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**4/((a + b*x)**2)**(3/2), x)","F",0
2026,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**3/((a + b*x)**2)**(3/2), x)","F",0
2027,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**2/((a + b*x)**2)**(3/2), x)","F",0
2028,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)/((a + b*x)**2)**(3/2), x)","F",0
2029,1,34,0,0.845983," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\begin{cases} - \frac{1}{b \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}} & \text{for}\: b \neq 0 \\\frac{a x}{\left(a^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(b*sqrt(a**2 + 2*a*b*x + b**2*x**2)), Ne(b, 0)), (a*x/(a**2)**(3/2), True))","A",0
2030,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{a + b x}{\left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)*((a + b*x)**2)**(3/2)), x)","F",0
2031,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{a + b x}{\left(d + e x\right)^{2} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)**2*((a + b*x)**2)**(3/2)), x)","F",0
2032,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{a + b x}{\left(d + e x\right)^{3} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)**3*((a + b*x)**2)**(3/2)), x)","F",0
2033,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**5/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{5}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**5/((a + b*x)**2)**(5/2), x)","F",0
2034,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**4/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{4}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**4/((a + b*x)**2)**(5/2), x)","F",0
2035,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**3/((a + b*x)**2)**(5/2), x)","F",0
2036,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**2/((a + b*x)**2)**(5/2), x)","F",0
2037,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)/((a + b*x)**2)**(5/2), x)","F",0
2038,1,97,0,1.567766," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\begin{cases} - \frac{1}{3 a^{2} b \sqrt{a^{2} + 2 a b x + b^{2} x^{2}} + 6 a b^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2}} + 3 b^{3} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}} & \text{for}\: b \neq 0 \\\frac{a x}{\left(a^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(3*a**2*b*sqrt(a**2 + 2*a*b*x + b**2*x**2) + 6*a*b**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2) + 3*b**3*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2)), Ne(b, 0)), (a*x/(a**2)**(5/2), True))","A",0
2039,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\int \frac{a + b x}{\left(d + e x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)*((a + b*x)**2)**(5/2)), x)","F",0
2040,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**2/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2041,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**3/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2042,1,654,0,9.575039," ","integrate((b*x+a)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \frac{2 a^{3} d^{4} \sqrt{d + e x}}{9 e} + \frac{8 a^{3} d^{3} x \sqrt{d + e x}}{9} + \frac{4 a^{3} d^{2} e x^{2} \sqrt{d + e x}}{3} + \frac{8 a^{3} d e^{2} x^{3} \sqrt{d + e x}}{9} + \frac{2 a^{3} e^{3} x^{4} \sqrt{d + e x}}{9} - \frac{4 a^{2} b d^{5} \sqrt{d + e x}}{33 e^{2}} + \frac{2 a^{2} b d^{4} x \sqrt{d + e x}}{33 e} + \frac{16 a^{2} b d^{3} x^{2} \sqrt{d + e x}}{11} + \frac{92 a^{2} b d^{2} e x^{3} \sqrt{d + e x}}{33} + \frac{68 a^{2} b d e^{2} x^{4} \sqrt{d + e x}}{33} + \frac{6 a^{2} b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{16 a b^{2} d^{6} \sqrt{d + e x}}{429 e^{3}} - \frac{8 a b^{2} d^{5} x \sqrt{d + e x}}{429 e^{2}} + \frac{2 a b^{2} d^{4} x^{2} \sqrt{d + e x}}{143 e} + \frac{424 a b^{2} d^{3} x^{3} \sqrt{d + e x}}{429} + \frac{916 a b^{2} d^{2} e x^{4} \sqrt{d + e x}}{429} + \frac{240 a b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{6 a b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{32 b^{3} d^{7} \sqrt{d + e x}}{6435 e^{4}} + \frac{16 b^{3} d^{6} x \sqrt{d + e x}}{6435 e^{3}} - \frac{4 b^{3} d^{5} x^{2} \sqrt{d + e x}}{2145 e^{2}} + \frac{2 b^{3} d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{320 b^{3} d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{412 b^{3} d^{2} e x^{5} \sqrt{d + e x}}{715} + \frac{92 b^{3} d e^{2} x^{6} \sqrt{d + e x}}{195} + \frac{2 b^{3} e^{3} x^{7} \sqrt{d + e x}}{15} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*d**4*sqrt(d + e*x)/(9*e) + 8*a**3*d**3*x*sqrt(d + e*x)/9 + 4*a**3*d**2*e*x**2*sqrt(d + e*x)/3 + 8*a**3*d*e**2*x**3*sqrt(d + e*x)/9 + 2*a**3*e**3*x**4*sqrt(d + e*x)/9 - 4*a**2*b*d**5*sqrt(d + e*x)/(33*e**2) + 2*a**2*b*d**4*x*sqrt(d + e*x)/(33*e) + 16*a**2*b*d**3*x**2*sqrt(d + e*x)/11 + 92*a**2*b*d**2*e*x**3*sqrt(d + e*x)/33 + 68*a**2*b*d*e**2*x**4*sqrt(d + e*x)/33 + 6*a**2*b*e**3*x**5*sqrt(d + e*x)/11 + 16*a*b**2*d**6*sqrt(d + e*x)/(429*e**3) - 8*a*b**2*d**5*x*sqrt(d + e*x)/(429*e**2) + 2*a*b**2*d**4*x**2*sqrt(d + e*x)/(143*e) + 424*a*b**2*d**3*x**3*sqrt(d + e*x)/429 + 916*a*b**2*d**2*e*x**4*sqrt(d + e*x)/429 + 240*a*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 6*a*b**2*e**3*x**6*sqrt(d + e*x)/13 - 32*b**3*d**7*sqrt(d + e*x)/(6435*e**4) + 16*b**3*d**6*x*sqrt(d + e*x)/(6435*e**3) - 4*b**3*d**5*x**2*sqrt(d + e*x)/(2145*e**2) + 2*b**3*d**4*x**3*sqrt(d + e*x)/(1287*e) + 320*b**3*d**3*x**4*sqrt(d + e*x)/1287 + 412*b**3*d**2*e*x**5*sqrt(d + e*x)/715 + 92*b**3*d*e**2*x**6*sqrt(d + e*x)/195 + 2*b**3*e**3*x**7*sqrt(d + e*x)/15, Ne(e, 0)), (d**(7/2)*(a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4), True))","A",0
2043,1,549,0,4.585526," ","integrate((b*x+a)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} \frac{2 a^{3} d^{3} \sqrt{d + e x}}{7 e} + \frac{6 a^{3} d^{2} x \sqrt{d + e x}}{7} + \frac{6 a^{3} d e x^{2} \sqrt{d + e x}}{7} + \frac{2 a^{3} e^{2} x^{3} \sqrt{d + e x}}{7} - \frac{4 a^{2} b d^{4} \sqrt{d + e x}}{21 e^{2}} + \frac{2 a^{2} b d^{3} x \sqrt{d + e x}}{21 e} + \frac{10 a^{2} b d^{2} x^{2} \sqrt{d + e x}}{7} + \frac{38 a^{2} b d e x^{3} \sqrt{d + e x}}{21} + \frac{2 a^{2} b e^{2} x^{4} \sqrt{d + e x}}{3} + \frac{16 a b^{2} d^{5} \sqrt{d + e x}}{231 e^{3}} - \frac{8 a b^{2} d^{4} x \sqrt{d + e x}}{231 e^{2}} + \frac{2 a b^{2} d^{3} x^{2} \sqrt{d + e x}}{77 e} + \frac{226 a b^{2} d^{2} x^{3} \sqrt{d + e x}}{231} + \frac{46 a b^{2} d e x^{4} \sqrt{d + e x}}{33} + \frac{6 a b^{2} e^{2} x^{5} \sqrt{d + e x}}{11} - \frac{32 b^{3} d^{6} \sqrt{d + e x}}{3003 e^{4}} + \frac{16 b^{3} d^{5} x \sqrt{d + e x}}{3003 e^{3}} - \frac{4 b^{3} d^{4} x^{2} \sqrt{d + e x}}{1001 e^{2}} + \frac{10 b^{3} d^{3} x^{3} \sqrt{d + e x}}{3003 e} + \frac{106 b^{3} d^{2} x^{4} \sqrt{d + e x}}{429} + \frac{54 b^{3} d e x^{5} \sqrt{d + e x}}{143} + \frac{2 b^{3} e^{2} x^{6} \sqrt{d + e x}}{13} & \text{for}\: e \neq 0 \\d^{\frac{5}{2}} \left(a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*d**3*sqrt(d + e*x)/(7*e) + 6*a**3*d**2*x*sqrt(d + e*x)/7 + 6*a**3*d*e*x**2*sqrt(d + e*x)/7 + 2*a**3*e**2*x**3*sqrt(d + e*x)/7 - 4*a**2*b*d**4*sqrt(d + e*x)/(21*e**2) + 2*a**2*b*d**3*x*sqrt(d + e*x)/(21*e) + 10*a**2*b*d**2*x**2*sqrt(d + e*x)/7 + 38*a**2*b*d*e*x**3*sqrt(d + e*x)/21 + 2*a**2*b*e**2*x**4*sqrt(d + e*x)/3 + 16*a*b**2*d**5*sqrt(d + e*x)/(231*e**3) - 8*a*b**2*d**4*x*sqrt(d + e*x)/(231*e**2) + 2*a*b**2*d**3*x**2*sqrt(d + e*x)/(77*e) + 226*a*b**2*d**2*x**3*sqrt(d + e*x)/231 + 46*a*b**2*d*e*x**4*sqrt(d + e*x)/33 + 6*a*b**2*e**2*x**5*sqrt(d + e*x)/11 - 32*b**3*d**6*sqrt(d + e*x)/(3003*e**4) + 16*b**3*d**5*x*sqrt(d + e*x)/(3003*e**3) - 4*b**3*d**4*x**2*sqrt(d + e*x)/(1001*e**2) + 10*b**3*d**3*x**3*sqrt(d + e*x)/(3003*e) + 106*b**3*d**2*x**4*sqrt(d + e*x)/429 + 54*b**3*d*e*x**5*sqrt(d + e*x)/143 + 2*b**3*e**2*x**6*sqrt(d + e*x)/13, Ne(e, 0)), (d**(5/2)*(a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4), True))","A",0
2044,1,386,0,16.766797," ","integrate((b*x+a)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2),x)","a^{3} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{6 a^{2} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{6 a^{2} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{6 a b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{6 a b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}}"," ",0,"a**3*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*a**2*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 6*a**2*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*a*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 6*a*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4","A",0
2045,1,146,0,4.576398," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{b^{3} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{3}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(3 a b^{2} e - 3 b^{3} d\right)}{7 e^{3}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(3 a^{2} b e^{2} - 6 a b^{2} d e + 3 b^{3} d^{2}\right)}{5 e^{3}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{3} e^{3} - 3 a^{2} b d e^{2} + 3 a b^{2} d^{2} e - b^{3} d^{3}\right)}{3 e^{3}}\right)}{e}"," ",0,"2*(b**3*(d + e*x)**(9/2)/(9*e**3) + (d + e*x)**(7/2)*(3*a*b**2*e - 3*b**3*d)/(7*e**3) + (d + e*x)**(5/2)*(3*a**2*b*e**2 - 6*a*b**2*d*e + 3*b**3*d**2)/(5*e**3) + (d + e*x)**(3/2)*(a**3*e**3 - 3*a**2*b*d*e**2 + 3*a*b**2*d**2*e - b**3*d**3)/(3*e**3))/e","A",0
2046,1,394,0,38.313618," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{3} d}{\sqrt{d + e x}} - 2 a^{3} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{6 a^{2} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{6 a^{2} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{6 a b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{6 a b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{2 b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{2 b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}}}{e} & \text{for}\: e \neq 0 \\\frac{\begin{cases} a^{3} x & \text{for}\: b = 0 \\\frac{a^{3} b x + \frac{3 a^{2} b^{2} x^{2}}{2} + a b^{3} x^{3} + \frac{b^{4} x^{4}}{4}}{b} & \text{otherwise} \end{cases}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**3*d/sqrt(d + e*x) - 2*a**3*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 6*a**2*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 6*a**2*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 6*a*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 6*a*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 2*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 2*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3)/e, Ne(e, 0)), (Piecewise((a**3*x, Eq(b, 0)), ((a**3*b*x + 3*a**2*b**2*x**2/2 + a*b**3*x**3 + b**4*x**4/4)/b, True))/sqrt(d), True))","A",0
2047,1,109,0,22.104676," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(3/2),x)","\frac{2 b^{3} \left(d + e x\right)^{\frac{5}{2}}}{5 e^{4}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(6 a b^{2} e - 6 b^{3} d\right)}{3 e^{4}} + \frac{\sqrt{d + e x} \left(6 a^{2} b e^{2} - 12 a b^{2} d e + 6 b^{3} d^{2}\right)}{e^{4}} - \frac{2 \left(a e - b d\right)^{3}}{e^{4} \sqrt{d + e x}}"," ",0,"2*b**3*(d + e*x)**(5/2)/(5*e**4) + (d + e*x)**(3/2)*(6*a*b**2*e - 6*b**3*d)/(3*e**4) + sqrt(d + e*x)*(6*a**2*b*e**2 - 12*a*b**2*d*e + 6*b**3*d**2)/e**4 - 2*(a*e - b*d)**3/(e**4*sqrt(d + e*x))","A",0
2048,1,461,0,1.552418," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(5/2),x)","\begin{cases} - \frac{2 a^{3} e^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 a^{2} b d e^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{18 a^{2} b e^{3} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{48 a b^{2} d^{2} e}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{72 a b^{2} d e^{2} x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{18 a b^{2} e^{3} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{32 b^{3} d^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{48 b^{3} d^{2} e x}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} - \frac{12 b^{3} d e^{2} x^{2}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} + \frac{2 b^{3} e^{3} x^{3}}{3 d e^{4} \sqrt{d + e x} + 3 e^{5} x \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}}{d^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*e**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*a**2*b*d*e**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 18*a**2*b*e**3*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 48*a*b**2*d**2*e/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 72*a*b**2*d*e**2*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 18*a*b**2*e**3*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 32*b**3*d**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 48*b**3*d**2*e*x/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) - 12*b**3*d*e**2*x**2/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)) + 2*b**3*e**3*x**3/(3*d*e**4*sqrt(d + e*x) + 3*e**5*x*sqrt(d + e*x)), Ne(e, 0)), ((a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)/d**(5/2), True))","A",0
2049,1,665,0,3.445674," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(7/2),x)","\begin{cases} - \frac{2 a^{3} e^{3}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{4 a^{2} b d e^{2}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{10 a^{2} b e^{3} x}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{16 a b^{2} d^{2} e}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{40 a b^{2} d e^{2} x}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} - \frac{30 a b^{2} e^{3} x^{2}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{32 b^{3} d^{3}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{80 b^{3} d^{2} e x}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{60 b^{3} d e^{2} x^{2}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} + \frac{10 b^{3} e^{3} x^{3}}{5 d^{2} e^{4} \sqrt{d + e x} + 10 d e^{5} x \sqrt{d + e x} + 5 e^{6} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*e**3/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 4*a**2*b*d*e**2/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 10*a**2*b*e**3*x/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 16*a*b**2*d**2*e/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 40*a*b**2*d*e**2*x/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) - 30*a*b**2*e**3*x**2/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 32*b**3*d**3/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 80*b**3*d**2*e*x/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 60*b**3*d*e**2*x**2/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)) + 10*b**3*e**3*x**3/(5*d**2*e**4*sqrt(d + e*x) + 10*d*e**5*x*sqrt(d + e*x) + 5*e**6*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)/d**(7/2), True))","A",0
2050,1,1187,0,15.957505," ","integrate((b*x+a)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","\begin{cases} \frac{2 a^{5} d^{4} \sqrt{d + e x}}{9 e} + \frac{8 a^{5} d^{3} x \sqrt{d + e x}}{9} + \frac{4 a^{5} d^{2} e x^{2} \sqrt{d + e x}}{3} + \frac{8 a^{5} d e^{2} x^{3} \sqrt{d + e x}}{9} + \frac{2 a^{5} e^{3} x^{4} \sqrt{d + e x}}{9} - \frac{20 a^{4} b d^{5} \sqrt{d + e x}}{99 e^{2}} + \frac{10 a^{4} b d^{4} x \sqrt{d + e x}}{99 e} + \frac{80 a^{4} b d^{3} x^{2} \sqrt{d + e x}}{33} + \frac{460 a^{4} b d^{2} e x^{3} \sqrt{d + e x}}{99} + \frac{340 a^{4} b d e^{2} x^{4} \sqrt{d + e x}}{99} + \frac{10 a^{4} b e^{3} x^{5} \sqrt{d + e x}}{11} + \frac{160 a^{3} b^{2} d^{6} \sqrt{d + e x}}{1287 e^{3}} - \frac{80 a^{3} b^{2} d^{5} x \sqrt{d + e x}}{1287 e^{2}} + \frac{20 a^{3} b^{2} d^{4} x^{2} \sqrt{d + e x}}{429 e} + \frac{4240 a^{3} b^{2} d^{3} x^{3} \sqrt{d + e x}}{1287} + \frac{9160 a^{3} b^{2} d^{2} e x^{4} \sqrt{d + e x}}{1287} + \frac{800 a^{3} b^{2} d e^{2} x^{5} \sqrt{d + e x}}{143} + \frac{20 a^{3} b^{2} e^{3} x^{6} \sqrt{d + e x}}{13} - \frac{64 a^{2} b^{3} d^{7} \sqrt{d + e x}}{1287 e^{4}} + \frac{32 a^{2} b^{3} d^{6} x \sqrt{d + e x}}{1287 e^{3}} - \frac{8 a^{2} b^{3} d^{5} x^{2} \sqrt{d + e x}}{429 e^{2}} + \frac{20 a^{2} b^{3} d^{4} x^{3} \sqrt{d + e x}}{1287 e} + \frac{3200 a^{2} b^{3} d^{3} x^{4} \sqrt{d + e x}}{1287} + \frac{824 a^{2} b^{3} d^{2} e x^{5} \sqrt{d + e x}}{143} + \frac{184 a^{2} b^{3} d e^{2} x^{6} \sqrt{d + e x}}{39} + \frac{4 a^{2} b^{3} e^{3} x^{7} \sqrt{d + e x}}{3} + \frac{256 a b^{4} d^{8} \sqrt{d + e x}}{21879 e^{5}} - \frac{128 a b^{4} d^{7} x \sqrt{d + e x}}{21879 e^{4}} + \frac{32 a b^{4} d^{6} x^{2} \sqrt{d + e x}}{7293 e^{3}} - \frac{80 a b^{4} d^{5} x^{3} \sqrt{d + e x}}{21879 e^{2}} + \frac{70 a b^{4} d^{4} x^{4} \sqrt{d + e x}}{21879 e} + \frac{2424 a b^{4} d^{3} x^{5} \sqrt{d + e x}}{2431} + \frac{1604 a b^{4} d^{2} e x^{6} \sqrt{d + e x}}{663} + \frac{104 a b^{4} d e^{2} x^{7} \sqrt{d + e x}}{51} + \frac{10 a b^{4} e^{3} x^{8} \sqrt{d + e x}}{17} - \frac{512 b^{5} d^{9} \sqrt{d + e x}}{415701 e^{6}} + \frac{256 b^{5} d^{8} x \sqrt{d + e x}}{415701 e^{5}} - \frac{64 b^{5} d^{7} x^{2} \sqrt{d + e x}}{138567 e^{4}} + \frac{160 b^{5} d^{6} x^{3} \sqrt{d + e x}}{415701 e^{3}} - \frac{140 b^{5} d^{5} x^{4} \sqrt{d + e x}}{415701 e^{2}} + \frac{14 b^{5} d^{4} x^{5} \sqrt{d + e x}}{46189 e} + \frac{2096 b^{5} d^{3} x^{6} \sqrt{d + e x}}{12597} + \frac{404 b^{5} d^{2} e x^{7} \sqrt{d + e x}}{969} + \frac{116 b^{5} d e^{2} x^{8} \sqrt{d + e x}}{323} + \frac{2 b^{5} e^{3} x^{9} \sqrt{d + e x}}{19} & \text{for}\: e \neq 0 \\d^{\frac{7}{2}} \left(a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**5*d**4*sqrt(d + e*x)/(9*e) + 8*a**5*d**3*x*sqrt(d + e*x)/9 + 4*a**5*d**2*e*x**2*sqrt(d + e*x)/3 + 8*a**5*d*e**2*x**3*sqrt(d + e*x)/9 + 2*a**5*e**3*x**4*sqrt(d + e*x)/9 - 20*a**4*b*d**5*sqrt(d + e*x)/(99*e**2) + 10*a**4*b*d**4*x*sqrt(d + e*x)/(99*e) + 80*a**4*b*d**3*x**2*sqrt(d + e*x)/33 + 460*a**4*b*d**2*e*x**3*sqrt(d + e*x)/99 + 340*a**4*b*d*e**2*x**4*sqrt(d + e*x)/99 + 10*a**4*b*e**3*x**5*sqrt(d + e*x)/11 + 160*a**3*b**2*d**6*sqrt(d + e*x)/(1287*e**3) - 80*a**3*b**2*d**5*x*sqrt(d + e*x)/(1287*e**2) + 20*a**3*b**2*d**4*x**2*sqrt(d + e*x)/(429*e) + 4240*a**3*b**2*d**3*x**3*sqrt(d + e*x)/1287 + 9160*a**3*b**2*d**2*e*x**4*sqrt(d + e*x)/1287 + 800*a**3*b**2*d*e**2*x**5*sqrt(d + e*x)/143 + 20*a**3*b**2*e**3*x**6*sqrt(d + e*x)/13 - 64*a**2*b**3*d**7*sqrt(d + e*x)/(1287*e**4) + 32*a**2*b**3*d**6*x*sqrt(d + e*x)/(1287*e**3) - 8*a**2*b**3*d**5*x**2*sqrt(d + e*x)/(429*e**2) + 20*a**2*b**3*d**4*x**3*sqrt(d + e*x)/(1287*e) + 3200*a**2*b**3*d**3*x**4*sqrt(d + e*x)/1287 + 824*a**2*b**3*d**2*e*x**5*sqrt(d + e*x)/143 + 184*a**2*b**3*d*e**2*x**6*sqrt(d + e*x)/39 + 4*a**2*b**3*e**3*x**7*sqrt(d + e*x)/3 + 256*a*b**4*d**8*sqrt(d + e*x)/(21879*e**5) - 128*a*b**4*d**7*x*sqrt(d + e*x)/(21879*e**4) + 32*a*b**4*d**6*x**2*sqrt(d + e*x)/(7293*e**3) - 80*a*b**4*d**5*x**3*sqrt(d + e*x)/(21879*e**2) + 70*a*b**4*d**4*x**4*sqrt(d + e*x)/(21879*e) + 2424*a*b**4*d**3*x**5*sqrt(d + e*x)/2431 + 1604*a*b**4*d**2*e*x**6*sqrt(d + e*x)/663 + 104*a*b**4*d*e**2*x**7*sqrt(d + e*x)/51 + 10*a*b**4*e**3*x**8*sqrt(d + e*x)/17 - 512*b**5*d**9*sqrt(d + e*x)/(415701*e**6) + 256*b**5*d**8*x*sqrt(d + e*x)/(415701*e**5) - 64*b**5*d**7*x**2*sqrt(d + e*x)/(138567*e**4) + 160*b**5*d**6*x**3*sqrt(d + e*x)/(415701*e**3) - 140*b**5*d**5*x**4*sqrt(d + e*x)/(415701*e**2) + 14*b**5*d**4*x**5*sqrt(d + e*x)/(46189*e) + 2096*b**5*d**3*x**6*sqrt(d + e*x)/12597 + 404*b**5*d**2*e*x**7*sqrt(d + e*x)/969 + 116*b**5*d*e**2*x**8*sqrt(d + e*x)/323 + 2*b**5*e**3*x**9*sqrt(d + e*x)/19, Ne(e, 0)), (d**(7/2)*(a**5*x + 5*a**4*b*x**2/2 + 10*a**3*b**2*x**3/3 + 5*a**2*b**3*x**4/2 + a*b**4*x**5 + b**5*x**6/6), True))","A",0
2051,1,1292,0,48.316123," ","integrate((b*x+a)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{5} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{5} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{10 a^{4} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{20 a^{4} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{10 a^{4} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{20 a^{3} b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{40 a^{3} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{20 a^{3} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{20 a^{2} b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{40 a^{2} b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{20 a^{2} b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{10 a b^{4} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{20 a b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{10 a b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{2 b^{5} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{4 b^{5} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{2 b^{5} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}}"," ",0,"a**5*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**5*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**5*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 10*a**4*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 20*a**4*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 10*a**4*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 20*a**3*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 40*a**3*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 20*a**3*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 20*a**2*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 40*a**2*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 20*a**2*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 10*a*b**4*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 20*a*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 10*a*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 2*b**5*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 4*b**5*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 2*b**5*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6","A",0
2052,1,763,0,30.564628," ","integrate((b*x+a)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**2,x)","a^{5} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{5} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{10 a^{4} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{10 a^{4} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{20 a^{3} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{20 a^{3} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{20 a^{2} b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{20 a^{2} b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{10 a b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{10 a b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{2 b^{5} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{2 b^{5} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}}"," ",0,"a**5*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**5*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 10*a**4*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 10*a**4*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 20*a**3*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 20*a**3*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 20*a**2*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 20*a**2*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 10*a*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 10*a*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 2*b**5*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 2*b**5*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6","A",0
2053,1,314,0,7.698768," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{b^{5} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{5}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(5 a b^{4} e - 5 b^{5} d\right)}{11 e^{5}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(10 a^{2} b^{3} e^{2} - 20 a b^{4} d e + 10 b^{5} d^{2}\right)}{9 e^{5}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(10 a^{3} b^{2} e^{3} - 30 a^{2} b^{3} d e^{2} + 30 a b^{4} d^{2} e - 10 b^{5} d^{3}\right)}{7 e^{5}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(5 a^{4} b e^{4} - 20 a^{3} b^{2} d e^{3} + 30 a^{2} b^{3} d^{2} e^{2} - 20 a b^{4} d^{3} e + 5 b^{5} d^{4}\right)}{5 e^{5}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{5} e^{5} - 5 a^{4} b d e^{4} + 10 a^{3} b^{2} d^{2} e^{3} - 10 a^{2} b^{3} d^{3} e^{2} + 5 a b^{4} d^{4} e - b^{5} d^{5}\right)}{3 e^{5}}\right)}{e}"," ",0,"2*(b**5*(d + e*x)**(13/2)/(13*e**5) + (d + e*x)**(11/2)*(5*a*b**4*e - 5*b**5*d)/(11*e**5) + (d + e*x)**(9/2)*(10*a**2*b**3*e**2 - 20*a*b**4*d*e + 10*b**5*d**2)/(9*e**5) + (d + e*x)**(7/2)*(10*a**3*b**2*e**3 - 30*a**2*b**3*d*e**2 + 30*a*b**4*d**2*e - 10*b**5*d**3)/(7*e**5) + (d + e*x)**(5/2)*(5*a**4*b*e**4 - 20*a**3*b**2*d*e**3 + 30*a**2*b**3*d**2*e**2 - 20*a*b**4*d**3*e + 5*b**5*d**4)/(5*e**5) + (d + e*x)**(3/2)*(a**5*e**5 - 5*a**4*b*d*e**4 + 10*a**3*b**2*d**2*e**3 - 10*a**2*b**3*d**3*e**2 + 5*a*b**4*d**4*e - b**5*d**5)/(3*e**5))/e","B",0
2054,1,740,0,84.599872," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{5} d}{\sqrt{d + e x}} - 2 a^{5} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{10 a^{4} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{10 a^{4} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{20 a^{3} b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{20 a^{3} b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{20 a^{2} b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{20 a^{2} b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{10 a b^{4} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{10 a b^{4} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{2 b^{5} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{2 b^{5} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}}}{e} & \text{for}\: e \neq 0 \\\frac{\begin{cases} a^{5} x & \text{for}\: b = 0 \\\frac{\left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{3}}{6 b} & \text{otherwise} \end{cases}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**5*d/sqrt(d + e*x) - 2*a**5*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 10*a**4*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 10*a**4*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 20*a**3*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 20*a**3*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 20*a**2*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 20*a**2*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 10*a*b**4*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 10*a*b**4*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 2*b**5*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 2*b**5*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5)/e, Ne(e, 0)), (Piecewise((a**5*x, Eq(b, 0)), ((a**2 + 2*a*b*x + b**2*x**2)**3/(6*b), True))/sqrt(d), True))","A",0
2055,1,243,0,49.192377," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(3/2),x)","\frac{2 b^{5} \left(d + e x\right)^{\frac{9}{2}}}{9 e^{6}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(10 a b^{4} e - 10 b^{5} d\right)}{7 e^{6}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(20 a^{2} b^{3} e^{2} - 40 a b^{4} d e + 20 b^{5} d^{2}\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(20 a^{3} b^{2} e^{3} - 60 a^{2} b^{3} d e^{2} + 60 a b^{4} d^{2} e - 20 b^{5} d^{3}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(10 a^{4} b e^{4} - 40 a^{3} b^{2} d e^{3} + 60 a^{2} b^{3} d^{2} e^{2} - 40 a b^{4} d^{3} e + 10 b^{5} d^{4}\right)}{e^{6}} - \frac{2 \left(a e - b d\right)^{5}}{e^{6} \sqrt{d + e x}}"," ",0,"2*b**5*(d + e*x)**(9/2)/(9*e**6) + (d + e*x)**(7/2)*(10*a*b**4*e - 10*b**5*d)/(7*e**6) + (d + e*x)**(5/2)*(20*a**2*b**3*e**2 - 40*a*b**4*d*e + 20*b**5*d**2)/(5*e**6) + (d + e*x)**(3/2)*(20*a**3*b**2*e**3 - 60*a**2*b**3*d*e**2 + 60*a*b**4*d**2*e - 20*b**5*d**3)/(3*e**6) + sqrt(d + e*x)*(10*a**4*b*e**4 - 40*a**3*b**2*d*e**3 + 60*a**2*b**3*d**2*e**2 - 40*a*b**4*d**3*e + 10*b**5*d**4)/e**6 - 2*(a*e - b*d)**5/(e**6*sqrt(d + e*x))","A",0
2056,1,196,0,59.861047," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(5/2),x)","\frac{2 b^{5} \left(d + e x\right)^{\frac{7}{2}}}{7 e^{6}} - \frac{10 b \left(a e - b d\right)^{4}}{e^{6} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(10 a b^{4} e - 10 b^{5} d\right)}{5 e^{6}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(20 a^{2} b^{3} e^{2} - 40 a b^{4} d e + 20 b^{5} d^{2}\right)}{3 e^{6}} + \frac{\sqrt{d + e x} \left(20 a^{3} b^{2} e^{3} - 60 a^{2} b^{3} d e^{2} + 60 a b^{4} d^{2} e - 20 b^{5} d^{3}\right)}{e^{6}} - \frac{2 \left(a e - b d\right)^{5}}{3 e^{6} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*b**5*(d + e*x)**(7/2)/(7*e**6) - 10*b*(a*e - b*d)**4/(e**6*sqrt(d + e*x)) + (d + e*x)**(5/2)*(10*a*b**4*e - 10*b**5*d)/(5*e**6) + (d + e*x)**(3/2)*(20*a**2*b**3*e**2 - 40*a*b**4*d*e + 20*b**5*d**2)/(3*e**6) + sqrt(d + e*x)*(20*a**3*b**2*e**3 - 60*a**2*b**3*d*e**2 + 60*a*b**4*d**2*e - 20*b**5*d**3)/e**6 - 2*(a*e - b*d)**5/(3*e**6*(d + e*x)**(3/2))","A",0
2057,1,1428,0,4.347856," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(7/2),x)","\begin{cases} - \frac{6 a^{5} e^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{20 a^{4} b d e^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{50 a^{4} b e^{5} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{160 a^{3} b^{2} d^{2} e^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{400 a^{3} b^{2} d e^{4} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{300 a^{3} b^{2} e^{5} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{960 a^{2} b^{3} d^{3} e^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{2400 a^{2} b^{3} d^{2} e^{3} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1800 a^{2} b^{3} d e^{4} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{300 a^{2} b^{3} e^{5} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{1280 a b^{4} d^{4} e}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{3200 a b^{4} d^{3} e^{2} x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{2400 a b^{4} d^{2} e^{3} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{400 a b^{4} d e^{4} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{50 a b^{4} e^{5} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{512 b^{5} d^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{1280 b^{5} d^{4} e x}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{960 b^{5} d^{3} e^{2} x^{2}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{160 b^{5} d^{2} e^{3} x^{3}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} - \frac{20 b^{5} d e^{4} x^{4}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} + \frac{6 b^{5} e^{5} x^{5}}{15 d^{2} e^{6} \sqrt{d + e x} + 30 d e^{7} x \sqrt{d + e x} + 15 e^{8} x^{2} \sqrt{d + e x}} & \text{for}\: e \neq 0 \\\frac{a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6}}{d^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**5*e**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 20*a**4*b*d*e**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 50*a**4*b*e**5*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 160*a**3*b**2*d**2*e**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 400*a**3*b**2*d*e**4*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 300*a**3*b**2*e**5*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 960*a**2*b**3*d**3*e**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 2400*a**2*b**3*d**2*e**3*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1800*a**2*b**3*d*e**4*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 300*a**2*b**3*e**5*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 1280*a*b**4*d**4*e/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 3200*a*b**4*d**3*e**2*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 2400*a*b**4*d**2*e**3*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 400*a*b**4*d*e**4*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 50*a*b**4*e**5*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 512*b**5*d**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 1280*b**5*d**4*e*x/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 960*b**5*d**3*e**2*x**2/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 160*b**5*d**2*e**3*x**3/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) - 20*b**5*d*e**4*x**4/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)) + 6*b**5*e**5*x**5/(15*d**2*e**6*sqrt(d + e*x) + 30*d*e**7*x*sqrt(d + e*x) + 15*e**8*x**2*sqrt(d + e*x)), Ne(e, 0)), ((a**5*x + 5*a**4*b*x**2/2 + 10*a**3*b**2*x**3/3 + 5*a**2*b**3*x**4/2 + a*b**4*x**5 + b**5*x**6/6)/d**(7/2), True))","A",0
2058,1,3046,0,101.432985," ","integrate((b*x+a)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{3} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{6 a^{7} d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{6 a^{7} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{2 a^{7} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e} + \frac{14 a^{6} b d^{3} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{42 a^{6} b d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{42 a^{6} b d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{14 a^{6} b \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{2}} + \frac{42 a^{5} b^{2} d^{3} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{126 a^{5} b^{2} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{126 a^{5} b^{2} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{42 a^{5} b^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{3}} + \frac{70 a^{4} b^{3} d^{3} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{210 a^{4} b^{3} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{210 a^{4} b^{3} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{70 a^{4} b^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{4}} + \frac{70 a^{3} b^{4} d^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{210 a^{3} b^{4} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{210 a^{3} b^{4} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{70 a^{3} b^{4} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{5}} + \frac{42 a^{2} b^{5} d^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{126 a^{2} b^{5} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{126 a^{2} b^{5} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{42 a^{2} b^{5} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{6}} + \frac{14 a b^{6} d^{3} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{42 a b^{6} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{42 a b^{6} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{14 a b^{6} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{7}} + \frac{2 b^{7} d^{3} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{6 b^{7} d^{2} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}} + \frac{6 b^{7} d \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{8}} + \frac{2 b^{7} \left(\frac{d^{10} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{9} \left(d + e x\right)^{\frac{5}{2}} + \frac{45 d^{8} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{40 d^{7} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{210 d^{6} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{252 d^{5} \left(d + e x\right)^{\frac{13}{2}}}{13} + 14 d^{4} \left(d + e x\right)^{\frac{15}{2}} - \frac{120 d^{3} \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{45 d^{2} \left(d + e x\right)^{\frac{19}{2}}}{19} - \frac{10 d \left(d + e x\right)^{\frac{21}{2}}}{21} + \frac{\left(d + e x\right)^{\frac{23}{2}}}{23}\right)}{e^{8}}"," ",0,"a**7*d**3*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 6*a**7*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*a**7*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 2*a**7*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e + 14*a**6*b*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 42*a**6*b*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 42*a**6*b*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 14*a**6*b*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**2 + 42*a**5*b**2*d**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 126*a**5*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 126*a**5*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 42*a**5*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**3 + 70*a**4*b**3*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 210*a**4*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 210*a**4*b**3*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 70*a**4*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 70*a**3*b**4*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 210*a**3*b**4*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 210*a**3*b**4*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 70*a**3*b**4*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 42*a**2*b**5*d**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 126*a**2*b**5*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 126*a**2*b**5*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 42*a**2*b**5*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**6 + 14*a*b**6*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 42*a*b**6*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 42*a*b**6*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 14*a*b**6*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7 + 2*b**7*d**3*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 6*b**7*d**2*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8 + 6*b**7*d*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**8 + 2*b**7*(d**10*(d + e*x)**(3/2)/3 - 2*d**9*(d + e*x)**(5/2) + 45*d**8*(d + e*x)**(7/2)/7 - 40*d**7*(d + e*x)**(9/2)/3 + 210*d**6*(d + e*x)**(11/2)/11 - 252*d**5*(d + e*x)**(13/2)/13 + 14*d**4*(d + e*x)**(15/2) - 120*d**3*(d + e*x)**(17/2)/17 + 45*d**2*(d + e*x)**(19/2)/19 - 10*d*(d + e*x)**(21/2)/21 + (d + e*x)**(23/2)/23)/e**8","A",0
2059,1,2096,0,70.414232," ","integrate((b*x+a)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d^{2} \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{4 a^{7} d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 a^{7} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e} + \frac{14 a^{6} b d^{2} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{28 a^{6} b d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{14 a^{6} b \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{2}} + \frac{42 a^{5} b^{2} d^{2} \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{84 a^{5} b^{2} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{42 a^{5} b^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{3}} + \frac{70 a^{4} b^{3} d^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{140 a^{4} b^{3} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{70 a^{4} b^{3} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{4}} + \frac{70 a^{3} b^{4} d^{2} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{140 a^{3} b^{4} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{70 a^{3} b^{4} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{5}} + \frac{42 a^{2} b^{5} d^{2} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{84 a^{2} b^{5} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{42 a^{2} b^{5} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{6}} + \frac{14 a b^{6} d^{2} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{28 a b^{6} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{14 a b^{6} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{7}} + \frac{2 b^{7} d^{2} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{4 b^{7} d \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}} + \frac{2 b^{7} \left(- \frac{d^{9} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{9 d^{8} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{36 d^{7} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{28 d^{6} \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{126 d^{5} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{126 d^{4} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{28 d^{3} \left(d + e x\right)^{\frac{15}{2}}}{5} + \frac{36 d^{2} \left(d + e x\right)^{\frac{17}{2}}}{17} - \frac{9 d \left(d + e x\right)^{\frac{19}{2}}}{19} + \frac{\left(d + e x\right)^{\frac{21}{2}}}{21}\right)}{e^{8}}"," ",0,"a**7*d**2*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 4*a**7*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*a**7*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e + 14*a**6*b*d**2*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 28*a**6*b*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 14*a**6*b*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 42*a**5*b**2*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 84*a**5*b**2*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 42*a**5*b**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 70*a**4*b**3*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 140*a**4*b**3*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 70*a**4*b**3*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 70*a**3*b**4*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 140*a**3*b**4*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 70*a**3*b**4*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 42*a**2*b**5*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 84*a**2*b**5*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 42*a**2*b**5*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 14*a*b**6*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 28*a*b**6*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 14*a*b**6*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*b**7*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 4*b**7*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8 + 2*b**7*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**8","A",0
2060,1,1265,0,45.364219," ","integrate((b*x+a)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)","a^{7} d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a^{7} \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{14 a^{6} b d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{14 a^{6} b \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{42 a^{5} b^{2} d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{42 a^{5} b^{2} \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{70 a^{4} b^{3} d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{70 a^{4} b^{3} \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{70 a^{3} b^{4} d \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} + \frac{70 a^{3} b^{4} \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{5}} + \frac{42 a^{2} b^{5} d \left(- \frac{d^{5} \left(d + e x\right)^{\frac{3}{2}}}{3} + d^{4} \left(d + e x\right)^{\frac{5}{2}} - \frac{10 d^{3} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{10 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{5 d \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} + \frac{42 a^{2} b^{5} \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{6}} + \frac{14 a b^{6} d \left(\frac{d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{6 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{15 d^{4} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{20 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{15 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{6 d \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}} + \frac{14 a b^{6} \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{7}} + \frac{2 b^{7} d \left(- \frac{d^{7} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{7 d^{6} \left(d + e x\right)^{\frac{5}{2}}}{5} - 3 d^{5} \left(d + e x\right)^{\frac{7}{2}} + \frac{35 d^{4} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{35 d^{3} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{21 d^{2} \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{7 d \left(d + e x\right)^{\frac{15}{2}}}{15} + \frac{\left(d + e x\right)^{\frac{17}{2}}}{17}\right)}{e^{8}} + \frac{2 b^{7} \left(\frac{d^{8} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{8 d^{7} \left(d + e x\right)^{\frac{5}{2}}}{5} + 4 d^{6} \left(d + e x\right)^{\frac{7}{2}} - \frac{56 d^{5} \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{70 d^{4} \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{56 d^{3} \left(d + e x\right)^{\frac{13}{2}}}{13} + \frac{28 d^{2} \left(d + e x\right)^{\frac{15}{2}}}{15} - \frac{8 d \left(d + e x\right)^{\frac{17}{2}}}{17} + \frac{\left(d + e x\right)^{\frac{19}{2}}}{19}\right)}{e^{8}}"," ",0,"a**7*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a**7*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 14*a**6*b*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 14*a**6*b*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 42*a**5*b**2*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 42*a**5*b**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 70*a**4*b**3*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 70*a**4*b**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 70*a**3*b**4*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 70*a**3*b**4*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 42*a**2*b**5*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 42*a**2*b**5*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 14*a*b**6*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 + 14*a*b**6*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 2*b**7*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 2*b**7*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8","A",0
2061,1,544,0,10.163005," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{b^{7} \left(d + e x\right)^{\frac{17}{2}}}{17 e^{7}} + \frac{\left(d + e x\right)^{\frac{15}{2}} \left(7 a b^{6} e - 7 b^{7} d\right)}{15 e^{7}} + \frac{\left(d + e x\right)^{\frac{13}{2}} \left(21 a^{2} b^{5} e^{2} - 42 a b^{6} d e + 21 b^{7} d^{2}\right)}{13 e^{7}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(35 a^{3} b^{4} e^{3} - 105 a^{2} b^{5} d e^{2} + 105 a b^{6} d^{2} e - 35 b^{7} d^{3}\right)}{11 e^{7}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(35 a^{4} b^{3} e^{4} - 140 a^{3} b^{4} d e^{3} + 210 a^{2} b^{5} d^{2} e^{2} - 140 a b^{6} d^{3} e + 35 b^{7} d^{4}\right)}{9 e^{7}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(21 a^{5} b^{2} e^{5} - 105 a^{4} b^{3} d e^{4} + 210 a^{3} b^{4} d^{2} e^{3} - 210 a^{2} b^{5} d^{3} e^{2} + 105 a b^{6} d^{4} e - 21 b^{7} d^{5}\right)}{7 e^{7}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(7 a^{6} b e^{6} - 42 a^{5} b^{2} d e^{5} + 105 a^{4} b^{3} d^{2} e^{4} - 140 a^{3} b^{4} d^{3} e^{3} + 105 a^{2} b^{5} d^{4} e^{2} - 42 a b^{6} d^{5} e + 7 b^{7} d^{6}\right)}{5 e^{7}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(a^{7} e^{7} - 7 a^{6} b d e^{6} + 21 a^{5} b^{2} d^{2} e^{5} - 35 a^{4} b^{3} d^{3} e^{4} + 35 a^{3} b^{4} d^{4} e^{3} - 21 a^{2} b^{5} d^{5} e^{2} + 7 a b^{6} d^{6} e - b^{7} d^{7}\right)}{3 e^{7}}\right)}{e}"," ",0,"2*(b**7*(d + e*x)**(17/2)/(17*e**7) + (d + e*x)**(15/2)*(7*a*b**6*e - 7*b**7*d)/(15*e**7) + (d + e*x)**(13/2)*(21*a**2*b**5*e**2 - 42*a*b**6*d*e + 21*b**7*d**2)/(13*e**7) + (d + e*x)**(11/2)*(35*a**3*b**4*e**3 - 105*a**2*b**5*d*e**2 + 105*a*b**6*d**2*e - 35*b**7*d**3)/(11*e**7) + (d + e*x)**(9/2)*(35*a**4*b**3*e**4 - 140*a**3*b**4*d*e**3 + 210*a**2*b**5*d**2*e**2 - 140*a*b**6*d**3*e + 35*b**7*d**4)/(9*e**7) + (d + e*x)**(7/2)*(21*a**5*b**2*e**5 - 105*a**4*b**3*d*e**4 + 210*a**3*b**4*d**2*e**3 - 210*a**2*b**5*d**3*e**2 + 105*a*b**6*d**4*e - 21*b**7*d**5)/(7*e**7) + (d + e*x)**(5/2)*(7*a**6*b*e**6 - 42*a**5*b**2*d*e**5 + 105*a**4*b**3*d**2*e**4 - 140*a**3*b**4*d**3*e**3 + 105*a**2*b**5*d**4*e**2 - 42*a*b**6*d**5*e + 7*b**7*d**6)/(5*e**7) + (d + e*x)**(3/2)*(a**7*e**7 - 7*a**6*b*d*e**6 + 21*a**5*b**2*d**2*e**5 - 35*a**4*b**3*d**3*e**4 + 35*a**3*b**4*d**4*e**3 - 21*a**2*b**5*d**5*e**2 + 7*a*b**6*d**6*e - b**7*d**7)/(3*e**7))/e","B",0
2062,1,1217,0,140.052246," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{7} d}{\sqrt{d + e x}} - 2 a^{7} \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - \frac{14 a^{6} b d \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right)}{e} - \frac{14 a^{6} b \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e} - \frac{42 a^{5} b^{2} d \left(\frac{d^{2}}{\sqrt{d + e x}} + 2 d \sqrt{d + e x} - \frac{\left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{e^{2}} - \frac{42 a^{5} b^{2} \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} - \frac{70 a^{4} b^{3} d \left(- \frac{d^{3}}{\sqrt{d + e x}} - 3 d^{2} \sqrt{d + e x} + d \left(d + e x\right)^{\frac{3}{2}} - \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{3}} - \frac{70 a^{4} b^{3} \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} - \frac{70 a^{3} b^{4} d \left(\frac{d^{4}}{\sqrt{d + e x}} + 4 d^{3} \sqrt{d + e x} - 2 d^{2} \left(d + e x\right)^{\frac{3}{2}} + \frac{4 d \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{4}} - \frac{70 a^{3} b^{4} \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} - \frac{42 a^{2} b^{5} d \left(- \frac{d^{5}}{\sqrt{d + e x}} - 5 d^{4} \sqrt{d + e x} + \frac{10 d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} - 2 d^{2} \left(d + e x\right)^{\frac{5}{2}} + \frac{5 d \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{5}} - \frac{42 a^{2} b^{5} \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{5}} - \frac{14 a b^{6} d \left(\frac{d^{6}}{\sqrt{d + e x}} + 6 d^{5} \sqrt{d + e x} - 5 d^{4} \left(d + e x\right)^{\frac{3}{2}} + 4 d^{3} \left(d + e x\right)^{\frac{5}{2}} - \frac{15 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{2 d \left(d + e x\right)^{\frac{9}{2}}}{3} - \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{6}} - \frac{14 a b^{6} \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{6}} - \frac{2 b^{7} d \left(- \frac{d^{7}}{\sqrt{d + e x}} - 7 d^{6} \sqrt{d + e x} + 7 d^{5} \left(d + e x\right)^{\frac{3}{2}} - 7 d^{4} \left(d + e x\right)^{\frac{5}{2}} + 5 d^{3} \left(d + e x\right)^{\frac{7}{2}} - \frac{7 d^{2} \left(d + e x\right)^{\frac{9}{2}}}{3} + \frac{7 d \left(d + e x\right)^{\frac{11}{2}}}{11} - \frac{\left(d + e x\right)^{\frac{13}{2}}}{13}\right)}{e^{7}} - \frac{2 b^{7} \left(\frac{d^{8}}{\sqrt{d + e x}} + 8 d^{7} \sqrt{d + e x} - \frac{28 d^{6} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{56 d^{5} \left(d + e x\right)^{\frac{5}{2}}}{5} - 10 d^{4} \left(d + e x\right)^{\frac{7}{2}} + \frac{56 d^{3} \left(d + e x\right)^{\frac{9}{2}}}{9} - \frac{28 d^{2} \left(d + e x\right)^{\frac{11}{2}}}{11} + \frac{8 d \left(d + e x\right)^{\frac{13}{2}}}{13} - \frac{\left(d + e x\right)^{\frac{15}{2}}}{15}\right)}{e^{7}}}{e} & \text{for}\: e \neq 0 \\\frac{\begin{cases} a^{7} x & \text{for}\: b = 0 \\\frac{\left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{4}}{8 b} & \text{otherwise} \end{cases}}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**7*d/sqrt(d + e*x) - 2*a**7*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 14*a**6*b*d*(-d/sqrt(d + e*x) - sqrt(d + e*x))/e - 14*a**6*b*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e - 42*a**5*b**2*d*(d**2/sqrt(d + e*x) + 2*d*sqrt(d + e*x) - (d + e*x)**(3/2)/3)/e**2 - 42*a**5*b**2*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**2 - 70*a**4*b**3*d*(-d**3/sqrt(d + e*x) - 3*d**2*sqrt(d + e*x) + d*(d + e*x)**(3/2) - (d + e*x)**(5/2)/5)/e**3 - 70*a**4*b**3*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**3 - 70*a**3*b**4*d*(d**4/sqrt(d + e*x) + 4*d**3*sqrt(d + e*x) - 2*d**2*(d + e*x)**(3/2) + 4*d*(d + e*x)**(5/2)/5 - (d + e*x)**(7/2)/7)/e**4 - 70*a**3*b**4*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**4 - 42*a**2*b**5*d*(-d**5/sqrt(d + e*x) - 5*d**4*sqrt(d + e*x) + 10*d**3*(d + e*x)**(3/2)/3 - 2*d**2*(d + e*x)**(5/2) + 5*d*(d + e*x)**(7/2)/7 - (d + e*x)**(9/2)/9)/e**5 - 42*a**2*b**5*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**5 - 14*a*b**6*d*(d**6/sqrt(d + e*x) + 6*d**5*sqrt(d + e*x) - 5*d**4*(d + e*x)**(3/2) + 4*d**3*(d + e*x)**(5/2) - 15*d**2*(d + e*x)**(7/2)/7 + 2*d*(d + e*x)**(9/2)/3 - (d + e*x)**(11/2)/11)/e**6 - 14*a*b**6*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**6 - 2*b**7*d*(-d**7/sqrt(d + e*x) - 7*d**6*sqrt(d + e*x) + 7*d**5*(d + e*x)**(3/2) - 7*d**4*(d + e*x)**(5/2) + 5*d**3*(d + e*x)**(7/2) - 7*d**2*(d + e*x)**(9/2)/3 + 7*d*(d + e*x)**(11/2)/11 - (d + e*x)**(13/2)/13)/e**7 - 2*b**7*(d**8/sqrt(d + e*x) + 8*d**7*sqrt(d + e*x) - 28*d**6*(d + e*x)**(3/2)/3 + 56*d**5*(d + e*x)**(5/2)/5 - 10*d**4*(d + e*x)**(7/2) + 56*d**3*(d + e*x)**(9/2)/9 - 28*d**2*(d + e*x)**(11/2)/11 + 8*d*(d + e*x)**(13/2)/13 - (d + e*x)**(15/2)/15)/e**7)/e, Ne(e, 0)), (Piecewise((a**7*x, Eq(b, 0)), ((a**2 + 2*a*b*x + b**2*x**2)**4/(8*b), True))/sqrt(d), True))","A",0
2063,1,439,0,99.355176," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(3/2),x)","\frac{2 b^{7} \left(d + e x\right)^{\frac{13}{2}}}{13 e^{8}} + \frac{\left(d + e x\right)^{\frac{11}{2}} \left(14 a b^{6} e - 14 b^{7} d\right)}{11 e^{8}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(42 a^{2} b^{5} e^{2} - 84 a b^{6} d e + 42 b^{7} d^{2}\right)}{9 e^{8}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(70 a^{3} b^{4} e^{3} - 210 a^{2} b^{5} d e^{2} + 210 a b^{6} d^{2} e - 70 b^{7} d^{3}\right)}{7 e^{8}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(70 a^{4} b^{3} e^{4} - 280 a^{3} b^{4} d e^{3} + 420 a^{2} b^{5} d^{2} e^{2} - 280 a b^{6} d^{3} e + 70 b^{7} d^{4}\right)}{5 e^{8}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(42 a^{5} b^{2} e^{5} - 210 a^{4} b^{3} d e^{4} + 420 a^{3} b^{4} d^{2} e^{3} - 420 a^{2} b^{5} d^{3} e^{2} + 210 a b^{6} d^{4} e - 42 b^{7} d^{5}\right)}{3 e^{8}} + \frac{\sqrt{d + e x} \left(14 a^{6} b e^{6} - 84 a^{5} b^{2} d e^{5} + 210 a^{4} b^{3} d^{2} e^{4} - 280 a^{3} b^{4} d^{3} e^{3} + 210 a^{2} b^{5} d^{4} e^{2} - 84 a b^{6} d^{5} e + 14 b^{7} d^{6}\right)}{e^{8}} - \frac{2 \left(a e - b d\right)^{7}}{e^{8} \sqrt{d + e x}}"," ",0,"2*b**7*(d + e*x)**(13/2)/(13*e**8) + (d + e*x)**(11/2)*(14*a*b**6*e - 14*b**7*d)/(11*e**8) + (d + e*x)**(9/2)*(42*a**2*b**5*e**2 - 84*a*b**6*d*e + 42*b**7*d**2)/(9*e**8) + (d + e*x)**(7/2)*(70*a**3*b**4*e**3 - 210*a**2*b**5*d*e**2 + 210*a*b**6*d**2*e - 70*b**7*d**3)/(7*e**8) + (d + e*x)**(5/2)*(70*a**4*b**3*e**4 - 280*a**3*b**4*d*e**3 + 420*a**2*b**5*d**2*e**2 - 280*a*b**6*d**3*e + 70*b**7*d**4)/(5*e**8) + (d + e*x)**(3/2)*(42*a**5*b**2*e**5 - 210*a**4*b**3*d*e**4 + 420*a**3*b**4*d**2*e**3 - 420*a**2*b**5*d**3*e**2 + 210*a*b**6*d**4*e - 42*b**7*d**5)/(3*e**8) + sqrt(d + e*x)*(14*a**6*b*e**6 - 84*a**5*b**2*d*e**5 + 210*a**4*b**3*d**2*e**4 - 280*a**3*b**4*d**3*e**3 + 210*a**2*b**5*d**4*e**2 - 84*a*b**6*d**5*e + 14*b**7*d**6)/e**8 - 2*(a*e - b*d)**7/(e**8*sqrt(d + e*x))","B",0
2064,1,360,0,113.694560," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(5/2),x)","\frac{2 b^{7} \left(d + e x\right)^{\frac{11}{2}}}{11 e^{8}} - \frac{14 b \left(a e - b d\right)^{6}}{e^{8} \sqrt{d + e x}} + \frac{\left(d + e x\right)^{\frac{9}{2}} \left(14 a b^{6} e - 14 b^{7} d\right)}{9 e^{8}} + \frac{\left(d + e x\right)^{\frac{7}{2}} \left(42 a^{2} b^{5} e^{2} - 84 a b^{6} d e + 42 b^{7} d^{2}\right)}{7 e^{8}} + \frac{\left(d + e x\right)^{\frac{5}{2}} \left(70 a^{3} b^{4} e^{3} - 210 a^{2} b^{5} d e^{2} + 210 a b^{6} d^{2} e - 70 b^{7} d^{3}\right)}{5 e^{8}} + \frac{\left(d + e x\right)^{\frac{3}{2}} \left(70 a^{4} b^{3} e^{4} - 280 a^{3} b^{4} d e^{3} + 420 a^{2} b^{5} d^{2} e^{2} - 280 a b^{6} d^{3} e + 70 b^{7} d^{4}\right)}{3 e^{8}} + \frac{\sqrt{d + e x} \left(42 a^{5} b^{2} e^{5} - 210 a^{4} b^{3} d e^{4} + 420 a^{3} b^{4} d^{2} e^{3} - 420 a^{2} b^{5} d^{3} e^{2} + 210 a b^{6} d^{4} e - 42 b^{7} d^{5}\right)}{e^{8}} - \frac{2 \left(a e - b d\right)^{7}}{3 e^{8} \left(d + e x\right)^{\frac{3}{2}}}"," ",0,"2*b**7*(d + e*x)**(11/2)/(11*e**8) - 14*b*(a*e - b*d)**6/(e**8*sqrt(d + e*x)) + (d + e*x)**(9/2)*(14*a*b**6*e - 14*b**7*d)/(9*e**8) + (d + e*x)**(7/2)*(42*a**2*b**5*e**2 - 84*a*b**6*d*e + 42*b**7*d**2)/(7*e**8) + (d + e*x)**(5/2)*(70*a**3*b**4*e**3 - 210*a**2*b**5*d*e**2 + 210*a*b**6*d**2*e - 70*b**7*d**3)/(5*e**8) + (d + e*x)**(3/2)*(70*a**4*b**3*e**4 - 280*a**3*b**4*d*e**3 + 420*a**2*b**5*d**2*e**2 - 280*a*b**6*d**3*e + 70*b**7*d**4)/(3*e**8) + sqrt(d + e*x)*(42*a**5*b**2*e**5 - 210*a**4*b**3*d*e**4 + 420*a**3*b**4*d**2*e**3 - 420*a**2*b**5*d**3*e**2 + 210*a*b**6*d**4*e - 42*b**7*d**5)/e**8 - 2*(a*e - b*d)**7/(3*e**8*(d + e*x)**(3/2))","A",0
2065,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2066,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2067,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2068,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2069,1,61,0,58.917224," ","integrate((b*x+a)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{2 \left(\frac{e \sqrt{d + e x}}{b} - \frac{e \left(a e - b d\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e - b d}{b}}} \right)}}{b^{2} \sqrt{\frac{a e - b d}{b}}}\right)}{e}"," ",0,"2*(e*sqrt(d + e*x)/b - e*(a*e - b*d)*atan(sqrt(d + e*x)/sqrt((a*e - b*d)/b))/(b**2*sqrt((a*e - b*d)/b)))/e","A",0
2070,1,44,0,96.514722," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)/(e*x+d)**(1/2),x)","- \frac{2 \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{b}{a e - b d}} \sqrt{d + e x}} \right)}}{\sqrt{\frac{b}{a e - b d}} \left(a e - b d\right)}"," ",0,"-2*atan(1/(sqrt(b/(a*e - b*d))*sqrt(d + e*x)))/(sqrt(b/(a*e - b*d))*(a*e - b*d))","A",0
2071,1,60,0,121.043542," ","integrate((b*x+a)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{2}{\sqrt{d + e x} \left(a e - b d\right)} - \frac{2 \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e - b d}{b}}} \right)}}{\sqrt{\frac{a e - b d}{b}} \left(a e - b d\right)}"," ",0,"-2/(sqrt(d + e*x)*(a*e - b*d)) - 2*atan(sqrt(d + e*x)/sqrt((a*e - b*d)/b))/(sqrt((a*e - b*d)/b)*(a*e - b*d))","A",0
2072,1,83,0,136.913158," ","integrate((b*x+a)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2),x)","\frac{2 b}{\sqrt{d + e x} \left(a e - b d\right)^{2}} + \frac{2 b \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e - b d}{b}}} \right)}}{\sqrt{\frac{a e - b d}{b}} \left(a e - b d\right)^{2}} - \frac{2}{3 \left(d + e x\right)^{\frac{3}{2}} \left(a e - b d\right)}"," ",0,"2*b/(sqrt(d + e*x)*(a*e - b*d)**2) + 2*b*atan(sqrt(d + e*x)/sqrt((a*e - b*d)/b))/(sqrt((a*e - b*d)/b)*(a*e - b*d)**2) - 2/(3*(d + e*x)**(3/2)*(a*e - b*d))","A",0
2073,1,109,0,140.180399," ","integrate((b*x+a)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2),x)","- \frac{2 b^{2}}{\sqrt{d + e x} \left(a e - b d\right)^{3}} - \frac{2 b^{2} \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{\frac{a e - b d}{b}}} \right)}}{\sqrt{\frac{a e - b d}{b}} \left(a e - b d\right)^{3}} + \frac{2 b}{3 \left(d + e x\right)^{\frac{3}{2}} \left(a e - b d\right)^{2}} - \frac{2}{5 \left(d + e x\right)^{\frac{5}{2}} \left(a e - b d\right)}"," ",0,"-2*b**2/(sqrt(d + e*x)*(a*e - b*d)**3) - 2*b**2*atan(sqrt(d + e*x)/sqrt((a*e - b*d)/b))/(sqrt((a*e - b*d)/b)*(a*e - b*d)**3) + 2*b/(3*(d + e*x)**(3/2)*(a*e - b*d)**2) - 2/(5*(d + e*x)**(5/2)*(a*e - b*d))","A",0
2074,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2075,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2076,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2077,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2078,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2079,-1,0,0,0.000000," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2080,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2081,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2082,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2083,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(11/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2084,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(9/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2085,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2086,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2087,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2088,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2089,-1,0,0,0.000000," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2090,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2091,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2092,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2093,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2094,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)*((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2095,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(1/2)*((b*x+a)**2)**(1/2),x)","\int \left(a + b x\right) \sqrt{d + e x} \sqrt{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((a + b*x)*sqrt(d + e*x)*sqrt((a + b*x)**2), x)","F",0
2096,0,0,0,0.000000," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\left(a + b x\right) \sqrt{\left(a + b x\right)^{2}}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*x)*sqrt((a + b*x)**2)/sqrt(d + e*x), x)","F",0
2097,0,0,0,0.000000," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\left(a + b x\right) \sqrt{\left(a + b x\right)^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*sqrt((a + b*x)**2)/(d + e*x)**(3/2), x)","F",0
2098,-1,0,0,0.000000," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2099,-1,0,0,0.000000," ","integrate((b*x+a)*((b*x+a)**2)**(1/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2100,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2101,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2102,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)*(e*x+d)**(1/2),x)","\int \left(a + b x\right) \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*sqrt(d + e*x)*((a + b*x)**2)**(3/2), x)","F",0
2103,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2104,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**(3/2), x)","F",0
2105,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**(5/2), x)","F",0
2106,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**(3/2)/(d + e*x)**(7/2), x)","F",0
2107,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2108,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2109,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2110,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2111,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2112,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)*(e*x+d)**(1/2),x)","\int \left(a + b x\right) \sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)*sqrt(d + e*x)*((a + b*x)**2)**(5/2), x)","F",0
2113,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2114,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2115,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2116,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2117,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2118,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2119,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2120,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2121,-1,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2122,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2123,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2124,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{\frac{3}{2}}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**(3/2)/sqrt((a + b*x)**2), x)","F",0
2125,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{\left(a + b x\right) \sqrt{d + e x}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((a + b*x)*sqrt(d + e*x)/sqrt((a + b*x)**2), x)","F",0
2126,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(1/2)/((b*x+a)**2)**(1/2),x)","\int \frac{a + b x}{\sqrt{d + e x} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((a + b*x)/(sqrt(d + e*x)*sqrt((a + b*x)**2)), x)","F",0
2127,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(3/2)/((b*x+a)**2)**(1/2),x)","\int \frac{a + b x}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)**(3/2)*sqrt((a + b*x)**2)), x)","F",0
2128,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(5/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2129,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(7/2)/((b*x+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2130,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2131,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2132,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{\frac{3}{2}}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**(3/2)/((a + b*x)**2)**(3/2), x)","F",0
2133,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(a + b x\right) \sqrt{d + e x}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)*sqrt(d + e*x)/((a + b*x)**2)**(3/2), x)","F",0
2134,0,0,0,0.000000," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{a + b x}{\sqrt{d + e x} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/(sqrt(d + e*x)*((a + b*x)**2)**(3/2)), x)","F",0
2135,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{a + b x}{\left(d + e x\right)^{\frac{3}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)**(3/2)*((a + b*x)**2)**(3/2)), x)","F",0
2136,0,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{a + b x}{\left(d + e x\right)^{\frac{5}{2}} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/((d + e*x)**(5/2)*((a + b*x)**2)**(3/2)), x)","F",0
2137,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2138,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2139,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2140,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2141,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**(1/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2142,-1,0,0,0.000000," ","integrate((b*x+a)/(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2143,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(3/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2144,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(5/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2145,-1,0,0,0.000000," ","integrate((b*x+a)/(e*x+d)**(7/2)/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2146,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2147,-1,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2148,1,4058,0,4.732541," ","integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2),x)","\begin{cases} d^{m} \left(a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{2 a^{3} e^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 a^{2} b d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{9 a^{2} b e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 a b^{2} d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{18 a b^{2} d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{18 a b^{2} e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 b^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 b^{3} d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 b^{3} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 b^{3} d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 b^{3} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 b^{3} d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 b^{3} e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{a^{3} e^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{3 a^{2} b d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 a^{2} b e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 a b^{2} d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{9 a b^{2} d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{12 a b^{2} d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{12 a b^{2} d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{6 a b^{2} e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 b^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 b^{3} d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 b^{3} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 b^{3} d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 b^{3} d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 b^{3} e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\- \frac{2 a^{3} e^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a^{2} b d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a^{2} b d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a^{2} b e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{12 a b^{2} d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{12 a b^{2} d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{12 a b^{2} d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 a b^{2} e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 b^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 b^{3} d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 b^{3} d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 b^{3} d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{b^{3} e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\\frac{a^{3} \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{3 a^{2} b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{3 a^{2} b x}{e} + \frac{3 a b^{2} d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{3 a b^{2} d x}{e^{2}} + \frac{3 a b^{2} x^{2}}{2 e} - \frac{b^{3} d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{b^{3} d^{2} x}{e^{3}} - \frac{b^{3} d x^{2}}{2 e^{2}} + \frac{b^{3} x^{3}}{3 e} & \text{for}\: m = -1 \\\frac{a^{3} d e^{3} m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 a^{3} d e^{3} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 a^{3} d e^{3} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a^{3} d e^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a^{3} e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 a^{3} e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 a^{3} e^{4} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a^{3} e^{4} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 a^{2} b d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{21 a^{2} b d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{36 a^{2} b d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 a^{2} b d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{21 a^{2} b d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{36 a^{2} b d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 a^{2} b e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a^{2} b e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{57 a^{2} b e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{36 a^{2} b e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 a b^{2} d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a b^{2} d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 a b^{2} d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{24 a b^{2} d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 a b^{2} d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{15 a b^{2} d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 a b^{2} d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 a b^{2} e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{21 a b^{2} e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{42 a b^{2} e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a b^{2} e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 b^{3} d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 b^{3} d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 b^{3} d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 b^{3} d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b^{3} d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 b^{3} d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 b^{3} d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b^{3} e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 b^{3} e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 b^{3} e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 b^{3} e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4), Eq(e, 0)), (-2*a**3*e**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*a**2*b*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 9*a**2*b*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*a*b**2*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 18*a*b**2*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 18*a*b**2*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*b**3*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*b**3*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*b**3*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*b**3*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*b**3*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*b**3*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*b**3*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-a**3*e**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 3*a**2*b*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*a**2*b*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*a*b**2*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 9*a*b**2*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 12*a*b**2*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 12*a*b**2*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 6*a*b**2*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*b**3*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*b**3*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*b**3*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*b**3*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*b**3*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*b**3*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (-2*a**3*e**3/(2*d*e**4 + 2*e**5*x) + 6*a**2*b*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*a**2*b*d*e**2/(2*d*e**4 + 2*e**5*x) + 6*a**2*b*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 12*a*b**2*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 12*a*b**2*d**2*e/(2*d*e**4 + 2*e**5*x) - 12*a*b**2*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*a*b**2*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 6*b**3*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*b**3*d**3/(2*d*e**4 + 2*e**5*x) + 6*b**3*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*b**3*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + b**3*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (a**3*log(d/e + x)/e - 3*a**2*b*d*log(d/e + x)/e**2 + 3*a**2*b*x/e + 3*a*b**2*d**2*log(d/e + x)/e**3 - 3*a*b**2*d*x/e**2 + 3*a*b**2*x**2/(2*e) - b**3*d**3*log(d/e + x)/e**4 + b**3*d**2*x/e**3 - b**3*d*x**2/(2*e**2) + b**3*x**3/(3*e), Eq(m, -1)), (a**3*d*e**3*m**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*a**3*d*e**3*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*a**3*d*e**3*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a**3*d*e**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a**3*e**4*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*a**3*e**4*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*a**3*e**4*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a**3*e**4*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*a**2*b*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 21*a**2*b*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 36*a**2*b*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*a**2*b*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 21*a**2*b*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 36*a**2*b*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*a**2*b*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a**2*b*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 57*a**2*b*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 36*a**2*b*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*a*b**2*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*b**2*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*a*b**2*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 24*a*b**2*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*a*b**2*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 15*a*b**2*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*a*b**2*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*a*b**2*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 21*a*b**2*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 42*a*b**2*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*b**2*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*b**3*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*b**3*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*b**3*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*b**3*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b**3*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*b**3*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*b**3*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b**3*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*b**3*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*b**3*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*b**3*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
2149,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2),x)","\int \frac{\left(d + e x\right)^{m}}{a + b x}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x), x)","F",0
2150,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**2,x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b x\right)^{3}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*x)**3, x)","F",0
2151,-2,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2152,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{m} \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**m*((a + b*x)**2)**(3/2), x)","F",0
2153,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(1/2),x)","\int \left(a + b x\right) \left(d + e x\right)^{m} \sqrt{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**m*sqrt((a + b*x)**2), x)","F",0
2154,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(1/2),x)","\int \frac{\left(a + b x\right) \left(d + e x\right)^{m}}{\sqrt{\left(a + b x\right)^{2}}}\, dx"," ",0,"Integral((a + b*x)*(d + e*x)**m/sqrt((a + b*x)**2), x)","F",0
2155,-2,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2156,-2,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2157,-2,0,0,0.000000," ","integrate((b*c*x+a*c)*(e*x+d)**(-3-2*p)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2158,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} a \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\int \frac{\left(a + b x\right) \left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{5}{2}}}\, dx & \text{for}\: p = - \frac{5}{2} \\- \frac{6 a^{3} e^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{11 a^{3} e^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{6 a^{2} b d e^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{9 a^{2} b d e^{2}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b e^{3} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{16 a^{2} b e^{3} x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{3 a b^{2} d^{2} e}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{12 a b^{2} d e^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{12 a b^{2} d e^{2} x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} e^{3} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{2 a b^{2} e^{3} x^{2}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{b^{3} d^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 b^{3} d^{2} e x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{6 b^{3} d e^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} e^{3} x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: p = -2 \\\int \frac{\left(a + b x\right) \left(d + e x\right)^{3}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\- \frac{a^{3} e^{3} \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{3 a^{2} d e^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} + \frac{a^{2} e^{3} x}{b^{3}} - \frac{3 a d^{2} e \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{3 a d e^{2} x}{b^{2}} - \frac{a e^{3} x^{2}}{2 b^{2}} + \frac{d^{3} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{3 d^{2} e x}{b} + \frac{3 d e^{2} x^{2}}{2 b} + \frac{e^{3} x^{3}}{3 b} & \text{for}\: p = -1 \\- \frac{3 a^{5} e^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{6 a^{4} b d e^{2} p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{15 a^{4} b d e^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{6 a^{4} b e^{3} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{6 a^{3} b^{2} d^{2} e p^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{27 a^{3} b^{2} d^{2} e p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{30 a^{3} b^{2} d^{2} e \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{12 a^{3} b^{2} d e^{2} p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{30 a^{3} b^{2} d e^{2} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{6 a^{3} b^{2} e^{3} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} - \frac{3 a^{3} b^{2} e^{3} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{4 a^{2} b^{3} d^{3} p^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{24 a^{2} b^{3} d^{3} p^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{47 a^{2} b^{3} d^{3} p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{30 a^{2} b^{3} d^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{12 a^{2} b^{3} d^{2} e p^{3} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{54 a^{2} b^{3} d^{2} e p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{60 a^{2} b^{3} d^{2} e p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{12 a^{2} b^{3} d e^{2} p^{3} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{36 a^{2} b^{3} d e^{2} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{15 a^{2} b^{3} d e^{2} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{4 a^{2} b^{3} e^{3} p^{3} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{6 a^{2} b^{3} e^{3} p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{2 a^{2} b^{3} e^{3} p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{8 a b^{4} d^{3} p^{3} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{48 a b^{4} d^{3} p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{94 a b^{4} d^{3} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{60 a b^{4} d^{3} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{24 a b^{4} d^{2} e p^{3} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{126 a b^{4} d^{2} e p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{201 a b^{4} d^{2} e p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{90 a b^{4} d^{2} e x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{24 a b^{4} d e^{2} p^{3} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{108 a b^{4} d e^{2} p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{144 a b^{4} d e^{2} p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{60 a b^{4} d e^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{8 a b^{4} e^{3} p^{3} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{30 a b^{4} e^{3} p^{2} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{37 a b^{4} e^{3} p x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{15 a b^{4} e^{3} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{4 b^{5} d^{3} p^{3} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{24 b^{5} d^{3} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{47 b^{5} d^{3} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{30 b^{5} d^{3} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{12 b^{5} d^{2} e p^{3} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{66 b^{5} d^{2} e p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{114 b^{5} d^{2} e p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{60 b^{5} d^{2} e x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{12 b^{5} d e^{2} p^{3} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{60 b^{5} d e^{2} p^{2} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{93 b^{5} d e^{2} p x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{45 b^{5} d e^{2} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{4 b^{5} e^{3} p^{3} x^{5} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{18 b^{5} e^{3} p^{2} x^{5} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{26 b^{5} e^{3} p x^{5} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} + \frac{12 b^{5} e^{3} x^{5} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{8 b^{4} p^{4} + 56 b^{4} p^{3} + 142 b^{4} p^{2} + 154 b^{4} p + 60 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4)*(a**2)**p, Eq(b, 0)), (Integral((a + b*x)*(d + e*x)**3/((a + b*x)**2)**(5/2), x), Eq(p, -5/2)), (-6*a**3*e**3*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 11*a**3*e**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 6*a**2*b*d*e**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 9*a**2*b*d*e**2/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*e**3*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 16*a**2*b*e**3*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 3*a*b**2*d**2*e/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 12*a*b**2*d*e**2*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 12*a*b**2*d*e**2*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*e**3*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 2*a*b**2*e**3*x**2/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - b**3*d**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*b**3*d**2*e*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 6*b**3*d*e**2*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*e**3*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(p, -2)), (Integral((a + b*x)*(d + e*x)**3/((a + b*x)**2)**(3/2), x), Eq(p, -3/2)), (-a**3*e**3*log(a/b + x)/b**4 + 3*a**2*d*e**2*log(a/b + x)/b**3 + a**2*e**3*x/b**3 - 3*a*d**2*e*log(a/b + x)/b**2 - 3*a*d*e**2*x/b**2 - a*e**3*x**2/(2*b**2) + d**3*log(a/b + x)/b + 3*d**2*e*x/b + 3*d*e**2*x**2/(2*b) + e**3*x**3/(3*b), Eq(p, -1)), (-3*a**5*e**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 6*a**4*b*d*e**2*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 15*a**4*b*d*e**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 6*a**4*b*e**3*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 6*a**3*b**2*d**2*e*p**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 27*a**3*b**2*d**2*e*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 30*a**3*b**2*d**2*e*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 12*a**3*b**2*d*e**2*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 30*a**3*b**2*d*e**2*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 6*a**3*b**2*e**3*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) - 3*a**3*b**2*e**3*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 4*a**2*b**3*d**3*p**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 24*a**2*b**3*d**3*p**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 47*a**2*b**3*d**3*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 30*a**2*b**3*d**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 12*a**2*b**3*d**2*e*p**3*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 54*a**2*b**3*d**2*e*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 60*a**2*b**3*d**2*e*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 12*a**2*b**3*d*e**2*p**3*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 36*a**2*b**3*d*e**2*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 15*a**2*b**3*d*e**2*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 4*a**2*b**3*e**3*p**3*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 6*a**2*b**3*e**3*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 2*a**2*b**3*e**3*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 8*a*b**4*d**3*p**3*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 48*a*b**4*d**3*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 94*a*b**4*d**3*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 60*a*b**4*d**3*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 24*a*b**4*d**2*e*p**3*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 126*a*b**4*d**2*e*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 201*a*b**4*d**2*e*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 90*a*b**4*d**2*e*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 24*a*b**4*d*e**2*p**3*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 108*a*b**4*d*e**2*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 144*a*b**4*d*e**2*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 60*a*b**4*d*e**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 8*a*b**4*e**3*p**3*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 30*a*b**4*e**3*p**2*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 37*a*b**4*e**3*p*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 15*a*b**4*e**3*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 4*b**5*d**3*p**3*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 24*b**5*d**3*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 47*b**5*d**3*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 30*b**5*d**3*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 12*b**5*d**2*e*p**3*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 66*b**5*d**2*e*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 114*b**5*d**2*e*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 60*b**5*d**2*e*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 12*b**5*d*e**2*p**3*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 60*b**5*d*e**2*p**2*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 93*b**5*d*e**2*p*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 45*b**5*d*e**2*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 4*b**5*e**3*p**3*x**5*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 18*b**5*e**3*p**2*x**5*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 26*b**5*e**3*p*x**5*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4) + 12*b**5*e**3*x**5*(a**2 + 2*a*b*x + b**2*x**2)**p/(8*b**4*p**4 + 56*b**4*p**3 + 142*b**4*p**2 + 154*b**4*p + 60*b**4), True))","F",0
2159,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)**2*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} a \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\frac{2 a^{2} e^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2} e^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{2 a b d e}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b e^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b e^{2} x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{b^{2} d^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{4 b^{2} d e x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} e^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: p = -2 \\\int \frac{\left(a + b x\right) \left(d + e x\right)^{2}}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\\frac{a^{2} e^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{2 a d e \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{a e^{2} x}{b^{2}} + \frac{d^{2} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{2 d e x}{b} + \frac{e^{2} x^{2}}{2 b} & \text{for}\: p = -1 \\\frac{a^{4} e^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} - \frac{2 a^{3} b d e p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} - \frac{4 a^{3} b d e \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} - \frac{2 a^{3} b e^{2} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{2 a^{2} b^{2} d^{2} p^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{7 a^{2} b^{2} d^{2} p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{6 a^{2} b^{2} d^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{4 a^{2} b^{2} d e p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{8 a^{2} b^{2} d e p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{2 a^{2} b^{2} e^{2} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{a^{2} b^{2} e^{2} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{4 a b^{3} d^{2} p^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{14 a b^{3} d^{2} p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{12 a b^{3} d^{2} x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{8 a b^{3} d e p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{22 a b^{3} d e p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{12 a b^{3} d e x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{4 a b^{3} e^{2} p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{8 a b^{3} e^{2} p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{4 a b^{3} e^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{2 b^{4} d^{2} p^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{7 b^{4} d^{2} p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{6 b^{4} d^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{4 b^{4} d e p^{2} x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{12 b^{4} d e p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{8 b^{4} d e x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{2 b^{4} e^{2} p^{2} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{5 b^{4} e^{2} p x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} + \frac{3 b^{4} e^{2} x^{4} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{3} p^{3} + 18 b^{3} p^{2} + 26 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(d**2*x + d*e*x**2 + e**2*x**3/3)*(a**2)**p, Eq(b, 0)), (2*a**2*e**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2*e**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - 2*a*b*d*e/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*e**2*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*e**2*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - b**2*d**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - 4*b**2*d*e*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*e**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(p, -2)), (Integral((a + b*x)*(d + e*x)**2/((a + b*x)**2)**(3/2), x), Eq(p, -3/2)), (a**2*e**2*log(a/b + x)/b**3 - 2*a*d*e*log(a/b + x)/b**2 - a*e**2*x/b**2 + d**2*log(a/b + x)/b + 2*d*e*x/b + e**2*x**2/(2*b), Eq(p, -1)), (a**4*e**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) - 2*a**3*b*d*e*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) - 4*a**3*b*d*e*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) - 2*a**3*b*e**2*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 2*a**2*b**2*d**2*p**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 7*a**2*b**2*d**2*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 6*a**2*b**2*d**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 4*a**2*b**2*d*e*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 8*a**2*b**2*d*e*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 2*a**2*b**2*e**2*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + a**2*b**2*e**2*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 4*a*b**3*d**2*p**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 14*a*b**3*d**2*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 12*a*b**3*d**2*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 8*a*b**3*d*e*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 22*a*b**3*d*e*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 12*a*b**3*d*e*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 4*a*b**3*e**2*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 8*a*b**3*e**2*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 4*a*b**3*e**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 2*b**4*d**2*p**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 7*b**4*d**2*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 6*b**4*d**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 4*b**4*d*e*p**2*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 12*b**4*d*e*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 8*b**4*d*e*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 2*b**4*e**2*p**2*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 5*b**4*e**2*p*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3) + 3*b**4*e**2*x**4*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**3*p**3 + 18*b**3*p**2 + 26*b**3*p + 12*b**3), True))","F",0
2160,0,0,0,0.000000," ","integrate((b*x+a)*(e*x+d)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} a \left(d x + \frac{e x^{2}}{2}\right) \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\int \frac{\left(a + b x\right) \left(d + e x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\- \frac{a e \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{d \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{e x}{b} & \text{for}\: p = -1 \\- \frac{a^{3} e \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{2 a^{2} b d p \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{3 a^{2} b d \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{2 a^{2} b e p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{4 a b^{2} d p x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{6 a b^{2} d x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{4 a b^{2} e p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{3 a b^{2} e x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{2 b^{3} d p x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{3 b^{3} d x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{2 b^{3} e p x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} + \frac{2 b^{3} e x^{3} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{4 b^{2} p^{2} + 10 b^{2} p + 6 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(d*x + e*x**2/2)*(a**2)**p, Eq(b, 0)), (Integral((a + b*x)*(d + e*x)/((a + b*x)**2)**(3/2), x), Eq(p, -3/2)), (-a*e*log(a/b + x)/b**2 + d*log(a/b + x)/b + e*x/b, Eq(p, -1)), (-a**3*e*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 2*a**2*b*d*p*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 3*a**2*b*d*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 2*a**2*b*e*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 4*a*b**2*d*p*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 6*a*b**2*d*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 4*a*b**2*e*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 3*a*b**2*e*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 2*b**3*d*p*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 3*b**3*d*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 2*b**3*e*p*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2) + 2*b**3*e*x**3*(a**2 + 2*a*b*x + b**2*x**2)**p/(4*b**2*p**2 + 10*b**2*p + 6*b**2), True))","F",0
2161,1,119,0,0.475157," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\begin{cases} \frac{x}{a} & \text{for}\: b = 0 \wedge p = -1 \\a x \left(a^{2}\right)^{p} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x \right)}}{b} & \text{for}\: p = -1 \\\frac{a^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{2 b p + 2 b} + \frac{2 a b x \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{2 b p + 2 b} + \frac{b^{2} x^{2} \left(a^{2} + 2 a b x + b^{2} x^{2}\right)^{p}}{2 b p + 2 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a, Eq(b, 0) & Eq(p, -1)), (a*x*(a**2)**p, Eq(b, 0)), (log(a/b + x)/b, Eq(p, -1)), (a**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(2*b*p + 2*b) + 2*a*b*x*(a**2 + 2*a*b*x + b**2*x**2)**p/(2*b*p + 2*b) + b**2*x**2*(a**2 + 2*a*b*x + b**2*x**2)**p/(2*b*p + 2*b), True))","A",0
2162,0,0,0,0.000000," ","integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**p/(e*x+d),x)","\int \frac{\left(a + b x\right) \left(\left(a + b x\right)^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral((a + b*x)*((a + b*x)**2)**p/(d + e*x), x)","F",0
2163,1,1488,0,7.824989," ","integrate((B*x+A)*(b*c*x+a*c)**m*(b**2*x**2+2*a*b*x+a**2)**3,x)","\begin{cases} a^{6} \left(a c\right)^{m} \left(A x + \frac{B x^{2}}{2}\right) & \text{for}\: b = 0 \\- \frac{A b}{a b^{2} c^{8} + b^{3} c^{8} x} + \frac{B a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} c^{8} + b^{3} c^{8} x} + \frac{B a}{a b^{2} c^{8} + b^{3} c^{8} x} + \frac{B b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} c^{8} + b^{3} c^{8} x} & \text{for}\: m = -8 \\\frac{A \log{\left(\frac{a}{b} + x \right)}}{b c^{7}} - \frac{B a \log{\left(\frac{a}{b} + x \right)}}{b^{2} c^{7}} + \frac{B x}{b c^{7}} & \text{for}\: m = -7 \\\frac{A a^{7} b m \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{8 A a^{7} b \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{7 A a^{6} b^{2} m x \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{56 A a^{6} b^{2} x \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{21 A a^{5} b^{3} m x^{2} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{168 A a^{5} b^{3} x^{2} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{35 A a^{4} b^{4} m x^{3} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{280 A a^{4} b^{4} x^{3} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{35 A a^{3} b^{5} m x^{4} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{280 A a^{3} b^{5} x^{4} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{21 A a^{2} b^{6} m x^{5} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{168 A a^{2} b^{6} x^{5} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{7 A a b^{7} m x^{6} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{56 A a b^{7} x^{6} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{A b^{8} m x^{7} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{8 A b^{8} x^{7} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} - \frac{B a^{8} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{B a^{7} b m x \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{7 B a^{6} b^{2} m x^{2} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{28 B a^{6} b^{2} x^{2} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{21 B a^{5} b^{3} m x^{3} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{112 B a^{5} b^{3} x^{3} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{35 B a^{4} b^{4} m x^{4} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{210 B a^{4} b^{4} x^{4} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{35 B a^{3} b^{5} m x^{5} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{224 B a^{3} b^{5} x^{5} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{21 B a^{2} b^{6} m x^{6} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{140 B a^{2} b^{6} x^{6} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{7 B a b^{7} m x^{7} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{48 B a b^{7} x^{7} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{B b^{8} m x^{8} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} + \frac{7 B b^{8} x^{8} \left(a c + b c x\right)^{m}}{b^{2} m^{2} + 15 b^{2} m + 56 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*(a*c)**m*(A*x + B*x**2/2), Eq(b, 0)), (-A*b/(a*b**2*c**8 + b**3*c**8*x) + B*a*log(a/b + x)/(a*b**2*c**8 + b**3*c**8*x) + B*a/(a*b**2*c**8 + b**3*c**8*x) + B*b*x*log(a/b + x)/(a*b**2*c**8 + b**3*c**8*x), Eq(m, -8)), (A*log(a/b + x)/(b*c**7) - B*a*log(a/b + x)/(b**2*c**7) + B*x/(b*c**7), Eq(m, -7)), (A*a**7*b*m*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 8*A*a**7*b*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 7*A*a**6*b**2*m*x*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 56*A*a**6*b**2*x*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 21*A*a**5*b**3*m*x**2*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 168*A*a**5*b**3*x**2*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 35*A*a**4*b**4*m*x**3*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 280*A*a**4*b**4*x**3*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 35*A*a**3*b**5*m*x**4*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 280*A*a**3*b**5*x**4*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 21*A*a**2*b**6*m*x**5*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 168*A*a**2*b**6*x**5*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 7*A*a*b**7*m*x**6*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 56*A*a*b**7*x**6*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + A*b**8*m*x**7*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 8*A*b**8*x**7*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) - B*a**8*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + B*a**7*b*m*x*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 7*B*a**6*b**2*m*x**2*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 28*B*a**6*b**2*x**2*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 21*B*a**5*b**3*m*x**3*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 112*B*a**5*b**3*x**3*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 35*B*a**4*b**4*m*x**4*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 210*B*a**4*b**4*x**4*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 35*B*a**3*b**5*m*x**5*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 224*B*a**3*b**5*x**5*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 21*B*a**2*b**6*m*x**6*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 140*B*a**2*b**6*x**6*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 7*B*a*b**7*m*x**7*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 48*B*a*b**7*x**7*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + B*b**8*m*x**8*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2) + 7*B*b**8*x**8*(a*c + b*c*x)**m/(b**2*m**2 + 15*b**2*m + 56*b**2), True))","A",0
2164,1,1268,0,5.733035," ","integrate((B*x+A)*(b*c*x+a*c)**m/(b**2*x**2+2*a*b*x+a**2)**3,x)","\begin{cases} \frac{\left(a c\right)^{m} \left(A x + \frac{B x^{2}}{2}\right)}{a^{6}} & \text{for}\: b = 0 \\- \frac{A b c^{4}}{a b^{2} + b^{3} x} + \frac{B a c^{4} \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{B a c^{4}}{a b^{2} + b^{3} x} + \frac{B b c^{4} x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: m = 4 \\\frac{A c^{5} \log{\left(\frac{a}{b} + x \right)}}{b} - \frac{B a c^{5} \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{B c^{5} x}{b} & \text{for}\: m = 5 \\\frac{A b m \left(a c + b c x\right)^{m}}{a^{5} b^{2} m^{2} - 9 a^{5} b^{2} m + 20 a^{5} b^{2} + 5 a^{4} b^{3} m^{2} x - 45 a^{4} b^{3} m x + 100 a^{4} b^{3} x + 10 a^{3} b^{4} m^{2} x^{2} - 90 a^{3} b^{4} m x^{2} + 200 a^{3} b^{4} x^{2} + 10 a^{2} b^{5} m^{2} x^{3} - 90 a^{2} b^{5} m x^{3} + 200 a^{2} b^{5} x^{3} + 5 a b^{6} m^{2} x^{4} - 45 a b^{6} m x^{4} + 100 a b^{6} x^{4} + b^{7} m^{2} x^{5} - 9 b^{7} m x^{5} + 20 b^{7} x^{5}} - \frac{4 A b \left(a c + b c x\right)^{m}}{a^{5} b^{2} m^{2} - 9 a^{5} b^{2} m + 20 a^{5} b^{2} + 5 a^{4} b^{3} m^{2} x - 45 a^{4} b^{3} m x + 100 a^{4} b^{3} x + 10 a^{3} b^{4} m^{2} x^{2} - 90 a^{3} b^{4} m x^{2} + 200 a^{3} b^{4} x^{2} + 10 a^{2} b^{5} m^{2} x^{3} - 90 a^{2} b^{5} m x^{3} + 200 a^{2} b^{5} x^{3} + 5 a b^{6} m^{2} x^{4} - 45 a b^{6} m x^{4} + 100 a b^{6} x^{4} + b^{7} m^{2} x^{5} - 9 b^{7} m x^{5} + 20 b^{7} x^{5}} - \frac{B a \left(a c + b c x\right)^{m}}{a^{5} b^{2} m^{2} - 9 a^{5} b^{2} m + 20 a^{5} b^{2} + 5 a^{4} b^{3} m^{2} x - 45 a^{4} b^{3} m x + 100 a^{4} b^{3} x + 10 a^{3} b^{4} m^{2} x^{2} - 90 a^{3} b^{4} m x^{2} + 200 a^{3} b^{4} x^{2} + 10 a^{2} b^{5} m^{2} x^{3} - 90 a^{2} b^{5} m x^{3} + 200 a^{2} b^{5} x^{3} + 5 a b^{6} m^{2} x^{4} - 45 a b^{6} m x^{4} + 100 a b^{6} x^{4} + b^{7} m^{2} x^{5} - 9 b^{7} m x^{5} + 20 b^{7} x^{5}} + \frac{B b m x \left(a c + b c x\right)^{m}}{a^{5} b^{2} m^{2} - 9 a^{5} b^{2} m + 20 a^{5} b^{2} + 5 a^{4} b^{3} m^{2} x - 45 a^{4} b^{3} m x + 100 a^{4} b^{3} x + 10 a^{3} b^{4} m^{2} x^{2} - 90 a^{3} b^{4} m x^{2} + 200 a^{3} b^{4} x^{2} + 10 a^{2} b^{5} m^{2} x^{3} - 90 a^{2} b^{5} m x^{3} + 200 a^{2} b^{5} x^{3} + 5 a b^{6} m^{2} x^{4} - 45 a b^{6} m x^{4} + 100 a b^{6} x^{4} + b^{7} m^{2} x^{5} - 9 b^{7} m x^{5} + 20 b^{7} x^{5}} - \frac{5 B b x \left(a c + b c x\right)^{m}}{a^{5} b^{2} m^{2} - 9 a^{5} b^{2} m + 20 a^{5} b^{2} + 5 a^{4} b^{3} m^{2} x - 45 a^{4} b^{3} m x + 100 a^{4} b^{3} x + 10 a^{3} b^{4} m^{2} x^{2} - 90 a^{3} b^{4} m x^{2} + 200 a^{3} b^{4} x^{2} + 10 a^{2} b^{5} m^{2} x^{3} - 90 a^{2} b^{5} m x^{3} + 200 a^{2} b^{5} x^{3} + 5 a b^{6} m^{2} x^{4} - 45 a b^{6} m x^{4} + 100 a b^{6} x^{4} + b^{7} m^{2} x^{5} - 9 b^{7} m x^{5} + 20 b^{7} x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a*c)**m*(A*x + B*x**2/2)/a**6, Eq(b, 0)), (-A*b*c**4/(a*b**2 + b**3*x) + B*a*c**4*log(a/b + x)/(a*b**2 + b**3*x) + B*a*c**4/(a*b**2 + b**3*x) + B*b*c**4*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(m, 4)), (A*c**5*log(a/b + x)/b - B*a*c**5*log(a/b + x)/b**2 + B*c**5*x/b, Eq(m, 5)), (A*b*m*(a*c + b*c*x)**m/(a**5*b**2*m**2 - 9*a**5*b**2*m + 20*a**5*b**2 + 5*a**4*b**3*m**2*x - 45*a**4*b**3*m*x + 100*a**4*b**3*x + 10*a**3*b**4*m**2*x**2 - 90*a**3*b**4*m*x**2 + 200*a**3*b**4*x**2 + 10*a**2*b**5*m**2*x**3 - 90*a**2*b**5*m*x**3 + 200*a**2*b**5*x**3 + 5*a*b**6*m**2*x**4 - 45*a*b**6*m*x**4 + 100*a*b**6*x**4 + b**7*m**2*x**5 - 9*b**7*m*x**5 + 20*b**7*x**5) - 4*A*b*(a*c + b*c*x)**m/(a**5*b**2*m**2 - 9*a**5*b**2*m + 20*a**5*b**2 + 5*a**4*b**3*m**2*x - 45*a**4*b**3*m*x + 100*a**4*b**3*x + 10*a**3*b**4*m**2*x**2 - 90*a**3*b**4*m*x**2 + 200*a**3*b**4*x**2 + 10*a**2*b**5*m**2*x**3 - 90*a**2*b**5*m*x**3 + 200*a**2*b**5*x**3 + 5*a*b**6*m**2*x**4 - 45*a*b**6*m*x**4 + 100*a*b**6*x**4 + b**7*m**2*x**5 - 9*b**7*m*x**5 + 20*b**7*x**5) - B*a*(a*c + b*c*x)**m/(a**5*b**2*m**2 - 9*a**5*b**2*m + 20*a**5*b**2 + 5*a**4*b**3*m**2*x - 45*a**4*b**3*m*x + 100*a**4*b**3*x + 10*a**3*b**4*m**2*x**2 - 90*a**3*b**4*m*x**2 + 200*a**3*b**4*x**2 + 10*a**2*b**5*m**2*x**3 - 90*a**2*b**5*m*x**3 + 200*a**2*b**5*x**3 + 5*a*b**6*m**2*x**4 - 45*a*b**6*m*x**4 + 100*a*b**6*x**4 + b**7*m**2*x**5 - 9*b**7*m*x**5 + 20*b**7*x**5) + B*b*m*x*(a*c + b*c*x)**m/(a**5*b**2*m**2 - 9*a**5*b**2*m + 20*a**5*b**2 + 5*a**4*b**3*m**2*x - 45*a**4*b**3*m*x + 100*a**4*b**3*x + 10*a**3*b**4*m**2*x**2 - 90*a**3*b**4*m*x**2 + 200*a**3*b**4*x**2 + 10*a**2*b**5*m**2*x**3 - 90*a**2*b**5*m*x**3 + 200*a**2*b**5*x**3 + 5*a*b**6*m**2*x**4 - 45*a*b**6*m*x**4 + 100*a*b**6*x**4 + b**7*m**2*x**5 - 9*b**7*m*x**5 + 20*b**7*x**5) - 5*B*b*x*(a*c + b*c*x)**m/(a**5*b**2*m**2 - 9*a**5*b**2*m + 20*a**5*b**2 + 5*a**4*b**3*m**2*x - 45*a**4*b**3*m*x + 100*a**4*b**3*x + 10*a**3*b**4*m**2*x**2 - 90*a**3*b**4*m*x**2 + 200*a**3*b**4*x**2 + 10*a**2*b**5*m**2*x**3 - 90*a**2*b**5*m*x**3 + 200*a**2*b**5*x**3 + 5*a*b**6*m**2*x**4 - 45*a*b**6*m*x**4 + 100*a*b**6*x**4 + b**7*m**2*x**5 - 9*b**7*m*x**5 + 20*b**7*x**5), True))","A",0
2165,0,0,0,0.000000," ","integrate((B*x+A)*(b*c*x+a*c)**m*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \left(c \left(a + b x\right)\right)^{m} \left(A + B x\right) \left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*(a + b*x))**m*(A + B*x)*((a + b*x)**2)**(3/2), x)","F",0
2166,0,0,0,0.000000," ","integrate((B*x+A)*(b*c*x+a*c)**m/(b**2*x**2+2*a*b*x+a**2)**(3/2),x)","\int \frac{\left(c \left(a + b x\right)\right)^{m} \left(A + B x\right)}{\left(\left(a + b x\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*(a + b*x))**m*(A + B*x)/((a + b*x)**2)**(3/2), x)","F",0
2167,-1,0,0,0.000000," ","integrate((b*c*x+a*c)**m*(g*x+f)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2168,-1,0,0,0.000000," ","integrate((b*c*x+a*c)**(-3-2*p)*(g*x+f)*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2169,-1,0,0,0.000000," ","integrate((b*x+a)*(b*c*x+a*c)**m*(b**2*x**2+2*a*b*x+a**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2170,1,270,0,3.924887," ","integrate((b*x+a)*(b*c*x+a*c)**m*(b**2*x**2+2*a*b*x+a**2)**3,x)","\begin{cases} \frac{x}{a c^{8}} & \text{for}\: b = 0 \wedge m = -8 \\a^{7} x \left(a c\right)^{m} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x \right)}}{b c^{8}} & \text{for}\: m = -8 \\\frac{a^{8} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{8 a^{7} b x \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{28 a^{6} b^{2} x^{2} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{56 a^{5} b^{3} x^{3} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{70 a^{4} b^{4} x^{4} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{56 a^{3} b^{5} x^{5} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{28 a^{2} b^{6} x^{6} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{8 a b^{7} x^{7} \left(a c + b c x\right)^{m}}{b m + 8 b} + \frac{b^{8} x^{8} \left(a c + b c x\right)^{m}}{b m + 8 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(a*c**8), Eq(b, 0) & Eq(m, -8)), (a**7*x*(a*c)**m, Eq(b, 0)), (log(a/b + x)/(b*c**8), Eq(m, -8)), (a**8*(a*c + b*c*x)**m/(b*m + 8*b) + 8*a**7*b*x*(a*c + b*c*x)**m/(b*m + 8*b) + 28*a**6*b**2*x**2*(a*c + b*c*x)**m/(b*m + 8*b) + 56*a**5*b**3*x**3*(a*c + b*c*x)**m/(b*m + 8*b) + 70*a**4*b**4*x**4*(a*c + b*c*x)**m/(b*m + 8*b) + 56*a**3*b**5*x**5*(a*c + b*c*x)**m/(b*m + 8*b) + 28*a**2*b**6*x**6*(a*c + b*c*x)**m/(b*m + 8*b) + 8*a*b**7*x**7*(a*c + b*c*x)**m/(b*m + 8*b) + b**8*x**8*(a*c + b*c*x)**m/(b*m + 8*b), True))","A",0
2171,1,136,0,4.178196," ","integrate((b*x+a)*(b*c*x+a*c)**m/(b**2*x**2+2*a*b*x+a**2)**3,x)","\begin{cases} \frac{c^{4} x}{a} & \text{for}\: b = 0 \wedge m = 4 \\\frac{x \left(a c\right)^{m}}{a^{5}} & \text{for}\: b = 0 \\\frac{c^{4} \log{\left(\frac{a}{b} + x \right)}}{b} & \text{for}\: m = 4 \\\frac{\left(a c + b c x\right)^{m}}{a^{4} b m - 4 a^{4} b + 4 a^{3} b^{2} m x - 16 a^{3} b^{2} x + 6 a^{2} b^{3} m x^{2} - 24 a^{2} b^{3} x^{2} + 4 a b^{4} m x^{3} - 16 a b^{4} x^{3} + b^{5} m x^{4} - 4 b^{5} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x/a, Eq(b, 0) & Eq(m, 4)), (x*(a*c)**m/a**5, Eq(b, 0)), (c**4*log(a/b + x)/b, Eq(m, 4)), ((a*c + b*c*x)**m/(a**4*b*m - 4*a**4*b + 4*a**3*b**2*m*x - 16*a**3*b**2*x + 6*a**2*b**3*m*x**2 - 24*a**2*b**3*x**2 + 4*a*b**4*m*x**3 - 16*a*b**4*x**3 + b**5*m*x**4 - 4*b**5*x**4), True))","A",0
2172,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{3} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**3*(f + g*x), x)","F",0
2173,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{2} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**2*(f + g*x), x)","F",0
2174,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right) \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)*(f + g*x), x)","F",0
2175,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{d + e x}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x), x)","F",0
2176,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**2, x)","F",0
2177,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**3, x)","F",0
2178,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**4, x)","F",0
2179,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**5, x)","F",0
2180,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**6,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**6, x)","F",0
2181,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**7,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**7, x)","F",0
2182,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**8,x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**8, x)","F",0
2183,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**3*(f + g*x), x)","F",0
2184,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**2*(f + g*x), x)","F",0
2185,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right) \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)*(f + g*x), x)","F",0
2186,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d),x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{d + e x}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x), x)","F",0
2187,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**2,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**2, x)","F",0
2188,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**3,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**3, x)","F",0
2189,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**4,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**4, x)","F",0
2190,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**5,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**5, x)","F",0
2191,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**6,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**6, x)","F",0
2192,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**7,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{7}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**7, x)","F",0
2193,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**8,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{8}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**8, x)","F",0
2194,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2195,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{3} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(d + e*x)**3*(f + g*x), x)","F",0
2196,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)^{2} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(d + e*x)**2*(f + g*x), x)","F",0
2197,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(d + e x\right) \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(d + e*x)*(f + g*x), x)","F",0
2198,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d),x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(f + g x\right)}{d + e x}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(f + g*x)/(d + e*x), x)","F",0
2199,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**2,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(f + g x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(f + g*x)/(d + e*x)**2, x)","F",0
2200,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**3,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(f + g*x)/(d + e*x)**3, x)","F",0
2201,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(f + g x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(f + g*x)/(d + e*x)**4, x)","F",0
2202,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**5,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(f + g x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(f + g*x)/(d + e*x)**5, x)","F",0
2203,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**6,x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(f + g x\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(f + g*x)/(d + e*x)**6, x)","F",0
2204,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2205,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2206,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2207,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2208,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2209,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{3} \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral((d + e*x)**3*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2210,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{2} \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral((d + e*x)**2*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2211,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right) \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral((d + e*x)*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2212,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)), x)","F",0
2213,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**2/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**2), x)","F",0
2214,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**3/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**3), x)","F",0
2215,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**4/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**4), x)","F",0
2216,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**5/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{5}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**5), x)","F",0
2217,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{3} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(3/2), x)","F",0
2218,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{2} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(3/2), x)","F",0
2219,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right) \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(3/2), x)","F",0
2220,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{f + g x}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)/((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)), x)","F",0
2221,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**2/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{f + g x}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((f + g*x)/((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**2), x)","F",0
2222,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**3/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{f + g x}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((f + g*x)/((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**3), x)","F",0
2223,0,0,0,0.000000," ","integrate((e*x+d)**5*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{5} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**5*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(5/2), x)","F",0
2224,0,0,0,0.000000," ","integrate((e*x+d)**4*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{4} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**4*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(5/2), x)","F",0
2225,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{3} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**3*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(5/2), x)","F",0
2226,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right)^{2} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)**2*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(5/2), x)","F",0
2227,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{\left(d + e x\right) \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x)*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(5/2), x)","F",0
2228,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{f + g x}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)/((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*(d + e*x)), x)","F",0
2229,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**2/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2230,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**3/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2231,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{\frac{5}{2}} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**(5/2)*(f + g*x), x)","F",0
2232,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**(3/2)*(f + g*x), x)","F",0
2233,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \sqrt{d + e x} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*sqrt(d + e*x)*(f + g*x), x)","F",0
2234,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/sqrt(d + e*x), x)","F",0
2235,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**(3/2), x)","F",0
2236,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**(5/2), x)","F",0
2237,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**(7/2), x)","F",0
2238,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**(9/2),x)","\int \frac{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(f + g x\right)}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(f + g*x)/(d + e*x)**(9/2), x)","F",0
2239,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2240,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2241,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**(3/2)*(f + g*x), x)","F",0
2242,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \sqrt{d + e x} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*sqrt(d + e*x)*(f + g*x), x)","F",0
2243,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2244,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**(3/2), x)","F",0
2245,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(5/2),x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**(5/2), x)","F",0
2246,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(7/2),x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**(7/2), x)","F",0
2247,0,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(9/2),x)","\int \frac{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(f + g*x)/(d + e*x)**(9/2), x)","F",0
2248,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2249,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2250,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2251,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2252,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}} \sqrt{d + e x} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(5/2)*sqrt(d + e*x)*(f + g*x), x)","F",0
2253,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2254,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2255,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2256,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2257,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2258,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2259,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2260,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2261,-1,0,0,0.000000," ","integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2262,0,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{5}{2}} \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral((d + e*x)**(5/2)*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2263,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2264,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2265,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(1/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*sqrt(d + e*x)), x)","F",0
2266,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(3/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**(3/2)), x)","F",0
2267,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(5/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{f + g x}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**(5/2)), x)","F",0
2268,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2269,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2270,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2271,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(3/2), x)","F",0
2272,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(3/2), x)","F",0
2273,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(1/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{f + g x}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \sqrt{d + e x}}\, dx"," ",0,"Integral((f + g*x)/((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*sqrt(d + e*x)), x)","F",0
2274,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(3/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{f + g x}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)/((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**(3/2)), x)","F",0
2275,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(5/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2276,-1,0,0,0.000000," ","integrate((e*x+d)**(13/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2277,-1,0,0,0.000000," ","integrate((e*x+d)**(11/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2278,-1,0,0,0.000000," ","integrate((e*x+d)**(9/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2279,-1,0,0,0.000000," ","integrate((e*x+d)**(7/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2280,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2281,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2282,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(5/2), x)","F",0
2283,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(1/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2284,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**(3/2)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2285,-2,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2286,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{m} \left(f + g x\right)\, dx"," ",0,"Integral((-(d + e*x)*(b*e - c*d + c*e*x))**(3/2)*(d + e*x)**m*(f + g*x), x)","F",0
2287,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)} \left(d + e x\right)^{m} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-(d + e*x)*(b*e - c*d + c*e*x))*(d + e*x)**m*(f + g*x), x)","F",0
2288,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{m} \left(f + g x\right)}{\sqrt{- \left(d + e x\right) \left(b e - c d + c e x\right)}}\, dx"," ",0,"Integral((d + e*x)**m*(f + g*x)/sqrt(-(d + e*x)*(b*e - c*d + c*e*x)), x)","F",0
2289,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{m} \left(f + g x\right)}{\left(- \left(d + e x\right) \left(b e - c d + c e x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**m*(f + g*x)/(-(d + e*x)*(b*e - c*d + c*e*x))**(3/2), x)","F",0
2290,-2,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
2291,1,173,0,16.860315," ","integrate((e*x+d)**m*(c*d*m-b*e*(1+m+p)-c*e*(2+m+2*p)*x)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**p,x)","\begin{cases} - b d \left(d + e x\right)^{m} \left(- b d e - b e^{2} x + c d^{2} - c e^{2} x^{2}\right)^{p} - b e x \left(d + e x\right)^{m} \left(- b d e - b e^{2} x + c d^{2} - c e^{2} x^{2}\right)^{p} + \frac{c d^{2} \left(d + e x\right)^{m} \left(- b d e - b e^{2} x + c d^{2} - c e^{2} x^{2}\right)^{p}}{e} - c e x^{2} \left(d + e x\right)^{m} \left(- b d e - b e^{2} x + c d^{2} - c e^{2} x^{2}\right)^{p} & \text{for}\: e \neq 0 \\c d d^{m} m x \left(c d^{2}\right)^{p} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b*d*(d + e*x)**m*(-b*d*e - b*e**2*x + c*d**2 - c*e**2*x**2)**p - b*e*x*(d + e*x)**m*(-b*d*e - b*e**2*x + c*d**2 - c*e**2*x**2)**p + c*d**2*(d + e*x)**m*(-b*d*e - b*e**2*x + c*d**2 - c*e**2*x**2)**p/e - c*e*x**2*(d + e*x)**m*(-b*d*e - b*e**2*x + c*d**2 - c*e**2*x**2)**p, Ne(e, 0)), (c*d*d**m*m*x*(c*d**2)**p, True))","A",0
2292,-1,0,0,0.000000," ","integrate((e*x+d)**(-3-2*p)*(g*x+f)*(d*(d*g*p+d*g+e*f)+e*(2*d*g*p+3*d*g+e*f)*x+e**2*g*(2+p)*x**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2293,-1,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)/(-c*g**2*x**2-b*g**2*x-b*f*g+c*f**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2294,1,70,0,0.082693," ","integrate((1+x)**4*(b*x+a)*(x**2-x+1)**4,x)","\frac{a x^{13}}{13} + \frac{2 a x^{10}}{5} + \frac{6 a x^{7}}{7} + a x^{4} + a x + \frac{b x^{14}}{14} + \frac{4 b x^{11}}{11} + \frac{3 b x^{8}}{4} + \frac{4 b x^{5}}{5} + \frac{b x^{2}}{2}"," ",0,"a*x**13/13 + 2*a*x**10/5 + 6*a*x**7/7 + a*x**4 + a*x + b*x**14/14 + 4*b*x**11/11 + 3*b*x**8/4 + 4*b*x**5/5 + b*x**2/2","A",0
2295,1,56,0,0.075602," ","integrate((1+x)**3*(b*x+a)*(x**2-x+1)**3,x)","\frac{a x^{10}}{10} + \frac{3 a x^{7}}{7} + \frac{3 a x^{4}}{4} + a x + \frac{b x^{11}}{11} + \frac{3 b x^{8}}{8} + \frac{3 b x^{5}}{5} + \frac{b x^{2}}{2}"," ",0,"a*x**10/10 + 3*a*x**7/7 + 3*a*x**4/4 + a*x + b*x**11/11 + 3*b*x**8/8 + 3*b*x**5/5 + b*x**2/2","A",0
2296,1,37,0,0.070666," ","integrate((1+x)**2*(b*x+a)*(x**2-x+1)**2,x)","\frac{a x^{7}}{7} + \frac{a x^{4}}{2} + a x + \frac{b x^{8}}{8} + \frac{2 b x^{5}}{5} + \frac{b x^{2}}{2}"," ",0,"a*x**7/7 + a*x**4/2 + a*x + b*x**8/8 + 2*b*x**5/5 + b*x**2/2","A",0
2297,1,22,0,0.064070," ","integrate((1+x)*(b*x+a)*(x**2-x+1),x)","\frac{a x^{4}}{4} + a x + \frac{b x^{5}}{5} + \frac{b x^{2}}{2}"," ",0,"a*x**4/4 + a*x + b*x**5/5 + b*x**2/2","A",0
2298,1,201,0,0.432333," ","integrate((b*x+a)/(1+x)/(x**2-x+1),x)","\frac{\left(a - b\right) \log{\left(x + \frac{a^{2} \left(a - b\right) + 2 a b^{2} + b \left(a - b\right)^{2}}{a^{3} + b^{3}} \right)}}{3} + \left(- \frac{a}{6} + \frac{b}{6} - \frac{\sqrt{3} i \left(a + b\right)}{6}\right) \log{\left(x + \frac{3 a^{2} \left(- \frac{a}{6} + \frac{b}{6} - \frac{\sqrt{3} i \left(a + b\right)}{6}\right) + 2 a b^{2} + 9 b \left(- \frac{a}{6} + \frac{b}{6} - \frac{\sqrt{3} i \left(a + b\right)}{6}\right)^{2}}{a^{3} + b^{3}} \right)} + \left(- \frac{a}{6} + \frac{b}{6} + \frac{\sqrt{3} i \left(a + b\right)}{6}\right) \log{\left(x + \frac{3 a^{2} \left(- \frac{a}{6} + \frac{b}{6} + \frac{\sqrt{3} i \left(a + b\right)}{6}\right) + 2 a b^{2} + 9 b \left(- \frac{a}{6} + \frac{b}{6} + \frac{\sqrt{3} i \left(a + b\right)}{6}\right)^{2}}{a^{3} + b^{3}} \right)}"," ",0,"(a - b)*log(x + (a**2*(a - b) + 2*a*b**2 + b*(a - b)**2)/(a**3 + b**3))/3 + (-a/6 + b/6 - sqrt(3)*I*(a + b)/6)*log(x + (3*a**2*(-a/6 + b/6 - sqrt(3)*I*(a + b)/6) + 2*a*b**2 + 9*b*(-a/6 + b/6 - sqrt(3)*I*(a + b)/6)**2)/(a**3 + b**3)) + (-a/6 + b/6 + sqrt(3)*I*(a + b)/6)*log(x + (3*a**2*(-a/6 + b/6 + sqrt(3)*I*(a + b)/6) + 2*a*b**2 + 9*b*(-a/6 + b/6 + sqrt(3)*I*(a + b)/6)**2)/(a**3 + b**3))","C",0
2299,1,238,0,0.586564," ","integrate((b*x+a)/(1+x)**2/(x**2-x+1)**2,x)","\frac{\left(2 a - b\right) \log{\left(x + \frac{4 a^{2} \left(2 a - b\right) + 4 a b^{2} + b \left(2 a - b\right)^{2}}{8 a^{3} + b^{3}} \right)}}{9} + \left(- \frac{a}{9} + \frac{b}{18} - \frac{\sqrt{3} i \left(2 a + b\right)}{18}\right) \log{\left(x + \frac{36 a^{2} \left(- \frac{a}{9} + \frac{b}{18} - \frac{\sqrt{3} i \left(2 a + b\right)}{18}\right) + 4 a b^{2} + 81 b \left(- \frac{a}{9} + \frac{b}{18} - \frac{\sqrt{3} i \left(2 a + b\right)}{18}\right)^{2}}{8 a^{3} + b^{3}} \right)} + \left(- \frac{a}{9} + \frac{b}{18} + \frac{\sqrt{3} i \left(2 a + b\right)}{18}\right) \log{\left(x + \frac{36 a^{2} \left(- \frac{a}{9} + \frac{b}{18} + \frac{\sqrt{3} i \left(2 a + b\right)}{18}\right) + 4 a b^{2} + 81 b \left(- \frac{a}{9} + \frac{b}{18} + \frac{\sqrt{3} i \left(2 a + b\right)}{18}\right)^{2}}{8 a^{3} + b^{3}} \right)} + \frac{a x + b x^{2}}{3 x^{3} + 3}"," ",0,"(2*a - b)*log(x + (4*a**2*(2*a - b) + 4*a*b**2 + b*(2*a - b)**2)/(8*a**3 + b**3))/9 + (-a/9 + b/18 - sqrt(3)*I*(2*a + b)/18)*log(x + (36*a**2*(-a/9 + b/18 - sqrt(3)*I*(2*a + b)/18) + 4*a*b**2 + 81*b*(-a/9 + b/18 - sqrt(3)*I*(2*a + b)/18)**2)/(8*a**3 + b**3)) + (-a/9 + b/18 + sqrt(3)*I*(2*a + b)/18)*log(x + (36*a**2*(-a/9 + b/18 + sqrt(3)*I*(2*a + b)/18) + 4*a*b**2 + 81*b*(-a/9 + b/18 + sqrt(3)*I*(2*a + b)/18)**2)/(8*a**3 + b**3)) + (a*x + b*x**2)/(3*x**3 + 3)","C",0
2300,1,292,0,0.708794," ","integrate((b*x+a)/(1+x)**3/(x**2-x+1)**3,x)","\frac{\left(5 a - 2 b\right) \log{\left(x + \frac{25 a^{2} \left(5 a - 2 b\right) + 40 a b^{2} + 2 b \left(5 a - 2 b\right)^{2}}{125 a^{3} + 8 b^{3}} \right)}}{27} + \left(- \frac{5 a}{54} + \frac{b}{27} - \frac{\sqrt{3} i \left(5 a + 2 b\right)}{54}\right) \log{\left(x + \frac{675 a^{2} \left(- \frac{5 a}{54} + \frac{b}{27} - \frac{\sqrt{3} i \left(5 a + 2 b\right)}{54}\right) + 40 a b^{2} + 1458 b \left(- \frac{5 a}{54} + \frac{b}{27} - \frac{\sqrt{3} i \left(5 a + 2 b\right)}{54}\right)^{2}}{125 a^{3} + 8 b^{3}} \right)} + \left(- \frac{5 a}{54} + \frac{b}{27} + \frac{\sqrt{3} i \left(5 a + 2 b\right)}{54}\right) \log{\left(x + \frac{675 a^{2} \left(- \frac{5 a}{54} + \frac{b}{27} + \frac{\sqrt{3} i \left(5 a + 2 b\right)}{54}\right) + 40 a b^{2} + 1458 b \left(- \frac{5 a}{54} + \frac{b}{27} + \frac{\sqrt{3} i \left(5 a + 2 b\right)}{54}\right)^{2}}{125 a^{3} + 8 b^{3}} \right)} + \frac{5 a x^{4} + 8 a x + 4 b x^{5} + 7 b x^{2}}{18 x^{6} + 36 x^{3} + 18}"," ",0,"(5*a - 2*b)*log(x + (25*a**2*(5*a - 2*b) + 40*a*b**2 + 2*b*(5*a - 2*b)**2)/(125*a**3 + 8*b**3))/27 + (-5*a/54 + b/27 - sqrt(3)*I*(5*a + 2*b)/54)*log(x + (675*a**2*(-5*a/54 + b/27 - sqrt(3)*I*(5*a + 2*b)/54) + 40*a*b**2 + 1458*b*(-5*a/54 + b/27 - sqrt(3)*I*(5*a + 2*b)/54)**2)/(125*a**3 + 8*b**3)) + (-5*a/54 + b/27 + sqrt(3)*I*(5*a + 2*b)/54)*log(x + (675*a**2*(-5*a/54 + b/27 + sqrt(3)*I*(5*a + 2*b)/54) + 40*a*b**2 + 1458*b*(-5*a/54 + b/27 + sqrt(3)*I*(5*a + 2*b)/54)**2)/(125*a**3 + 8*b**3)) + (5*a*x**4 + 8*a*x + 4*b*x**5 + 7*b*x**2)/(18*x**6 + 36*x**3 + 18)","C",0
2301,0,0,0,0.000000," ","integrate((1+x)**(3/2)*(b*x+a)*(x**2-x+1)**(3/2),x)","\int \left(a + b x\right) \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2), x)","F",0
2302,0,0,0,0.000000," ","integrate((1+x)**(1/2)*(b*x+a)*(x**2-x+1)**(1/2),x)","\int \left(a + b x\right) \sqrt{x + 1} \sqrt{x^{2} - x + 1}\, dx"," ",0,"Integral((a + b*x)*sqrt(x + 1)*sqrt(x**2 - x + 1), x)","F",0
2303,0,0,0,0.000000," ","integrate((b*x+a)/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{a + b x}{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral((a + b*x)/(sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
2304,0,0,0,0.000000," ","integrate((b*x+a)/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{a + b x}{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)/((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
2305,0,0,0,0.000000," ","integrate((b*x+a)/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{a + b x}{\left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)/((x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
2306,1,332,0,0.113647," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+b*x+a),x)","A a d^{4} x + \frac{B c e^{4} x^{8}}{8} + x^{7} \left(\frac{A c e^{4}}{7} + \frac{B b e^{4}}{7} + \frac{4 B c d e^{3}}{7}\right) + x^{6} \left(\frac{A b e^{4}}{6} + \frac{2 A c d e^{3}}{3} + \frac{B a e^{4}}{6} + \frac{2 B b d e^{3}}{3} + B c d^{2} e^{2}\right) + x^{5} \left(\frac{A a e^{4}}{5} + \frac{4 A b d e^{3}}{5} + \frac{6 A c d^{2} e^{2}}{5} + \frac{4 B a d e^{3}}{5} + \frac{6 B b d^{2} e^{2}}{5} + \frac{4 B c d^{3} e}{5}\right) + x^{4} \left(A a d e^{3} + \frac{3 A b d^{2} e^{2}}{2} + A c d^{3} e + \frac{3 B a d^{2} e^{2}}{2} + B b d^{3} e + \frac{B c d^{4}}{4}\right) + x^{3} \left(2 A a d^{2} e^{2} + \frac{4 A b d^{3} e}{3} + \frac{A c d^{4}}{3} + \frac{4 B a d^{3} e}{3} + \frac{B b d^{4}}{3}\right) + x^{2} \left(2 A a d^{3} e + \frac{A b d^{4}}{2} + \frac{B a d^{4}}{2}\right)"," ",0,"A*a*d**4*x + B*c*e**4*x**8/8 + x**7*(A*c*e**4/7 + B*b*e**4/7 + 4*B*c*d*e**3/7) + x**6*(A*b*e**4/6 + 2*A*c*d*e**3/3 + B*a*e**4/6 + 2*B*b*d*e**3/3 + B*c*d**2*e**2) + x**5*(A*a*e**4/5 + 4*A*b*d*e**3/5 + 6*A*c*d**2*e**2/5 + 4*B*a*d*e**3/5 + 6*B*b*d**2*e**2/5 + 4*B*c*d**3*e/5) + x**4*(A*a*d*e**3 + 3*A*b*d**2*e**2/2 + A*c*d**3*e + 3*B*a*d**2*e**2/2 + B*b*d**3*e + B*c*d**4/4) + x**3*(2*A*a*d**2*e**2 + 4*A*b*d**3*e/3 + A*c*d**4/3 + 4*B*a*d**3*e/3 + B*b*d**4/3) + x**2*(2*A*a*d**3*e + A*b*d**4/2 + B*a*d**4/2)","B",0
2307,1,252,0,0.102348," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x+a),x)","A a d^{3} x + \frac{B c e^{3} x^{7}}{7} + x^{6} \left(\frac{A c e^{3}}{6} + \frac{B b e^{3}}{6} + \frac{B c d e^{2}}{2}\right) + x^{5} \left(\frac{A b e^{3}}{5} + \frac{3 A c d e^{2}}{5} + \frac{B a e^{3}}{5} + \frac{3 B b d e^{2}}{5} + \frac{3 B c d^{2} e}{5}\right) + x^{4} \left(\frac{A a e^{3}}{4} + \frac{3 A b d e^{2}}{4} + \frac{3 A c d^{2} e}{4} + \frac{3 B a d e^{2}}{4} + \frac{3 B b d^{2} e}{4} + \frac{B c d^{3}}{4}\right) + x^{3} \left(A a d e^{2} + A b d^{2} e + \frac{A c d^{3}}{3} + B a d^{2} e + \frac{B b d^{3}}{3}\right) + x^{2} \left(\frac{3 A a d^{2} e}{2} + \frac{A b d^{3}}{2} + \frac{B a d^{3}}{2}\right)"," ",0,"A*a*d**3*x + B*c*e**3*x**7/7 + x**6*(A*c*e**3/6 + B*b*e**3/6 + B*c*d*e**2/2) + x**5*(A*b*e**3/5 + 3*A*c*d*e**2/5 + B*a*e**3/5 + 3*B*b*d*e**2/5 + 3*B*c*d**2*e/5) + x**4*(A*a*e**3/4 + 3*A*b*d*e**2/4 + 3*A*c*d**2*e/4 + 3*B*a*d*e**2/4 + 3*B*b*d**2*e/4 + B*c*d**3/4) + x**3*(A*a*d*e**2 + A*b*d**2*e + A*c*d**3/3 + B*a*d**2*e + B*b*d**3/3) + x**2*(3*A*a*d**2*e/2 + A*b*d**3/2 + B*a*d**3/2)","B",0
2308,1,172,0,0.093119," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x+a),x)","A a d^{2} x + \frac{B c e^{2} x^{6}}{6} + x^{5} \left(\frac{A c e^{2}}{5} + \frac{B b e^{2}}{5} + \frac{2 B c d e}{5}\right) + x^{4} \left(\frac{A b e^{2}}{4} + \frac{A c d e}{2} + \frac{B a e^{2}}{4} + \frac{B b d e}{2} + \frac{B c d^{2}}{4}\right) + x^{3} \left(\frac{A a e^{2}}{3} + \frac{2 A b d e}{3} + \frac{A c d^{2}}{3} + \frac{2 B a d e}{3} + \frac{B b d^{2}}{3}\right) + x^{2} \left(A a d e + \frac{A b d^{2}}{2} + \frac{B a d^{2}}{2}\right)"," ",0,"A*a*d**2*x + B*c*e**2*x**6/6 + x**5*(A*c*e**2/5 + B*b*e**2/5 + 2*B*c*d*e/5) + x**4*(A*b*e**2/4 + A*c*d*e/2 + B*a*e**2/4 + B*b*d*e/2 + B*c*d**2/4) + x**3*(A*a*e**2/3 + 2*A*b*d*e/3 + A*c*d**2/3 + 2*B*a*d*e/3 + B*b*d**2/3) + x**2*(A*a*d*e + A*b*d**2/2 + B*a*d**2/2)","A",0
2309,1,94,0,0.076151," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x+a),x)","A a d x + \frac{B c e x^{5}}{5} + x^{4} \left(\frac{A c e}{4} + \frac{B b e}{4} + \frac{B c d}{4}\right) + x^{3} \left(\frac{A b e}{3} + \frac{A c d}{3} + \frac{B a e}{3} + \frac{B b d}{3}\right) + x^{2} \left(\frac{A a e}{2} + \frac{A b d}{2} + \frac{B a d}{2}\right)"," ",0,"A*a*d*x + B*c*e*x**5/5 + x**4*(A*c*e/4 + B*b*e/4 + B*c*d/4) + x**3*(A*b*e/3 + A*c*d/3 + B*a*e/3 + B*b*d/3) + x**2*(A*a*e/2 + A*b*d/2 + B*a*d/2)","A",0
2310,1,39,0,0.068104," ","integrate((B*x+A)*(c*x**2+b*x+a),x)","A a x + \frac{B c x^{4}}{4} + x^{3} \left(\frac{A c}{3} + \frac{B b}{3}\right) + x^{2} \left(\frac{A b}{2} + \frac{B a}{2}\right)"," ",0,"A*a*x + B*c*x**4/4 + x**3*(A*c/3 + B*b/3) + x**2*(A*b/2 + B*a/2)","A",0
2311,1,107,0,0.433296," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d),x)","\frac{B c x^{3}}{3 e} + x^{2} \left(\frac{A c}{2 e} + \frac{B b}{2 e} - \frac{B c d}{2 e^{2}}\right) + x \left(\frac{A b}{e} - \frac{A c d}{e^{2}} + \frac{B a}{e} - \frac{B b d}{e^{2}} + \frac{B c d^{2}}{e^{3}}\right) - \frac{\left(- A e + B d\right) \left(a e^{2} - b d e + c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x**3/(3*e) + x**2*(A*c/(2*e) + B*b/(2*e) - B*c*d/(2*e**2)) + x*(A*b/e - A*c*d/e**2 + B*a/e - B*b*d/e**2 + B*c*d**2/e**3) - (-A*e + B*d)*(a*e**2 - b*d*e + c*d**2)*log(d + e*x)/e**4","A",0
2312,1,143,0,1.040132," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d)**2,x)","\frac{B c x^{2}}{2 e^{2}} + x \left(\frac{A c}{e^{2}} + \frac{B b}{e^{2}} - \frac{2 B c d}{e^{3}}\right) + \frac{- A a e^{3} + A b d e^{2} - A c d^{2} e + B a d e^{2} - B b d^{2} e + B c d^{3}}{d e^{4} + e^{5} x} + \frac{\left(A b e^{2} - 2 A c d e + B a e^{2} - 2 B b d e + 3 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x**2/(2*e**2) + x*(A*c/e**2 + B*b/e**2 - 2*B*c*d/e**3) + (-A*a*e**3 + A*b*d*e**2 - A*c*d**2*e + B*a*d*e**2 - B*b*d**2*e + B*c*d**3)/(d*e**4 + e**5*x) + (A*b*e**2 - 2*A*c*d*e + B*a*e**2 - 2*B*b*d*e + 3*B*c*d**2)*log(d + e*x)/e**4","A",0
2313,1,162,0,4.702584," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d)**3,x)","\frac{B c x}{e^{3}} + \frac{- A a e^{3} - A b d e^{2} + 3 A c d^{2} e - B a d e^{2} + 3 B b d^{2} e - 5 B c d^{3} + x \left(- 2 A b e^{3} + 4 A c d e^{2} - 2 B a e^{3} + 4 B b d e^{2} - 6 B c d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{\left(A c e + B b e - 3 B c d\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"B*c*x/e**3 + (-A*a*e**3 - A*b*d*e**2 + 3*A*c*d**2*e - B*a*d*e**2 + 3*B*b*d**2*e - 5*B*c*d**3 + x*(-2*A*b*e**3 + 4*A*c*d*e**2 - 2*B*a*e**3 + 4*B*b*d*e**2 - 6*B*c*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + (A*c*e + B*b*e - 3*B*c*d)*log(d + e*x)/e**4","A",0
2314,1,184,0,16.197827," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d)**4,x)","\frac{B c \log{\left(d + e x \right)}}{e^{4}} + \frac{- 2 A a e^{3} - A b d e^{2} - 2 A c d^{2} e - B a d e^{2} - 2 B b d^{2} e + 11 B c d^{3} + x^{2} \left(- 6 A c e^{3} - 6 B b e^{3} + 18 B c d e^{2}\right) + x \left(- 3 A b e^{3} - 6 A c d e^{2} - 3 B a e^{3} - 6 B b d e^{2} + 27 B c d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"B*c*log(d + e*x)/e**4 + (-2*A*a*e**3 - A*b*d*e**2 - 2*A*c*d**2*e - B*a*d*e**2 - 2*B*b*d**2*e + 11*B*c*d**3 + x**2*(-6*A*c*e**3 - 6*B*b*e**3 + 18*B*c*d*e**2) + x*(-3*A*b*e**3 - 6*A*c*d*e**2 - 3*B*a*e**3 - 6*B*b*d*e**2 + 27*B*c*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
2315,1,194,0,45.729802," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d)**5,x)","\frac{- 3 A a e^{3} - A b d e^{2} - A c d^{2} e - B a d e^{2} - B b d^{2} e - 3 B c d^{3} - 12 B c e^{3} x^{3} + x^{2} \left(- 6 A c e^{3} - 6 B b e^{3} - 18 B c d e^{2}\right) + x \left(- 4 A b e^{3} - 4 A c d e^{2} - 4 B a e^{3} - 4 B b d e^{2} - 12 B c d^{2} e\right)}{12 d^{4} e^{4} + 48 d^{3} e^{5} x + 72 d^{2} e^{6} x^{2} + 48 d e^{7} x^{3} + 12 e^{8} x^{4}}"," ",0,"(-3*A*a*e**3 - A*b*d*e**2 - A*c*d**2*e - B*a*d*e**2 - B*b*d**2*e - 3*B*c*d**3 - 12*B*c*e**3*x**3 + x**2*(-6*A*c*e**3 - 6*B*b*e**3 - 18*B*c*d*e**2) + x*(-4*A*b*e**3 - 4*A*c*d*e**2 - 4*B*a*e**3 - 4*B*b*d*e**2 - 12*B*c*d**2*e))/(12*d**4*e**4 + 48*d**3*e**5*x + 72*d**2*e**6*x**2 + 48*d*e**7*x**3 + 12*e**8*x**4)","A",0
2316,1,212,0,114.504439," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d)**6,x)","\frac{- 12 A a e^{3} - 3 A b d e^{2} - 2 A c d^{2} e - 3 B a d e^{2} - 2 B b d^{2} e - 3 B c d^{3} - 30 B c e^{3} x^{3} + x^{2} \left(- 20 A c e^{3} - 20 B b e^{3} - 30 B c d e^{2}\right) + x \left(- 15 A b e^{3} - 10 A c d e^{2} - 15 B a e^{3} - 10 B b d e^{2} - 15 B c d^{2} e\right)}{60 d^{5} e^{4} + 300 d^{4} e^{5} x + 600 d^{3} e^{6} x^{2} + 600 d^{2} e^{7} x^{3} + 300 d e^{8} x^{4} + 60 e^{9} x^{5}}"," ",0,"(-12*A*a*e**3 - 3*A*b*d*e**2 - 2*A*c*d**2*e - 3*B*a*d*e**2 - 2*B*b*d**2*e - 3*B*c*d**3 - 30*B*c*e**3*x**3 + x**2*(-20*A*c*e**3 - 20*B*b*e**3 - 30*B*c*d*e**2) + x*(-15*A*b*e**3 - 10*A*c*d*e**2 - 15*B*a*e**3 - 10*B*b*d*e**2 - 15*B*c*d**2*e))/(60*d**5*e**4 + 300*d**4*e**5*x + 600*d**3*e**6*x**2 + 600*d**2*e**7*x**3 + 300*d*e**8*x**4 + 60*e**9*x**5)","A",0
2317,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2318,1,957,0,0.236789," ","integrate((B*x+A)*(e*x+d)**5*(c*x**2+b*x+a)**2,x)","A a^{2} d^{5} x + \frac{B c^{2} e^{5} x^{11}}{11} + x^{10} \left(\frac{A c^{2} e^{5}}{10} + \frac{B b c e^{5}}{5} + \frac{B c^{2} d e^{4}}{2}\right) + x^{9} \left(\frac{2 A b c e^{5}}{9} + \frac{5 A c^{2} d e^{4}}{9} + \frac{2 B a c e^{5}}{9} + \frac{B b^{2} e^{5}}{9} + \frac{10 B b c d e^{4}}{9} + \frac{10 B c^{2} d^{2} e^{3}}{9}\right) + x^{8} \left(\frac{A a c e^{5}}{4} + \frac{A b^{2} e^{5}}{8} + \frac{5 A b c d e^{4}}{4} + \frac{5 A c^{2} d^{2} e^{3}}{4} + \frac{B a b e^{5}}{4} + \frac{5 B a c d e^{4}}{4} + \frac{5 B b^{2} d e^{4}}{8} + \frac{5 B b c d^{2} e^{3}}{2} + \frac{5 B c^{2} d^{3} e^{2}}{4}\right) + x^{7} \left(\frac{2 A a b e^{5}}{7} + \frac{10 A a c d e^{4}}{7} + \frac{5 A b^{2} d e^{4}}{7} + \frac{20 A b c d^{2} e^{3}}{7} + \frac{10 A c^{2} d^{3} e^{2}}{7} + \frac{B a^{2} e^{5}}{7} + \frac{10 B a b d e^{4}}{7} + \frac{20 B a c d^{2} e^{3}}{7} + \frac{10 B b^{2} d^{2} e^{3}}{7} + \frac{20 B b c d^{3} e^{2}}{7} + \frac{5 B c^{2} d^{4} e}{7}\right) + x^{6} \left(\frac{A a^{2} e^{5}}{6} + \frac{5 A a b d e^{4}}{3} + \frac{10 A a c d^{2} e^{3}}{3} + \frac{5 A b^{2} d^{2} e^{3}}{3} + \frac{10 A b c d^{3} e^{2}}{3} + \frac{5 A c^{2} d^{4} e}{6} + \frac{5 B a^{2} d e^{4}}{6} + \frac{10 B a b d^{2} e^{3}}{3} + \frac{10 B a c d^{3} e^{2}}{3} + \frac{5 B b^{2} d^{3} e^{2}}{3} + \frac{5 B b c d^{4} e}{3} + \frac{B c^{2} d^{5}}{6}\right) + x^{5} \left(A a^{2} d e^{4} + 4 A a b d^{2} e^{3} + 4 A a c d^{3} e^{2} + 2 A b^{2} d^{3} e^{2} + 2 A b c d^{4} e + \frac{A c^{2} d^{5}}{5} + 2 B a^{2} d^{2} e^{3} + 4 B a b d^{3} e^{2} + 2 B a c d^{4} e + B b^{2} d^{4} e + \frac{2 B b c d^{5}}{5}\right) + x^{4} \left(\frac{5 A a^{2} d^{2} e^{3}}{2} + 5 A a b d^{3} e^{2} + \frac{5 A a c d^{4} e}{2} + \frac{5 A b^{2} d^{4} e}{4} + \frac{A b c d^{5}}{2} + \frac{5 B a^{2} d^{3} e^{2}}{2} + \frac{5 B a b d^{4} e}{2} + \frac{B a c d^{5}}{2} + \frac{B b^{2} d^{5}}{4}\right) + x^{3} \left(\frac{10 A a^{2} d^{3} e^{2}}{3} + \frac{10 A a b d^{4} e}{3} + \frac{2 A a c d^{5}}{3} + \frac{A b^{2} d^{5}}{3} + \frac{5 B a^{2} d^{4} e}{3} + \frac{2 B a b d^{5}}{3}\right) + x^{2} \left(\frac{5 A a^{2} d^{4} e}{2} + A a b d^{5} + \frac{B a^{2} d^{5}}{2}\right)"," ",0,"A*a**2*d**5*x + B*c**2*e**5*x**11/11 + x**10*(A*c**2*e**5/10 + B*b*c*e**5/5 + B*c**2*d*e**4/2) + x**9*(2*A*b*c*e**5/9 + 5*A*c**2*d*e**4/9 + 2*B*a*c*e**5/9 + B*b**2*e**5/9 + 10*B*b*c*d*e**4/9 + 10*B*c**2*d**2*e**3/9) + x**8*(A*a*c*e**5/4 + A*b**2*e**5/8 + 5*A*b*c*d*e**4/4 + 5*A*c**2*d**2*e**3/4 + B*a*b*e**5/4 + 5*B*a*c*d*e**4/4 + 5*B*b**2*d*e**4/8 + 5*B*b*c*d**2*e**3/2 + 5*B*c**2*d**3*e**2/4) + x**7*(2*A*a*b*e**5/7 + 10*A*a*c*d*e**4/7 + 5*A*b**2*d*e**4/7 + 20*A*b*c*d**2*e**3/7 + 10*A*c**2*d**3*e**2/7 + B*a**2*e**5/7 + 10*B*a*b*d*e**4/7 + 20*B*a*c*d**2*e**3/7 + 10*B*b**2*d**2*e**3/7 + 20*B*b*c*d**3*e**2/7 + 5*B*c**2*d**4*e/7) + x**6*(A*a**2*e**5/6 + 5*A*a*b*d*e**4/3 + 10*A*a*c*d**2*e**3/3 + 5*A*b**2*d**2*e**3/3 + 10*A*b*c*d**3*e**2/3 + 5*A*c**2*d**4*e/6 + 5*B*a**2*d*e**4/6 + 10*B*a*b*d**2*e**3/3 + 10*B*a*c*d**3*e**2/3 + 5*B*b**2*d**3*e**2/3 + 5*B*b*c*d**4*e/3 + B*c**2*d**5/6) + x**5*(A*a**2*d*e**4 + 4*A*a*b*d**2*e**3 + 4*A*a*c*d**3*e**2 + 2*A*b**2*d**3*e**2 + 2*A*b*c*d**4*e + A*c**2*d**5/5 + 2*B*a**2*d**2*e**3 + 4*B*a*b*d**3*e**2 + 2*B*a*c*d**4*e + B*b**2*d**4*e + 2*B*b*c*d**5/5) + x**4*(5*A*a**2*d**2*e**3/2 + 5*A*a*b*d**3*e**2 + 5*A*a*c*d**4*e/2 + 5*A*b**2*d**4*e/4 + A*b*c*d**5/2 + 5*B*a**2*d**3*e**2/2 + 5*B*a*b*d**4*e/2 + B*a*c*d**5/2 + B*b**2*d**5/4) + x**3*(10*A*a**2*d**3*e**2/3 + 10*A*a*b*d**4*e/3 + 2*A*a*c*d**5/3 + A*b**2*d**5/3 + 5*B*a**2*d**4*e/3 + 2*B*a*b*d**5/3) + x**2*(5*A*a**2*d**4*e/2 + A*a*b*d**5 + B*a**2*d**5/2)","B",0
2319,1,765,0,0.175452," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+b*x+a)**2,x)","A a^{2} d^{4} x + \frac{B c^{2} e^{4} x^{10}}{10} + x^{9} \left(\frac{A c^{2} e^{4}}{9} + \frac{2 B b c e^{4}}{9} + \frac{4 B c^{2} d e^{3}}{9}\right) + x^{8} \left(\frac{A b c e^{4}}{4} + \frac{A c^{2} d e^{3}}{2} + \frac{B a c e^{4}}{4} + \frac{B b^{2} e^{4}}{8} + B b c d e^{3} + \frac{3 B c^{2} d^{2} e^{2}}{4}\right) + x^{7} \left(\frac{2 A a c e^{4}}{7} + \frac{A b^{2} e^{4}}{7} + \frac{8 A b c d e^{3}}{7} + \frac{6 A c^{2} d^{2} e^{2}}{7} + \frac{2 B a b e^{4}}{7} + \frac{8 B a c d e^{3}}{7} + \frac{4 B b^{2} d e^{3}}{7} + \frac{12 B b c d^{2} e^{2}}{7} + \frac{4 B c^{2} d^{3} e}{7}\right) + x^{6} \left(\frac{A a b e^{4}}{3} + \frac{4 A a c d e^{3}}{3} + \frac{2 A b^{2} d e^{3}}{3} + 2 A b c d^{2} e^{2} + \frac{2 A c^{2} d^{3} e}{3} + \frac{B a^{2} e^{4}}{6} + \frac{4 B a b d e^{3}}{3} + 2 B a c d^{2} e^{2} + B b^{2} d^{2} e^{2} + \frac{4 B b c d^{3} e}{3} + \frac{B c^{2} d^{4}}{6}\right) + x^{5} \left(\frac{A a^{2} e^{4}}{5} + \frac{8 A a b d e^{3}}{5} + \frac{12 A a c d^{2} e^{2}}{5} + \frac{6 A b^{2} d^{2} e^{2}}{5} + \frac{8 A b c d^{3} e}{5} + \frac{A c^{2} d^{4}}{5} + \frac{4 B a^{2} d e^{3}}{5} + \frac{12 B a b d^{2} e^{2}}{5} + \frac{8 B a c d^{3} e}{5} + \frac{4 B b^{2} d^{3} e}{5} + \frac{2 B b c d^{4}}{5}\right) + x^{4} \left(A a^{2} d e^{3} + 3 A a b d^{2} e^{2} + 2 A a c d^{3} e + A b^{2} d^{3} e + \frac{A b c d^{4}}{2} + \frac{3 B a^{2} d^{2} e^{2}}{2} + 2 B a b d^{3} e + \frac{B a c d^{4}}{2} + \frac{B b^{2} d^{4}}{4}\right) + x^{3} \left(2 A a^{2} d^{2} e^{2} + \frac{8 A a b d^{3} e}{3} + \frac{2 A a c d^{4}}{3} + \frac{A b^{2} d^{4}}{3} + \frac{4 B a^{2} d^{3} e}{3} + \frac{2 B a b d^{4}}{3}\right) + x^{2} \left(2 A a^{2} d^{3} e + A a b d^{4} + \frac{B a^{2} d^{4}}{2}\right)"," ",0,"A*a**2*d**4*x + B*c**2*e**4*x**10/10 + x**9*(A*c**2*e**4/9 + 2*B*b*c*e**4/9 + 4*B*c**2*d*e**3/9) + x**8*(A*b*c*e**4/4 + A*c**2*d*e**3/2 + B*a*c*e**4/4 + B*b**2*e**4/8 + B*b*c*d*e**3 + 3*B*c**2*d**2*e**2/4) + x**7*(2*A*a*c*e**4/7 + A*b**2*e**4/7 + 8*A*b*c*d*e**3/7 + 6*A*c**2*d**2*e**2/7 + 2*B*a*b*e**4/7 + 8*B*a*c*d*e**3/7 + 4*B*b**2*d*e**3/7 + 12*B*b*c*d**2*e**2/7 + 4*B*c**2*d**3*e/7) + x**6*(A*a*b*e**4/3 + 4*A*a*c*d*e**3/3 + 2*A*b**2*d*e**3/3 + 2*A*b*c*d**2*e**2 + 2*A*c**2*d**3*e/3 + B*a**2*e**4/6 + 4*B*a*b*d*e**3/3 + 2*B*a*c*d**2*e**2 + B*b**2*d**2*e**2 + 4*B*b*c*d**3*e/3 + B*c**2*d**4/6) + x**5*(A*a**2*e**4/5 + 8*A*a*b*d*e**3/5 + 12*A*a*c*d**2*e**2/5 + 6*A*b**2*d**2*e**2/5 + 8*A*b*c*d**3*e/5 + A*c**2*d**4/5 + 4*B*a**2*d*e**3/5 + 12*B*a*b*d**2*e**2/5 + 8*B*a*c*d**3*e/5 + 4*B*b**2*d**3*e/5 + 2*B*b*c*d**4/5) + x**4*(A*a**2*d*e**3 + 3*A*a*b*d**2*e**2 + 2*A*a*c*d**3*e + A*b**2*d**3*e + A*b*c*d**4/2 + 3*B*a**2*d**2*e**2/2 + 2*B*a*b*d**3*e + B*a*c*d**4/2 + B*b**2*d**4/4) + x**3*(2*A*a**2*d**2*e**2 + 8*A*a*b*d**3*e/3 + 2*A*a*c*d**4/3 + A*b**2*d**4/3 + 4*B*a**2*d**3*e/3 + 2*B*a*b*d**4/3) + x**2*(2*A*a**2*d**3*e + A*a*b*d**4 + B*a**2*d**4/2)","B",0
2320,1,583,0,0.151132," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x+a)**2,x)","A a^{2} d^{3} x + \frac{B c^{2} e^{3} x^{9}}{9} + x^{8} \left(\frac{A c^{2} e^{3}}{8} + \frac{B b c e^{3}}{4} + \frac{3 B c^{2} d e^{2}}{8}\right) + x^{7} \left(\frac{2 A b c e^{3}}{7} + \frac{3 A c^{2} d e^{2}}{7} + \frac{2 B a c e^{3}}{7} + \frac{B b^{2} e^{3}}{7} + \frac{6 B b c d e^{2}}{7} + \frac{3 B c^{2} d^{2} e}{7}\right) + x^{6} \left(\frac{A a c e^{3}}{3} + \frac{A b^{2} e^{3}}{6} + A b c d e^{2} + \frac{A c^{2} d^{2} e}{2} + \frac{B a b e^{3}}{3} + B a c d e^{2} + \frac{B b^{2} d e^{2}}{2} + B b c d^{2} e + \frac{B c^{2} d^{3}}{6}\right) + x^{5} \left(\frac{2 A a b e^{3}}{5} + \frac{6 A a c d e^{2}}{5} + \frac{3 A b^{2} d e^{2}}{5} + \frac{6 A b c d^{2} e}{5} + \frac{A c^{2} d^{3}}{5} + \frac{B a^{2} e^{3}}{5} + \frac{6 B a b d e^{2}}{5} + \frac{6 B a c d^{2} e}{5} + \frac{3 B b^{2} d^{2} e}{5} + \frac{2 B b c d^{3}}{5}\right) + x^{4} \left(\frac{A a^{2} e^{3}}{4} + \frac{3 A a b d e^{2}}{2} + \frac{3 A a c d^{2} e}{2} + \frac{3 A b^{2} d^{2} e}{4} + \frac{A b c d^{3}}{2} + \frac{3 B a^{2} d e^{2}}{4} + \frac{3 B a b d^{2} e}{2} + \frac{B a c d^{3}}{2} + \frac{B b^{2} d^{3}}{4}\right) + x^{3} \left(A a^{2} d e^{2} + 2 A a b d^{2} e + \frac{2 A a c d^{3}}{3} + \frac{A b^{2} d^{3}}{3} + B a^{2} d^{2} e + \frac{2 B a b d^{3}}{3}\right) + x^{2} \left(\frac{3 A a^{2} d^{2} e}{2} + A a b d^{3} + \frac{B a^{2} d^{3}}{2}\right)"," ",0,"A*a**2*d**3*x + B*c**2*e**3*x**9/9 + x**8*(A*c**2*e**3/8 + B*b*c*e**3/4 + 3*B*c**2*d*e**2/8) + x**7*(2*A*b*c*e**3/7 + 3*A*c**2*d*e**2/7 + 2*B*a*c*e**3/7 + B*b**2*e**3/7 + 6*B*b*c*d*e**2/7 + 3*B*c**2*d**2*e/7) + x**6*(A*a*c*e**3/3 + A*b**2*e**3/6 + A*b*c*d*e**2 + A*c**2*d**2*e/2 + B*a*b*e**3/3 + B*a*c*d*e**2 + B*b**2*d*e**2/2 + B*b*c*d**2*e + B*c**2*d**3/6) + x**5*(2*A*a*b*e**3/5 + 6*A*a*c*d*e**2/5 + 3*A*b**2*d*e**2/5 + 6*A*b*c*d**2*e/5 + A*c**2*d**3/5 + B*a**2*e**3/5 + 6*B*a*b*d*e**2/5 + 6*B*a*c*d**2*e/5 + 3*B*b**2*d**2*e/5 + 2*B*b*c*d**3/5) + x**4*(A*a**2*e**3/4 + 3*A*a*b*d*e**2/2 + 3*A*a*c*d**2*e/2 + 3*A*b**2*d**2*e/4 + A*b*c*d**3/2 + 3*B*a**2*d*e**2/4 + 3*B*a*b*d**2*e/2 + B*a*c*d**3/2 + B*b**2*d**3/4) + x**3*(A*a**2*d*e**2 + 2*A*a*b*d**2*e + 2*A*a*c*d**3/3 + A*b**2*d**3/3 + B*a**2*d**2*e + 2*B*a*b*d**3/3) + x**2*(3*A*a**2*d**2*e/2 + A*a*b*d**3 + B*a**2*d**3/2)","A",0
2321,1,405,0,0.129212," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x+a)**2,x)","A a^{2} d^{2} x + \frac{B c^{2} e^{2} x^{8}}{8} + x^{7} \left(\frac{A c^{2} e^{2}}{7} + \frac{2 B b c e^{2}}{7} + \frac{2 B c^{2} d e}{7}\right) + x^{6} \left(\frac{A b c e^{2}}{3} + \frac{A c^{2} d e}{3} + \frac{B a c e^{2}}{3} + \frac{B b^{2} e^{2}}{6} + \frac{2 B b c d e}{3} + \frac{B c^{2} d^{2}}{6}\right) + x^{5} \left(\frac{2 A a c e^{2}}{5} + \frac{A b^{2} e^{2}}{5} + \frac{4 A b c d e}{5} + \frac{A c^{2} d^{2}}{5} + \frac{2 B a b e^{2}}{5} + \frac{4 B a c d e}{5} + \frac{2 B b^{2} d e}{5} + \frac{2 B b c d^{2}}{5}\right) + x^{4} \left(\frac{A a b e^{2}}{2} + A a c d e + \frac{A b^{2} d e}{2} + \frac{A b c d^{2}}{2} + \frac{B a^{2} e^{2}}{4} + B a b d e + \frac{B a c d^{2}}{2} + \frac{B b^{2} d^{2}}{4}\right) + x^{3} \left(\frac{A a^{2} e^{2}}{3} + \frac{4 A a b d e}{3} + \frac{2 A a c d^{2}}{3} + \frac{A b^{2} d^{2}}{3} + \frac{2 B a^{2} d e}{3} + \frac{2 B a b d^{2}}{3}\right) + x^{2} \left(A a^{2} d e + A a b d^{2} + \frac{B a^{2} d^{2}}{2}\right)"," ",0,"A*a**2*d**2*x + B*c**2*e**2*x**8/8 + x**7*(A*c**2*e**2/7 + 2*B*b*c*e**2/7 + 2*B*c**2*d*e/7) + x**6*(A*b*c*e**2/3 + A*c**2*d*e/3 + B*a*c*e**2/3 + B*b**2*e**2/6 + 2*B*b*c*d*e/3 + B*c**2*d**2/6) + x**5*(2*A*a*c*e**2/5 + A*b**2*e**2/5 + 4*A*b*c*d*e/5 + A*c**2*d**2/5 + 2*B*a*b*e**2/5 + 4*B*a*c*d*e/5 + 2*B*b**2*d*e/5 + 2*B*b*c*d**2/5) + x**4*(A*a*b*e**2/2 + A*a*c*d*e + A*b**2*d*e/2 + A*b*c*d**2/2 + B*a**2*e**2/4 + B*a*b*d*e + B*a*c*d**2/2 + B*b**2*d**2/4) + x**3*(A*a**2*e**2/3 + 4*A*a*b*d*e/3 + 2*A*a*c*d**2/3 + A*b**2*d**2/3 + 2*B*a**2*d*e/3 + 2*B*a*b*d**2/3) + x**2*(A*a**2*d*e + A*a*b*d**2 + B*a**2*d**2/2)","A",0
2322,1,231,0,0.103730," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x+a)**2,x)","A a^{2} d x + \frac{B c^{2} e x^{7}}{7} + x^{6} \left(\frac{A c^{2} e}{6} + \frac{B b c e}{3} + \frac{B c^{2} d}{6}\right) + x^{5} \left(\frac{2 A b c e}{5} + \frac{A c^{2} d}{5} + \frac{2 B a c e}{5} + \frac{B b^{2} e}{5} + \frac{2 B b c d}{5}\right) + x^{4} \left(\frac{A a c e}{2} + \frac{A b^{2} e}{4} + \frac{A b c d}{2} + \frac{B a b e}{2} + \frac{B a c d}{2} + \frac{B b^{2} d}{4}\right) + x^{3} \left(\frac{2 A a b e}{3} + \frac{2 A a c d}{3} + \frac{A b^{2} d}{3} + \frac{B a^{2} e}{3} + \frac{2 B a b d}{3}\right) + x^{2} \left(\frac{A a^{2} e}{2} + A a b d + \frac{B a^{2} d}{2}\right)"," ",0,"A*a**2*d*x + B*c**2*e*x**7/7 + x**6*(A*c**2*e/6 + B*b*c*e/3 + B*c**2*d/6) + x**5*(2*A*b*c*e/5 + A*c**2*d/5 + 2*B*a*c*e/5 + B*b**2*e/5 + 2*B*b*c*d/5) + x**4*(A*a*c*e/2 + A*b**2*e/4 + A*b*c*d/2 + B*a*b*e/2 + B*a*c*d/2 + B*b**2*d/4) + x**3*(2*A*a*b*e/3 + 2*A*a*c*d/3 + A*b**2*d/3 + B*a**2*e/3 + 2*B*a*b*d/3) + x**2*(A*a**2*e/2 + A*a*b*d + B*a**2*d/2)","A",0
2323,1,100,0,0.085458," ","integrate((B*x+A)*(c*x**2+b*x+a)**2,x)","A a^{2} x + \frac{B c^{2} x^{6}}{6} + x^{5} \left(\frac{A c^{2}}{5} + \frac{2 B b c}{5}\right) + x^{4} \left(\frac{A b c}{2} + \frac{B a c}{2} + \frac{B b^{2}}{4}\right) + x^{3} \left(\frac{2 A a c}{3} + \frac{A b^{2}}{3} + \frac{2 B a b}{3}\right) + x^{2} \left(A a b + \frac{B a^{2}}{2}\right)"," ",0,"A*a**2*x + B*c**2*x**6/6 + x**5*(A*c**2/5 + 2*B*b*c/5) + x**4*(A*b*c/2 + B*a*c/2 + B*b**2/4) + x**3*(2*A*a*c/3 + A*b**2/3 + 2*B*a*b/3) + x**2*(A*a*b + B*a**2/2)","A",0
2324,1,372,0,1.138596," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d),x)","\frac{B c^{2} x^{5}}{5 e} + x^{4} \left(\frac{A c^{2}}{4 e} + \frac{B b c}{2 e} - \frac{B c^{2} d}{4 e^{2}}\right) + x^{3} \left(\frac{2 A b c}{3 e} - \frac{A c^{2} d}{3 e^{2}} + \frac{2 B a c}{3 e} + \frac{B b^{2}}{3 e} - \frac{2 B b c d}{3 e^{2}} + \frac{B c^{2} d^{2}}{3 e^{3}}\right) + x^{2} \left(\frac{A a c}{e} + \frac{A b^{2}}{2 e} - \frac{A b c d}{e^{2}} + \frac{A c^{2} d^{2}}{2 e^{3}} + \frac{B a b}{e} - \frac{B a c d}{e^{2}} - \frac{B b^{2} d}{2 e^{2}} + \frac{B b c d^{2}}{e^{3}} - \frac{B c^{2} d^{3}}{2 e^{4}}\right) + x \left(\frac{2 A a b}{e} - \frac{2 A a c d}{e^{2}} - \frac{A b^{2} d}{e^{2}} + \frac{2 A b c d^{2}}{e^{3}} - \frac{A c^{2} d^{3}}{e^{4}} + \frac{B a^{2}}{e} - \frac{2 B a b d}{e^{2}} + \frac{2 B a c d^{2}}{e^{3}} + \frac{B b^{2} d^{2}}{e^{3}} - \frac{2 B b c d^{3}}{e^{4}} + \frac{B c^{2} d^{4}}{e^{5}}\right) - \frac{\left(- A e + B d\right) \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**5/(5*e) + x**4*(A*c**2/(4*e) + B*b*c/(2*e) - B*c**2*d/(4*e**2)) + x**3*(2*A*b*c/(3*e) - A*c**2*d/(3*e**2) + 2*B*a*c/(3*e) + B*b**2/(3*e) - 2*B*b*c*d/(3*e**2) + B*c**2*d**2/(3*e**3)) + x**2*(A*a*c/e + A*b**2/(2*e) - A*b*c*d/e**2 + A*c**2*d**2/(2*e**3) + B*a*b/e - B*a*c*d/e**2 - B*b**2*d/(2*e**2) + B*b*c*d**2/e**3 - B*c**2*d**3/(2*e**4)) + x*(2*A*a*b/e - 2*A*a*c*d/e**2 - A*b**2*d/e**2 + 2*A*b*c*d**2/e**3 - A*c**2*d**3/e**4 + B*a**2/e - 2*B*a*b*d/e**2 + 2*B*a*c*d**2/e**3 + B*b**2*d**2/e**3 - 2*B*b*c*d**3/e**4 + B*c**2*d**4/e**5) - (-A*e + B*d)*(a*e**2 - b*d*e + c*d**2)**2*log(d + e*x)/e**6","A",0
2325,1,442,0,4.411769," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**2,x)","\frac{B c^{2} x^{4}}{4 e^{2}} + x^{3} \left(\frac{A c^{2}}{3 e^{2}} + \frac{2 B b c}{3 e^{2}} - \frac{2 B c^{2} d}{3 e^{3}}\right) + x^{2} \left(\frac{A b c}{e^{2}} - \frac{A c^{2} d}{e^{3}} + \frac{B a c}{e^{2}} + \frac{B b^{2}}{2 e^{2}} - \frac{2 B b c d}{e^{3}} + \frac{3 B c^{2} d^{2}}{2 e^{4}}\right) + x \left(\frac{2 A a c}{e^{2}} + \frac{A b^{2}}{e^{2}} - \frac{4 A b c d}{e^{3}} + \frac{3 A c^{2} d^{2}}{e^{4}} + \frac{2 B a b}{e^{2}} - \frac{4 B a c d}{e^{3}} - \frac{2 B b^{2} d}{e^{3}} + \frac{6 B b c d^{2}}{e^{4}} - \frac{4 B c^{2} d^{3}}{e^{5}}\right) + \frac{- A a^{2} e^{5} + 2 A a b d e^{4} - 2 A a c d^{2} e^{3} - A b^{2} d^{2} e^{3} + 2 A b c d^{3} e^{2} - A c^{2} d^{4} e + B a^{2} d e^{4} - 2 B a b d^{2} e^{3} + 2 B a c d^{3} e^{2} + B b^{2} d^{3} e^{2} - 2 B b c d^{4} e + B c^{2} d^{5}}{d e^{6} + e^{7} x} + \frac{\left(a e^{2} - b d e + c d^{2}\right) \left(2 A b e^{2} - 4 A c d e + B a e^{2} - 3 B b d e + 5 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**4/(4*e**2) + x**3*(A*c**2/(3*e**2) + 2*B*b*c/(3*e**2) - 2*B*c**2*d/(3*e**3)) + x**2*(A*b*c/e**2 - A*c**2*d/e**3 + B*a*c/e**2 + B*b**2/(2*e**2) - 2*B*b*c*d/e**3 + 3*B*c**2*d**2/(2*e**4)) + x*(2*A*a*c/e**2 + A*b**2/e**2 - 4*A*b*c*d/e**3 + 3*A*c**2*d**2/e**4 + 2*B*a*b/e**2 - 4*B*a*c*d/e**3 - 2*B*b**2*d/e**3 + 6*B*b*c*d**2/e**4 - 4*B*c**2*d**3/e**5) + (-A*a**2*e**5 + 2*A*a*b*d*e**4 - 2*A*a*c*d**2*e**3 - A*b**2*d**2*e**3 + 2*A*b*c*d**3*e**2 - A*c**2*d**4*e + B*a**2*d*e**4 - 2*B*a*b*d**2*e**3 + 2*B*a*c*d**3*e**2 + B*b**2*d**3*e**2 - 2*B*b*c*d**4*e + B*c**2*d**5)/(d*e**6 + e**7*x) + (a*e**2 - b*d*e + c*d**2)*(2*A*b*e**2 - 4*A*c*d*e + B*a*e**2 - 3*B*b*d*e + 5*B*c*d**2)*log(d + e*x)/e**6","A",0
2326,1,534,0,28.799167," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**3,x)","\frac{B c^{2} x^{3}}{3 e^{3}} + x^{2} \left(\frac{A c^{2}}{2 e^{3}} + \frac{B b c}{e^{3}} - \frac{3 B c^{2} d}{2 e^{4}}\right) + x \left(\frac{2 A b c}{e^{3}} - \frac{3 A c^{2} d}{e^{4}} + \frac{2 B a c}{e^{3}} + \frac{B b^{2}}{e^{3}} - \frac{6 B b c d}{e^{4}} + \frac{6 B c^{2} d^{2}}{e^{5}}\right) + \frac{- A a^{2} e^{5} - 2 A a b d e^{4} + 6 A a c d^{2} e^{3} + 3 A b^{2} d^{2} e^{3} - 10 A b c d^{3} e^{2} + 7 A c^{2} d^{4} e - B a^{2} d e^{4} + 6 B a b d^{2} e^{3} - 10 B a c d^{3} e^{2} - 5 B b^{2} d^{3} e^{2} + 14 B b c d^{4} e - 9 B c^{2} d^{5} + x \left(- 4 A a b e^{5} + 8 A a c d e^{4} + 4 A b^{2} d e^{4} - 12 A b c d^{2} e^{3} + 8 A c^{2} d^{3} e^{2} - 2 B a^{2} e^{5} + 8 B a b d e^{4} - 12 B a c d^{2} e^{3} - 6 B b^{2} d^{2} e^{3} + 16 B b c d^{3} e^{2} - 10 B c^{2} d^{4} e\right)}{2 d^{2} e^{6} + 4 d e^{7} x + 2 e^{8} x^{2}} + \frac{\left(2 A a c e^{3} + A b^{2} e^{3} - 6 A b c d e^{2} + 6 A c^{2} d^{2} e + 2 B a b e^{3} - 6 B a c d e^{2} - 3 B b^{2} d e^{2} + 12 B b c d^{2} e - 10 B c^{2} d^{3}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**3/(3*e**3) + x**2*(A*c**2/(2*e**3) + B*b*c/e**3 - 3*B*c**2*d/(2*e**4)) + x*(2*A*b*c/e**3 - 3*A*c**2*d/e**4 + 2*B*a*c/e**3 + B*b**2/e**3 - 6*B*b*c*d/e**4 + 6*B*c**2*d**2/e**5) + (-A*a**2*e**5 - 2*A*a*b*d*e**4 + 6*A*a*c*d**2*e**3 + 3*A*b**2*d**2*e**3 - 10*A*b*c*d**3*e**2 + 7*A*c**2*d**4*e - B*a**2*d*e**4 + 6*B*a*b*d**2*e**3 - 10*B*a*c*d**3*e**2 - 5*B*b**2*d**3*e**2 + 14*B*b*c*d**4*e - 9*B*c**2*d**5 + x*(-4*A*a*b*e**5 + 8*A*a*c*d*e**4 + 4*A*b**2*d*e**4 - 12*A*b*c*d**2*e**3 + 8*A*c**2*d**3*e**2 - 2*B*a**2*e**5 + 8*B*a*b*d*e**4 - 12*B*a*c*d**2*e**3 - 6*B*b**2*d**2*e**3 + 16*B*b*c*d**3*e**2 - 10*B*c**2*d**4*e))/(2*d**2*e**6 + 4*d*e**7*x + 2*e**8*x**2) + (2*A*a*c*e**3 + A*b**2*e**3 - 6*A*b*c*d*e**2 + 6*A*c**2*d**2*e + 2*B*a*b*e**3 - 6*B*a*c*d*e**2 - 3*B*b**2*d*e**2 + 12*B*b*c*d**2*e - 10*B*c**2*d**3)*log(d + e*x)/e**6","A",0
2327,1,547,0,152.975724," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**4,x)","\frac{B c^{2} x^{2}}{2 e^{4}} + x \left(\frac{A c^{2}}{e^{4}} + \frac{2 B b c}{e^{4}} - \frac{4 B c^{2} d}{e^{5}}\right) + \frac{- 2 A a^{2} e^{5} - 2 A a b d e^{4} - 4 A a c d^{2} e^{3} - 2 A b^{2} d^{2} e^{3} + 22 A b c d^{3} e^{2} - 26 A c^{2} d^{4} e - B a^{2} d e^{4} - 4 B a b d^{2} e^{3} + 22 B a c d^{3} e^{2} + 11 B b^{2} d^{3} e^{2} - 52 B b c d^{4} e + 47 B c^{2} d^{5} + x^{2} \left(- 12 A a c e^{5} - 6 A b^{2} e^{5} + 36 A b c d e^{4} - 36 A c^{2} d^{2} e^{3} - 12 B a b e^{5} + 36 B a c d e^{4} + 18 B b^{2} d e^{4} - 72 B b c d^{2} e^{3} + 60 B c^{2} d^{3} e^{2}\right) + x \left(- 6 A a b e^{5} - 12 A a c d e^{4} - 6 A b^{2} d e^{4} + 54 A b c d^{2} e^{3} - 60 A c^{2} d^{3} e^{2} - 3 B a^{2} e^{5} - 12 B a b d e^{4} + 54 B a c d^{2} e^{3} + 27 B b^{2} d^{2} e^{3} - 120 B b c d^{3} e^{2} + 105 B c^{2} d^{4} e\right)}{6 d^{3} e^{6} + 18 d^{2} e^{7} x + 18 d e^{8} x^{2} + 6 e^{9} x^{3}} + \frac{\left(2 A b c e^{2} - 4 A c^{2} d e + 2 B a c e^{2} + B b^{2} e^{2} - 8 B b c d e + 10 B c^{2} d^{2}\right) \log{\left(d + e x \right)}}{e^{6}}"," ",0,"B*c**2*x**2/(2*e**4) + x*(A*c**2/e**4 + 2*B*b*c/e**4 - 4*B*c**2*d/e**5) + (-2*A*a**2*e**5 - 2*A*a*b*d*e**4 - 4*A*a*c*d**2*e**3 - 2*A*b**2*d**2*e**3 + 22*A*b*c*d**3*e**2 - 26*A*c**2*d**4*e - B*a**2*d*e**4 - 4*B*a*b*d**2*e**3 + 22*B*a*c*d**3*e**2 + 11*B*b**2*d**3*e**2 - 52*B*b*c*d**4*e + 47*B*c**2*d**5 + x**2*(-12*A*a*c*e**5 - 6*A*b**2*e**5 + 36*A*b*c*d*e**4 - 36*A*c**2*d**2*e**3 - 12*B*a*b*e**5 + 36*B*a*c*d*e**4 + 18*B*b**2*d*e**4 - 72*B*b*c*d**2*e**3 + 60*B*c**2*d**3*e**2) + x*(-6*A*a*b*e**5 - 12*A*a*c*d*e**4 - 6*A*b**2*d*e**4 + 54*A*b*c*d**2*e**3 - 60*A*c**2*d**3*e**2 - 3*B*a**2*e**5 - 12*B*a*b*d*e**4 + 54*B*a*c*d**2*e**3 + 27*B*b**2*d**2*e**3 - 120*B*b*c*d**3*e**2 + 105*B*c**2*d**4*e))/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + (2*A*b*c*e**2 - 4*A*c**2*d*e + 2*B*a*c*e**2 + B*b**2*e**2 - 8*B*b*c*d*e + 10*B*c**2*d**2)*log(d + e*x)/e**6","A",0
2328,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2329,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2330,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2331,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2332,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**2/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2333,1,1731,0,0.276774," ","integrate((B*x+A)*(e*x+d)**5*(c*x**2+b*x+a)**3,x)","A a^{3} d^{5} x + \frac{B c^{3} e^{5} x^{13}}{13} + x^{12} \left(\frac{A c^{3} e^{5}}{12} + \frac{B b c^{2} e^{5}}{4} + \frac{5 B c^{3} d e^{4}}{12}\right) + x^{11} \left(\frac{3 A b c^{2} e^{5}}{11} + \frac{5 A c^{3} d e^{4}}{11} + \frac{3 B a c^{2} e^{5}}{11} + \frac{3 B b^{2} c e^{5}}{11} + \frac{15 B b c^{2} d e^{4}}{11} + \frac{10 B c^{3} d^{2} e^{3}}{11}\right) + x^{10} \left(\frac{3 A a c^{2} e^{5}}{10} + \frac{3 A b^{2} c e^{5}}{10} + \frac{3 A b c^{2} d e^{4}}{2} + A c^{3} d^{2} e^{3} + \frac{3 B a b c e^{5}}{5} + \frac{3 B a c^{2} d e^{4}}{2} + \frac{B b^{3} e^{5}}{10} + \frac{3 B b^{2} c d e^{4}}{2} + 3 B b c^{2} d^{2} e^{3} + B c^{3} d^{3} e^{2}\right) + x^{9} \left(\frac{2 A a b c e^{5}}{3} + \frac{5 A a c^{2} d e^{4}}{3} + \frac{A b^{3} e^{5}}{9} + \frac{5 A b^{2} c d e^{4}}{3} + \frac{10 A b c^{2} d^{2} e^{3}}{3} + \frac{10 A c^{3} d^{3} e^{2}}{9} + \frac{B a^{2} c e^{5}}{3} + \frac{B a b^{2} e^{5}}{3} + \frac{10 B a b c d e^{4}}{3} + \frac{10 B a c^{2} d^{2} e^{3}}{3} + \frac{5 B b^{3} d e^{4}}{9} + \frac{10 B b^{2} c d^{2} e^{3}}{3} + \frac{10 B b c^{2} d^{3} e^{2}}{3} + \frac{5 B c^{3} d^{4} e}{9}\right) + x^{8} \left(\frac{3 A a^{2} c e^{5}}{8} + \frac{3 A a b^{2} e^{5}}{8} + \frac{15 A a b c d e^{4}}{4} + \frac{15 A a c^{2} d^{2} e^{3}}{4} + \frac{5 A b^{3} d e^{4}}{8} + \frac{15 A b^{2} c d^{2} e^{3}}{4} + \frac{15 A b c^{2} d^{3} e^{2}}{4} + \frac{5 A c^{3} d^{4} e}{8} + \frac{3 B a^{2} b e^{5}}{8} + \frac{15 B a^{2} c d e^{4}}{8} + \frac{15 B a b^{2} d e^{4}}{8} + \frac{15 B a b c d^{2} e^{3}}{2} + \frac{15 B a c^{2} d^{3} e^{2}}{4} + \frac{5 B b^{3} d^{2} e^{3}}{4} + \frac{15 B b^{2} c d^{3} e^{2}}{4} + \frac{15 B b c^{2} d^{4} e}{8} + \frac{B c^{3} d^{5}}{8}\right) + x^{7} \left(\frac{3 A a^{2} b e^{5}}{7} + \frac{15 A a^{2} c d e^{4}}{7} + \frac{15 A a b^{2} d e^{4}}{7} + \frac{60 A a b c d^{2} e^{3}}{7} + \frac{30 A a c^{2} d^{3} e^{2}}{7} + \frac{10 A b^{3} d^{2} e^{3}}{7} + \frac{30 A b^{2} c d^{3} e^{2}}{7} + \frac{15 A b c^{2} d^{4} e}{7} + \frac{A c^{3} d^{5}}{7} + \frac{B a^{3} e^{5}}{7} + \frac{15 B a^{2} b d e^{4}}{7} + \frac{30 B a^{2} c d^{2} e^{3}}{7} + \frac{30 B a b^{2} d^{2} e^{3}}{7} + \frac{60 B a b c d^{3} e^{2}}{7} + \frac{15 B a c^{2} d^{4} e}{7} + \frac{10 B b^{3} d^{3} e^{2}}{7} + \frac{15 B b^{2} c d^{4} e}{7} + \frac{3 B b c^{2} d^{5}}{7}\right) + x^{6} \left(\frac{A a^{3} e^{5}}{6} + \frac{5 A a^{2} b d e^{4}}{2} + 5 A a^{2} c d^{2} e^{3} + 5 A a b^{2} d^{2} e^{3} + 10 A a b c d^{3} e^{2} + \frac{5 A a c^{2} d^{4} e}{2} + \frac{5 A b^{3} d^{3} e^{2}}{3} + \frac{5 A b^{2} c d^{4} e}{2} + \frac{A b c^{2} d^{5}}{2} + \frac{5 B a^{3} d e^{4}}{6} + 5 B a^{2} b d^{2} e^{3} + 5 B a^{2} c d^{3} e^{2} + 5 B a b^{2} d^{3} e^{2} + 5 B a b c d^{4} e + \frac{B a c^{2} d^{5}}{2} + \frac{5 B b^{3} d^{4} e}{6} + \frac{B b^{2} c d^{5}}{2}\right) + x^{5} \left(A a^{3} d e^{4} + 6 A a^{2} b d^{2} e^{3} + 6 A a^{2} c d^{3} e^{2} + 6 A a b^{2} d^{3} e^{2} + 6 A a b c d^{4} e + \frac{3 A a c^{2} d^{5}}{5} + A b^{3} d^{4} e + \frac{3 A b^{2} c d^{5}}{5} + 2 B a^{3} d^{2} e^{3} + 6 B a^{2} b d^{3} e^{2} + 3 B a^{2} c d^{4} e + 3 B a b^{2} d^{4} e + \frac{6 B a b c d^{5}}{5} + \frac{B b^{3} d^{5}}{5}\right) + x^{4} \left(\frac{5 A a^{3} d^{2} e^{3}}{2} + \frac{15 A a^{2} b d^{3} e^{2}}{2} + \frac{15 A a^{2} c d^{4} e}{4} + \frac{15 A a b^{2} d^{4} e}{4} + \frac{3 A a b c d^{5}}{2} + \frac{A b^{3} d^{5}}{4} + \frac{5 B a^{3} d^{3} e^{2}}{2} + \frac{15 B a^{2} b d^{4} e}{4} + \frac{3 B a^{2} c d^{5}}{4} + \frac{3 B a b^{2} d^{5}}{4}\right) + x^{3} \left(\frac{10 A a^{3} d^{3} e^{2}}{3} + 5 A a^{2} b d^{4} e + A a^{2} c d^{5} + A a b^{2} d^{5} + \frac{5 B a^{3} d^{4} e}{3} + B a^{2} b d^{5}\right) + x^{2} \left(\frac{5 A a^{3} d^{4} e}{2} + \frac{3 A a^{2} b d^{5}}{2} + \frac{B a^{3} d^{5}}{2}\right)"," ",0,"A*a**3*d**5*x + B*c**3*e**5*x**13/13 + x**12*(A*c**3*e**5/12 + B*b*c**2*e**5/4 + 5*B*c**3*d*e**4/12) + x**11*(3*A*b*c**2*e**5/11 + 5*A*c**3*d*e**4/11 + 3*B*a*c**2*e**5/11 + 3*B*b**2*c*e**5/11 + 15*B*b*c**2*d*e**4/11 + 10*B*c**3*d**2*e**3/11) + x**10*(3*A*a*c**2*e**5/10 + 3*A*b**2*c*e**5/10 + 3*A*b*c**2*d*e**4/2 + A*c**3*d**2*e**3 + 3*B*a*b*c*e**5/5 + 3*B*a*c**2*d*e**4/2 + B*b**3*e**5/10 + 3*B*b**2*c*d*e**4/2 + 3*B*b*c**2*d**2*e**3 + B*c**3*d**3*e**2) + x**9*(2*A*a*b*c*e**5/3 + 5*A*a*c**2*d*e**4/3 + A*b**3*e**5/9 + 5*A*b**2*c*d*e**4/3 + 10*A*b*c**2*d**2*e**3/3 + 10*A*c**3*d**3*e**2/9 + B*a**2*c*e**5/3 + B*a*b**2*e**5/3 + 10*B*a*b*c*d*e**4/3 + 10*B*a*c**2*d**2*e**3/3 + 5*B*b**3*d*e**4/9 + 10*B*b**2*c*d**2*e**3/3 + 10*B*b*c**2*d**3*e**2/3 + 5*B*c**3*d**4*e/9) + x**8*(3*A*a**2*c*e**5/8 + 3*A*a*b**2*e**5/8 + 15*A*a*b*c*d*e**4/4 + 15*A*a*c**2*d**2*e**3/4 + 5*A*b**3*d*e**4/8 + 15*A*b**2*c*d**2*e**3/4 + 15*A*b*c**2*d**3*e**2/4 + 5*A*c**3*d**4*e/8 + 3*B*a**2*b*e**5/8 + 15*B*a**2*c*d*e**4/8 + 15*B*a*b**2*d*e**4/8 + 15*B*a*b*c*d**2*e**3/2 + 15*B*a*c**2*d**3*e**2/4 + 5*B*b**3*d**2*e**3/4 + 15*B*b**2*c*d**3*e**2/4 + 15*B*b*c**2*d**4*e/8 + B*c**3*d**5/8) + x**7*(3*A*a**2*b*e**5/7 + 15*A*a**2*c*d*e**4/7 + 15*A*a*b**2*d*e**4/7 + 60*A*a*b*c*d**2*e**3/7 + 30*A*a*c**2*d**3*e**2/7 + 10*A*b**3*d**2*e**3/7 + 30*A*b**2*c*d**3*e**2/7 + 15*A*b*c**2*d**4*e/7 + A*c**3*d**5/7 + B*a**3*e**5/7 + 15*B*a**2*b*d*e**4/7 + 30*B*a**2*c*d**2*e**3/7 + 30*B*a*b**2*d**2*e**3/7 + 60*B*a*b*c*d**3*e**2/7 + 15*B*a*c**2*d**4*e/7 + 10*B*b**3*d**3*e**2/7 + 15*B*b**2*c*d**4*e/7 + 3*B*b*c**2*d**5/7) + x**6*(A*a**3*e**5/6 + 5*A*a**2*b*d*e**4/2 + 5*A*a**2*c*d**2*e**3 + 5*A*a*b**2*d**2*e**3 + 10*A*a*b*c*d**3*e**2 + 5*A*a*c**2*d**4*e/2 + 5*A*b**3*d**3*e**2/3 + 5*A*b**2*c*d**4*e/2 + A*b*c**2*d**5/2 + 5*B*a**3*d*e**4/6 + 5*B*a**2*b*d**2*e**3 + 5*B*a**2*c*d**3*e**2 + 5*B*a*b**2*d**3*e**2 + 5*B*a*b*c*d**4*e + B*a*c**2*d**5/2 + 5*B*b**3*d**4*e/6 + B*b**2*c*d**5/2) + x**5*(A*a**3*d*e**4 + 6*A*a**2*b*d**2*e**3 + 6*A*a**2*c*d**3*e**2 + 6*A*a*b**2*d**3*e**2 + 6*A*a*b*c*d**4*e + 3*A*a*c**2*d**5/5 + A*b**3*d**4*e + 3*A*b**2*c*d**5/5 + 2*B*a**3*d**2*e**3 + 6*B*a**2*b*d**3*e**2 + 3*B*a**2*c*d**4*e + 3*B*a*b**2*d**4*e + 6*B*a*b*c*d**5/5 + B*b**3*d**5/5) + x**4*(5*A*a**3*d**2*e**3/2 + 15*A*a**2*b*d**3*e**2/2 + 15*A*a**2*c*d**4*e/4 + 15*A*a*b**2*d**4*e/4 + 3*A*a*b*c*d**5/2 + A*b**3*d**5/4 + 5*B*a**3*d**3*e**2/2 + 15*B*a**2*b*d**4*e/4 + 3*B*a**2*c*d**5/4 + 3*B*a*b**2*d**5/4) + x**3*(10*A*a**3*d**3*e**2/3 + 5*A*a**2*b*d**4*e + A*a**2*c*d**5 + A*a*b**2*d**5 + 5*B*a**3*d**4*e/3 + B*a**2*b*d**5) + x**2*(5*A*a**3*d**4*e/2 + 3*A*a**2*b*d**5/2 + B*a**3*d**5/2)","B",0
2334,1,1401,0,0.235022," ","integrate((B*x+A)*(e*x+d)**4*(c*x**2+b*x+a)**3,x)","A a^{3} d^{4} x + \frac{B c^{3} e^{4} x^{12}}{12} + x^{11} \left(\frac{A c^{3} e^{4}}{11} + \frac{3 B b c^{2} e^{4}}{11} + \frac{4 B c^{3} d e^{3}}{11}\right) + x^{10} \left(\frac{3 A b c^{2} e^{4}}{10} + \frac{2 A c^{3} d e^{3}}{5} + \frac{3 B a c^{2} e^{4}}{10} + \frac{3 B b^{2} c e^{4}}{10} + \frac{6 B b c^{2} d e^{3}}{5} + \frac{3 B c^{3} d^{2} e^{2}}{5}\right) + x^{9} \left(\frac{A a c^{2} e^{4}}{3} + \frac{A b^{2} c e^{4}}{3} + \frac{4 A b c^{2} d e^{3}}{3} + \frac{2 A c^{3} d^{2} e^{2}}{3} + \frac{2 B a b c e^{4}}{3} + \frac{4 B a c^{2} d e^{3}}{3} + \frac{B b^{3} e^{4}}{9} + \frac{4 B b^{2} c d e^{3}}{3} + 2 B b c^{2} d^{2} e^{2} + \frac{4 B c^{3} d^{3} e}{9}\right) + x^{8} \left(\frac{3 A a b c e^{4}}{4} + \frac{3 A a c^{2} d e^{3}}{2} + \frac{A b^{3} e^{4}}{8} + \frac{3 A b^{2} c d e^{3}}{2} + \frac{9 A b c^{2} d^{2} e^{2}}{4} + \frac{A c^{3} d^{3} e}{2} + \frac{3 B a^{2} c e^{4}}{8} + \frac{3 B a b^{2} e^{4}}{8} + 3 B a b c d e^{3} + \frac{9 B a c^{2} d^{2} e^{2}}{4} + \frac{B b^{3} d e^{3}}{2} + \frac{9 B b^{2} c d^{2} e^{2}}{4} + \frac{3 B b c^{2} d^{3} e}{2} + \frac{B c^{3} d^{4}}{8}\right) + x^{7} \left(\frac{3 A a^{2} c e^{4}}{7} + \frac{3 A a b^{2} e^{4}}{7} + \frac{24 A a b c d e^{3}}{7} + \frac{18 A a c^{2} d^{2} e^{2}}{7} + \frac{4 A b^{3} d e^{3}}{7} + \frac{18 A b^{2} c d^{2} e^{2}}{7} + \frac{12 A b c^{2} d^{3} e}{7} + \frac{A c^{3} d^{4}}{7} + \frac{3 B a^{2} b e^{4}}{7} + \frac{12 B a^{2} c d e^{3}}{7} + \frac{12 B a b^{2} d e^{3}}{7} + \frac{36 B a b c d^{2} e^{2}}{7} + \frac{12 B a c^{2} d^{3} e}{7} + \frac{6 B b^{3} d^{2} e^{2}}{7} + \frac{12 B b^{2} c d^{3} e}{7} + \frac{3 B b c^{2} d^{4}}{7}\right) + x^{6} \left(\frac{A a^{2} b e^{4}}{2} + 2 A a^{2} c d e^{3} + 2 A a b^{2} d e^{3} + 6 A a b c d^{2} e^{2} + 2 A a c^{2} d^{3} e + A b^{3} d^{2} e^{2} + 2 A b^{2} c d^{3} e + \frac{A b c^{2} d^{4}}{2} + \frac{B a^{3} e^{4}}{6} + 2 B a^{2} b d e^{3} + 3 B a^{2} c d^{2} e^{2} + 3 B a b^{2} d^{2} e^{2} + 4 B a b c d^{3} e + \frac{B a c^{2} d^{4}}{2} + \frac{2 B b^{3} d^{3} e}{3} + \frac{B b^{2} c d^{4}}{2}\right) + x^{5} \left(\frac{A a^{3} e^{4}}{5} + \frac{12 A a^{2} b d e^{3}}{5} + \frac{18 A a^{2} c d^{2} e^{2}}{5} + \frac{18 A a b^{2} d^{2} e^{2}}{5} + \frac{24 A a b c d^{3} e}{5} + \frac{3 A a c^{2} d^{4}}{5} + \frac{4 A b^{3} d^{3} e}{5} + \frac{3 A b^{2} c d^{4}}{5} + \frac{4 B a^{3} d e^{3}}{5} + \frac{18 B a^{2} b d^{2} e^{2}}{5} + \frac{12 B a^{2} c d^{3} e}{5} + \frac{12 B a b^{2} d^{3} e}{5} + \frac{6 B a b c d^{4}}{5} + \frac{B b^{3} d^{4}}{5}\right) + x^{4} \left(A a^{3} d e^{3} + \frac{9 A a^{2} b d^{2} e^{2}}{2} + 3 A a^{2} c d^{3} e + 3 A a b^{2} d^{3} e + \frac{3 A a b c d^{4}}{2} + \frac{A b^{3} d^{4}}{4} + \frac{3 B a^{3} d^{2} e^{2}}{2} + 3 B a^{2} b d^{3} e + \frac{3 B a^{2} c d^{4}}{4} + \frac{3 B a b^{2} d^{4}}{4}\right) + x^{3} \left(2 A a^{3} d^{2} e^{2} + 4 A a^{2} b d^{3} e + A a^{2} c d^{4} + A a b^{2} d^{4} + \frac{4 B a^{3} d^{3} e}{3} + B a^{2} b d^{4}\right) + x^{2} \left(2 A a^{3} d^{3} e + \frac{3 A a^{2} b d^{4}}{2} + \frac{B a^{3} d^{4}}{2}\right)"," ",0,"A*a**3*d**4*x + B*c**3*e**4*x**12/12 + x**11*(A*c**3*e**4/11 + 3*B*b*c**2*e**4/11 + 4*B*c**3*d*e**3/11) + x**10*(3*A*b*c**2*e**4/10 + 2*A*c**3*d*e**3/5 + 3*B*a*c**2*e**4/10 + 3*B*b**2*c*e**4/10 + 6*B*b*c**2*d*e**3/5 + 3*B*c**3*d**2*e**2/5) + x**9*(A*a*c**2*e**4/3 + A*b**2*c*e**4/3 + 4*A*b*c**2*d*e**3/3 + 2*A*c**3*d**2*e**2/3 + 2*B*a*b*c*e**4/3 + 4*B*a*c**2*d*e**3/3 + B*b**3*e**4/9 + 4*B*b**2*c*d*e**3/3 + 2*B*b*c**2*d**2*e**2 + 4*B*c**3*d**3*e/9) + x**8*(3*A*a*b*c*e**4/4 + 3*A*a*c**2*d*e**3/2 + A*b**3*e**4/8 + 3*A*b**2*c*d*e**3/2 + 9*A*b*c**2*d**2*e**2/4 + A*c**3*d**3*e/2 + 3*B*a**2*c*e**4/8 + 3*B*a*b**2*e**4/8 + 3*B*a*b*c*d*e**3 + 9*B*a*c**2*d**2*e**2/4 + B*b**3*d*e**3/2 + 9*B*b**2*c*d**2*e**2/4 + 3*B*b*c**2*d**3*e/2 + B*c**3*d**4/8) + x**7*(3*A*a**2*c*e**4/7 + 3*A*a*b**2*e**4/7 + 24*A*a*b*c*d*e**3/7 + 18*A*a*c**2*d**2*e**2/7 + 4*A*b**3*d*e**3/7 + 18*A*b**2*c*d**2*e**2/7 + 12*A*b*c**2*d**3*e/7 + A*c**3*d**4/7 + 3*B*a**2*b*e**4/7 + 12*B*a**2*c*d*e**3/7 + 12*B*a*b**2*d*e**3/7 + 36*B*a*b*c*d**2*e**2/7 + 12*B*a*c**2*d**3*e/7 + 6*B*b**3*d**2*e**2/7 + 12*B*b**2*c*d**3*e/7 + 3*B*b*c**2*d**4/7) + x**6*(A*a**2*b*e**4/2 + 2*A*a**2*c*d*e**3 + 2*A*a*b**2*d*e**3 + 6*A*a*b*c*d**2*e**2 + 2*A*a*c**2*d**3*e + A*b**3*d**2*e**2 + 2*A*b**2*c*d**3*e + A*b*c**2*d**4/2 + B*a**3*e**4/6 + 2*B*a**2*b*d*e**3 + 3*B*a**2*c*d**2*e**2 + 3*B*a*b**2*d**2*e**2 + 4*B*a*b*c*d**3*e + B*a*c**2*d**4/2 + 2*B*b**3*d**3*e/3 + B*b**2*c*d**4/2) + x**5*(A*a**3*e**4/5 + 12*A*a**2*b*d*e**3/5 + 18*A*a**2*c*d**2*e**2/5 + 18*A*a*b**2*d**2*e**2/5 + 24*A*a*b*c*d**3*e/5 + 3*A*a*c**2*d**4/5 + 4*A*b**3*d**3*e/5 + 3*A*b**2*c*d**4/5 + 4*B*a**3*d*e**3/5 + 18*B*a**2*b*d**2*e**2/5 + 12*B*a**2*c*d**3*e/5 + 12*B*a*b**2*d**3*e/5 + 6*B*a*b*c*d**4/5 + B*b**3*d**4/5) + x**4*(A*a**3*d*e**3 + 9*A*a**2*b*d**2*e**2/2 + 3*A*a**2*c*d**3*e + 3*A*a*b**2*d**3*e + 3*A*a*b*c*d**4/2 + A*b**3*d**4/4 + 3*B*a**3*d**2*e**2/2 + 3*B*a**2*b*d**3*e + 3*B*a**2*c*d**4/4 + 3*B*a*b**2*d**4/4) + x**3*(2*A*a**3*d**2*e**2 + 4*A*a**2*b*d**3*e + A*a**2*c*d**4 + A*a*b**2*d**4 + 4*B*a**3*d**3*e/3 + B*a**2*b*d**4) + x**2*(2*A*a**3*d**3*e + 3*A*a**2*b*d**4/2 + B*a**3*d**4/2)","B",0
2335,1,1080,0,0.201682," ","integrate((B*x+A)*(e*x+d)**3*(c*x**2+b*x+a)**3,x)","A a^{3} d^{3} x + \frac{B c^{3} e^{3} x^{11}}{11} + x^{10} \left(\frac{A c^{3} e^{3}}{10} + \frac{3 B b c^{2} e^{3}}{10} + \frac{3 B c^{3} d e^{2}}{10}\right) + x^{9} \left(\frac{A b c^{2} e^{3}}{3} + \frac{A c^{3} d e^{2}}{3} + \frac{B a c^{2} e^{3}}{3} + \frac{B b^{2} c e^{3}}{3} + B b c^{2} d e^{2} + \frac{B c^{3} d^{2} e}{3}\right) + x^{8} \left(\frac{3 A a c^{2} e^{3}}{8} + \frac{3 A b^{2} c e^{3}}{8} + \frac{9 A b c^{2} d e^{2}}{8} + \frac{3 A c^{3} d^{2} e}{8} + \frac{3 B a b c e^{3}}{4} + \frac{9 B a c^{2} d e^{2}}{8} + \frac{B b^{3} e^{3}}{8} + \frac{9 B b^{2} c d e^{2}}{8} + \frac{9 B b c^{2} d^{2} e}{8} + \frac{B c^{3} d^{3}}{8}\right) + x^{7} \left(\frac{6 A a b c e^{3}}{7} + \frac{9 A a c^{2} d e^{2}}{7} + \frac{A b^{3} e^{3}}{7} + \frac{9 A b^{2} c d e^{2}}{7} + \frac{9 A b c^{2} d^{2} e}{7} + \frac{A c^{3} d^{3}}{7} + \frac{3 B a^{2} c e^{3}}{7} + \frac{3 B a b^{2} e^{3}}{7} + \frac{18 B a b c d e^{2}}{7} + \frac{9 B a c^{2} d^{2} e}{7} + \frac{3 B b^{3} d e^{2}}{7} + \frac{9 B b^{2} c d^{2} e}{7} + \frac{3 B b c^{2} d^{3}}{7}\right) + x^{6} \left(\frac{A a^{2} c e^{3}}{2} + \frac{A a b^{2} e^{3}}{2} + 3 A a b c d e^{2} + \frac{3 A a c^{2} d^{2} e}{2} + \frac{A b^{3} d e^{2}}{2} + \frac{3 A b^{2} c d^{2} e}{2} + \frac{A b c^{2} d^{3}}{2} + \frac{B a^{2} b e^{3}}{2} + \frac{3 B a^{2} c d e^{2}}{2} + \frac{3 B a b^{2} d e^{2}}{2} + 3 B a b c d^{2} e + \frac{B a c^{2} d^{3}}{2} + \frac{B b^{3} d^{2} e}{2} + \frac{B b^{2} c d^{3}}{2}\right) + x^{5} \left(\frac{3 A a^{2} b e^{3}}{5} + \frac{9 A a^{2} c d e^{2}}{5} + \frac{9 A a b^{2} d e^{2}}{5} + \frac{18 A a b c d^{2} e}{5} + \frac{3 A a c^{2} d^{3}}{5} + \frac{3 A b^{3} d^{2} e}{5} + \frac{3 A b^{2} c d^{3}}{5} + \frac{B a^{3} e^{3}}{5} + \frac{9 B a^{2} b d e^{2}}{5} + \frac{9 B a^{2} c d^{2} e}{5} + \frac{9 B a b^{2} d^{2} e}{5} + \frac{6 B a b c d^{3}}{5} + \frac{B b^{3} d^{3}}{5}\right) + x^{4} \left(\frac{A a^{3} e^{3}}{4} + \frac{9 A a^{2} b d e^{2}}{4} + \frac{9 A a^{2} c d^{2} e}{4} + \frac{9 A a b^{2} d^{2} e}{4} + \frac{3 A a b c d^{3}}{2} + \frac{A b^{3} d^{3}}{4} + \frac{3 B a^{3} d e^{2}}{4} + \frac{9 B a^{2} b d^{2} e}{4} + \frac{3 B a^{2} c d^{3}}{4} + \frac{3 B a b^{2} d^{3}}{4}\right) + x^{3} \left(A a^{3} d e^{2} + 3 A a^{2} b d^{2} e + A a^{2} c d^{3} + A a b^{2} d^{3} + B a^{3} d^{2} e + B a^{2} b d^{3}\right) + x^{2} \left(\frac{3 A a^{3} d^{2} e}{2} + \frac{3 A a^{2} b d^{3}}{2} + \frac{B a^{3} d^{3}}{2}\right)"," ",0,"A*a**3*d**3*x + B*c**3*e**3*x**11/11 + x**10*(A*c**3*e**3/10 + 3*B*b*c**2*e**3/10 + 3*B*c**3*d*e**2/10) + x**9*(A*b*c**2*e**3/3 + A*c**3*d*e**2/3 + B*a*c**2*e**3/3 + B*b**2*c*e**3/3 + B*b*c**2*d*e**2 + B*c**3*d**2*e/3) + x**8*(3*A*a*c**2*e**3/8 + 3*A*b**2*c*e**3/8 + 9*A*b*c**2*d*e**2/8 + 3*A*c**3*d**2*e/8 + 3*B*a*b*c*e**3/4 + 9*B*a*c**2*d*e**2/8 + B*b**3*e**3/8 + 9*B*b**2*c*d*e**2/8 + 9*B*b*c**2*d**2*e/8 + B*c**3*d**3/8) + x**7*(6*A*a*b*c*e**3/7 + 9*A*a*c**2*d*e**2/7 + A*b**3*e**3/7 + 9*A*b**2*c*d*e**2/7 + 9*A*b*c**2*d**2*e/7 + A*c**3*d**3/7 + 3*B*a**2*c*e**3/7 + 3*B*a*b**2*e**3/7 + 18*B*a*b*c*d*e**2/7 + 9*B*a*c**2*d**2*e/7 + 3*B*b**3*d*e**2/7 + 9*B*b**2*c*d**2*e/7 + 3*B*b*c**2*d**3/7) + x**6*(A*a**2*c*e**3/2 + A*a*b**2*e**3/2 + 3*A*a*b*c*d*e**2 + 3*A*a*c**2*d**2*e/2 + A*b**3*d*e**2/2 + 3*A*b**2*c*d**2*e/2 + A*b*c**2*d**3/2 + B*a**2*b*e**3/2 + 3*B*a**2*c*d*e**2/2 + 3*B*a*b**2*d*e**2/2 + 3*B*a*b*c*d**2*e + B*a*c**2*d**3/2 + B*b**3*d**2*e/2 + B*b**2*c*d**3/2) + x**5*(3*A*a**2*b*e**3/5 + 9*A*a**2*c*d*e**2/5 + 9*A*a*b**2*d*e**2/5 + 18*A*a*b*c*d**2*e/5 + 3*A*a*c**2*d**3/5 + 3*A*b**3*d**2*e/5 + 3*A*b**2*c*d**3/5 + B*a**3*e**3/5 + 9*B*a**2*b*d*e**2/5 + 9*B*a**2*c*d**2*e/5 + 9*B*a*b**2*d**2*e/5 + 6*B*a*b*c*d**3/5 + B*b**3*d**3/5) + x**4*(A*a**3*e**3/4 + 9*A*a**2*b*d*e**2/4 + 9*A*a**2*c*d**2*e/4 + 9*A*a*b**2*d**2*e/4 + 3*A*a*b*c*d**3/2 + A*b**3*d**3/4 + 3*B*a**3*d*e**2/4 + 9*B*a**2*b*d**2*e/4 + 3*B*a**2*c*d**3/4 + 3*B*a*b**2*d**3/4) + x**3*(A*a**3*d*e**2 + 3*A*a**2*b*d**2*e + A*a**2*c*d**3 + A*a*b**2*d**3 + B*a**3*d**2*e + B*a**2*b*d**3) + x**2*(3*A*a**3*d**2*e/2 + 3*A*a**2*b*d**3/2 + B*a**3*d**3/2)","B",0
2336,1,753,0,0.165721," ","integrate((B*x+A)*(e*x+d)**2*(c*x**2+b*x+a)**3,x)","A a^{3} d^{2} x + \frac{B c^{3} e^{2} x^{10}}{10} + x^{9} \left(\frac{A c^{3} e^{2}}{9} + \frac{B b c^{2} e^{2}}{3} + \frac{2 B c^{3} d e}{9}\right) + x^{8} \left(\frac{3 A b c^{2} e^{2}}{8} + \frac{A c^{3} d e}{4} + \frac{3 B a c^{2} e^{2}}{8} + \frac{3 B b^{2} c e^{2}}{8} + \frac{3 B b c^{2} d e}{4} + \frac{B c^{3} d^{2}}{8}\right) + x^{7} \left(\frac{3 A a c^{2} e^{2}}{7} + \frac{3 A b^{2} c e^{2}}{7} + \frac{6 A b c^{2} d e}{7} + \frac{A c^{3} d^{2}}{7} + \frac{6 B a b c e^{2}}{7} + \frac{6 B a c^{2} d e}{7} + \frac{B b^{3} e^{2}}{7} + \frac{6 B b^{2} c d e}{7} + \frac{3 B b c^{2} d^{2}}{7}\right) + x^{6} \left(A a b c e^{2} + A a c^{2} d e + \frac{A b^{3} e^{2}}{6} + A b^{2} c d e + \frac{A b c^{2} d^{2}}{2} + \frac{B a^{2} c e^{2}}{2} + \frac{B a b^{2} e^{2}}{2} + 2 B a b c d e + \frac{B a c^{2} d^{2}}{2} + \frac{B b^{3} d e}{3} + \frac{B b^{2} c d^{2}}{2}\right) + x^{5} \left(\frac{3 A a^{2} c e^{2}}{5} + \frac{3 A a b^{2} e^{2}}{5} + \frac{12 A a b c d e}{5} + \frac{3 A a c^{2} d^{2}}{5} + \frac{2 A b^{3} d e}{5} + \frac{3 A b^{2} c d^{2}}{5} + \frac{3 B a^{2} b e^{2}}{5} + \frac{6 B a^{2} c d e}{5} + \frac{6 B a b^{2} d e}{5} + \frac{6 B a b c d^{2}}{5} + \frac{B b^{3} d^{2}}{5}\right) + x^{4} \left(\frac{3 A a^{2} b e^{2}}{4} + \frac{3 A a^{2} c d e}{2} + \frac{3 A a b^{2} d e}{2} + \frac{3 A a b c d^{2}}{2} + \frac{A b^{3} d^{2}}{4} + \frac{B a^{3} e^{2}}{4} + \frac{3 B a^{2} b d e}{2} + \frac{3 B a^{2} c d^{2}}{4} + \frac{3 B a b^{2} d^{2}}{4}\right) + x^{3} \left(\frac{A a^{3} e^{2}}{3} + 2 A a^{2} b d e + A a^{2} c d^{2} + A a b^{2} d^{2} + \frac{2 B a^{3} d e}{3} + B a^{2} b d^{2}\right) + x^{2} \left(A a^{3} d e + \frac{3 A a^{2} b d^{2}}{2} + \frac{B a^{3} d^{2}}{2}\right)"," ",0,"A*a**3*d**2*x + B*c**3*e**2*x**10/10 + x**9*(A*c**3*e**2/9 + B*b*c**2*e**2/3 + 2*B*c**3*d*e/9) + x**8*(3*A*b*c**2*e**2/8 + A*c**3*d*e/4 + 3*B*a*c**2*e**2/8 + 3*B*b**2*c*e**2/8 + 3*B*b*c**2*d*e/4 + B*c**3*d**2/8) + x**7*(3*A*a*c**2*e**2/7 + 3*A*b**2*c*e**2/7 + 6*A*b*c**2*d*e/7 + A*c**3*d**2/7 + 6*B*a*b*c*e**2/7 + 6*B*a*c**2*d*e/7 + B*b**3*e**2/7 + 6*B*b**2*c*d*e/7 + 3*B*b*c**2*d**2/7) + x**6*(A*a*b*c*e**2 + A*a*c**2*d*e + A*b**3*e**2/6 + A*b**2*c*d*e + A*b*c**2*d**2/2 + B*a**2*c*e**2/2 + B*a*b**2*e**2/2 + 2*B*a*b*c*d*e + B*a*c**2*d**2/2 + B*b**3*d*e/3 + B*b**2*c*d**2/2) + x**5*(3*A*a**2*c*e**2/5 + 3*A*a*b**2*e**2/5 + 12*A*a*b*c*d*e/5 + 3*A*a*c**2*d**2/5 + 2*A*b**3*d*e/5 + 3*A*b**2*c*d**2/5 + 3*B*a**2*b*e**2/5 + 6*B*a**2*c*d*e/5 + 6*B*a*b**2*d*e/5 + 6*B*a*b*c*d**2/5 + B*b**3*d**2/5) + x**4*(3*A*a**2*b*e**2/4 + 3*A*a**2*c*d*e/2 + 3*A*a*b**2*d*e/2 + 3*A*a*b*c*d**2/2 + A*b**3*d**2/4 + B*a**3*e**2/4 + 3*B*a**2*b*d*e/2 + 3*B*a**2*c*d**2/4 + 3*B*a*b**2*d**2/4) + x**3*(A*a**3*e**2/3 + 2*A*a**2*b*d*e + A*a**2*c*d**2 + A*a*b**2*d**2 + 2*B*a**3*d*e/3 + B*a**2*b*d**2) + x**2*(A*a**3*d*e + 3*A*a**2*b*d**2/2 + B*a**3*d**2/2)","A",0
2337,1,435,0,0.126089," ","integrate((B*x+A)*(e*x+d)*(c*x**2+b*x+a)**3,x)","A a^{3} d x + \frac{B c^{3} e x^{9}}{9} + x^{8} \left(\frac{A c^{3} e}{8} + \frac{3 B b c^{2} e}{8} + \frac{B c^{3} d}{8}\right) + x^{7} \left(\frac{3 A b c^{2} e}{7} + \frac{A c^{3} d}{7} + \frac{3 B a c^{2} e}{7} + \frac{3 B b^{2} c e}{7} + \frac{3 B b c^{2} d}{7}\right) + x^{6} \left(\frac{A a c^{2} e}{2} + \frac{A b^{2} c e}{2} + \frac{A b c^{2} d}{2} + B a b c e + \frac{B a c^{2} d}{2} + \frac{B b^{3} e}{6} + \frac{B b^{2} c d}{2}\right) + x^{5} \left(\frac{6 A a b c e}{5} + \frac{3 A a c^{2} d}{5} + \frac{A b^{3} e}{5} + \frac{3 A b^{2} c d}{5} + \frac{3 B a^{2} c e}{5} + \frac{3 B a b^{2} e}{5} + \frac{6 B a b c d}{5} + \frac{B b^{3} d}{5}\right) + x^{4} \left(\frac{3 A a^{2} c e}{4} + \frac{3 A a b^{2} e}{4} + \frac{3 A a b c d}{2} + \frac{A b^{3} d}{4} + \frac{3 B a^{2} b e}{4} + \frac{3 B a^{2} c d}{4} + \frac{3 B a b^{2} d}{4}\right) + x^{3} \left(A a^{2} b e + A a^{2} c d + A a b^{2} d + \frac{B a^{3} e}{3} + B a^{2} b d\right) + x^{2} \left(\frac{A a^{3} e}{2} + \frac{3 A a^{2} b d}{2} + \frac{B a^{3} d}{2}\right)"," ",0,"A*a**3*d*x + B*c**3*e*x**9/9 + x**8*(A*c**3*e/8 + 3*B*b*c**2*e/8 + B*c**3*d/8) + x**7*(3*A*b*c**2*e/7 + A*c**3*d/7 + 3*B*a*c**2*e/7 + 3*B*b**2*c*e/7 + 3*B*b*c**2*d/7) + x**6*(A*a*c**2*e/2 + A*b**2*c*e/2 + A*b*c**2*d/2 + B*a*b*c*e + B*a*c**2*d/2 + B*b**3*e/6 + B*b**2*c*d/2) + x**5*(6*A*a*b*c*e/5 + 3*A*a*c**2*d/5 + A*b**3*e/5 + 3*A*b**2*c*d/5 + 3*B*a**2*c*e/5 + 3*B*a*b**2*e/5 + 6*B*a*b*c*d/5 + B*b**3*d/5) + x**4*(3*A*a**2*c*e/4 + 3*A*a*b**2*e/4 + 3*A*a*b*c*d/2 + A*b**3*d/4 + 3*B*a**2*b*e/4 + 3*B*a**2*c*d/4 + 3*B*a*b**2*d/4) + x**3*(A*a**2*b*e + A*a**2*c*d + A*a*b**2*d + B*a**3*e/3 + B*a**2*b*d) + x**2*(A*a**3*e/2 + 3*A*a**2*b*d/2 + B*a**3*d/2)","A",0
2338,1,190,0,0.100401," ","integrate((B*x+A)*(c*x**2+b*x+a)**3,x)","A a^{3} x + \frac{B c^{3} x^{8}}{8} + x^{7} \left(\frac{A c^{3}}{7} + \frac{3 B b c^{2}}{7}\right) + x^{6} \left(\frac{A b c^{2}}{2} + \frac{B a c^{2}}{2} + \frac{B b^{2} c}{2}\right) + x^{5} \left(\frac{3 A a c^{2}}{5} + \frac{3 A b^{2} c}{5} + \frac{6 B a b c}{5} + \frac{B b^{3}}{5}\right) + x^{4} \left(\frac{3 A a b c}{2} + \frac{A b^{3}}{4} + \frac{3 B a^{2} c}{4} + \frac{3 B a b^{2}}{4}\right) + x^{3} \left(A a^{2} c + A a b^{2} + B a^{2} b\right) + x^{2} \left(\frac{3 A a^{2} b}{2} + \frac{B a^{3}}{2}\right)"," ",0,"A*a**3*x + B*c**3*x**8/8 + x**7*(A*c**3/7 + 3*B*b*c**2/7) + x**6*(A*b*c**2/2 + B*a*c**2/2 + B*b**2*c/2) + x**5*(3*A*a*c**2/5 + 3*A*b**2*c/5 + 6*B*a*b*c/5 + B*b**3/5) + x**4*(3*A*a*b*c/2 + A*b**3/4 + 3*B*a**2*c/4 + 3*B*a*b**2/4) + x**3*(A*a**2*c + A*a*b**2 + B*a**2*b) + x**2*(3*A*a**2*b/2 + B*a**3/2)","A",0
2339,1,979,0,2.133350," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d),x)","\frac{B c^{3} x^{7}}{7 e} + x^{6} \left(\frac{A c^{3}}{6 e} + \frac{B b c^{2}}{2 e} - \frac{B c^{3} d}{6 e^{2}}\right) + x^{5} \left(\frac{3 A b c^{2}}{5 e} - \frac{A c^{3} d}{5 e^{2}} + \frac{3 B a c^{2}}{5 e} + \frac{3 B b^{2} c}{5 e} - \frac{3 B b c^{2} d}{5 e^{2}} + \frac{B c^{3} d^{2}}{5 e^{3}}\right) + x^{4} \left(\frac{3 A a c^{2}}{4 e} + \frac{3 A b^{2} c}{4 e} - \frac{3 A b c^{2} d}{4 e^{2}} + \frac{A c^{3} d^{2}}{4 e^{3}} + \frac{3 B a b c}{2 e} - \frac{3 B a c^{2} d}{4 e^{2}} + \frac{B b^{3}}{4 e} - \frac{3 B b^{2} c d}{4 e^{2}} + \frac{3 B b c^{2} d^{2}}{4 e^{3}} - \frac{B c^{3} d^{3}}{4 e^{4}}\right) + x^{3} \left(\frac{2 A a b c}{e} - \frac{A a c^{2} d}{e^{2}} + \frac{A b^{3}}{3 e} - \frac{A b^{2} c d}{e^{2}} + \frac{A b c^{2} d^{2}}{e^{3}} - \frac{A c^{3} d^{3}}{3 e^{4}} + \frac{B a^{2} c}{e} + \frac{B a b^{2}}{e} - \frac{2 B a b c d}{e^{2}} + \frac{B a c^{2} d^{2}}{e^{3}} - \frac{B b^{3} d}{3 e^{2}} + \frac{B b^{2} c d^{2}}{e^{3}} - \frac{B b c^{2} d^{3}}{e^{4}} + \frac{B c^{3} d^{4}}{3 e^{5}}\right) + x^{2} \left(\frac{3 A a^{2} c}{2 e} + \frac{3 A a b^{2}}{2 e} - \frac{3 A a b c d}{e^{2}} + \frac{3 A a c^{2} d^{2}}{2 e^{3}} - \frac{A b^{3} d}{2 e^{2}} + \frac{3 A b^{2} c d^{2}}{2 e^{3}} - \frac{3 A b c^{2} d^{3}}{2 e^{4}} + \frac{A c^{3} d^{4}}{2 e^{5}} + \frac{3 B a^{2} b}{2 e} - \frac{3 B a^{2} c d}{2 e^{2}} - \frac{3 B a b^{2} d}{2 e^{2}} + \frac{3 B a b c d^{2}}{e^{3}} - \frac{3 B a c^{2} d^{3}}{2 e^{4}} + \frac{B b^{3} d^{2}}{2 e^{3}} - \frac{3 B b^{2} c d^{3}}{2 e^{4}} + \frac{3 B b c^{2} d^{4}}{2 e^{5}} - \frac{B c^{3} d^{5}}{2 e^{6}}\right) + x \left(\frac{3 A a^{2} b}{e} - \frac{3 A a^{2} c d}{e^{2}} - \frac{3 A a b^{2} d}{e^{2}} + \frac{6 A a b c d^{2}}{e^{3}} - \frac{3 A a c^{2} d^{3}}{e^{4}} + \frac{A b^{3} d^{2}}{e^{3}} - \frac{3 A b^{2} c d^{3}}{e^{4}} + \frac{3 A b c^{2} d^{4}}{e^{5}} - \frac{A c^{3} d^{5}}{e^{6}} + \frac{B a^{3}}{e} - \frac{3 B a^{2} b d}{e^{2}} + \frac{3 B a^{2} c d^{2}}{e^{3}} + \frac{3 B a b^{2} d^{2}}{e^{3}} - \frac{6 B a b c d^{3}}{e^{4}} + \frac{3 B a c^{2} d^{4}}{e^{5}} - \frac{B b^{3} d^{3}}{e^{4}} + \frac{3 B b^{2} c d^{4}}{e^{5}} - \frac{3 B b c^{2} d^{5}}{e^{6}} + \frac{B c^{3} d^{6}}{e^{7}}\right) - \frac{\left(- A e + B d\right) \left(a e^{2} - b d e + c d^{2}\right)^{3} \log{\left(d + e x \right)}}{e^{8}}"," ",0,"B*c**3*x**7/(7*e) + x**6*(A*c**3/(6*e) + B*b*c**2/(2*e) - B*c**3*d/(6*e**2)) + x**5*(3*A*b*c**2/(5*e) - A*c**3*d/(5*e**2) + 3*B*a*c**2/(5*e) + 3*B*b**2*c/(5*e) - 3*B*b*c**2*d/(5*e**2) + B*c**3*d**2/(5*e**3)) + x**4*(3*A*a*c**2/(4*e) + 3*A*b**2*c/(4*e) - 3*A*b*c**2*d/(4*e**2) + A*c**3*d**2/(4*e**3) + 3*B*a*b*c/(2*e) - 3*B*a*c**2*d/(4*e**2) + B*b**3/(4*e) - 3*B*b**2*c*d/(4*e**2) + 3*B*b*c**2*d**2/(4*e**3) - B*c**3*d**3/(4*e**4)) + x**3*(2*A*a*b*c/e - A*a*c**2*d/e**2 + A*b**3/(3*e) - A*b**2*c*d/e**2 + A*b*c**2*d**2/e**3 - A*c**3*d**3/(3*e**4) + B*a**2*c/e + B*a*b**2/e - 2*B*a*b*c*d/e**2 + B*a*c**2*d**2/e**3 - B*b**3*d/(3*e**2) + B*b**2*c*d**2/e**3 - B*b*c**2*d**3/e**4 + B*c**3*d**4/(3*e**5)) + x**2*(3*A*a**2*c/(2*e) + 3*A*a*b**2/(2*e) - 3*A*a*b*c*d/e**2 + 3*A*a*c**2*d**2/(2*e**3) - A*b**3*d/(2*e**2) + 3*A*b**2*c*d**2/(2*e**3) - 3*A*b*c**2*d**3/(2*e**4) + A*c**3*d**4/(2*e**5) + 3*B*a**2*b/(2*e) - 3*B*a**2*c*d/(2*e**2) - 3*B*a*b**2*d/(2*e**2) + 3*B*a*b*c*d**2/e**3 - 3*B*a*c**2*d**3/(2*e**4) + B*b**3*d**2/(2*e**3) - 3*B*b**2*c*d**3/(2*e**4) + 3*B*b*c**2*d**4/(2*e**5) - B*c**3*d**5/(2*e**6)) + x*(3*A*a**2*b/e - 3*A*a**2*c*d/e**2 - 3*A*a*b**2*d/e**2 + 6*A*a*b*c*d**2/e**3 - 3*A*a*c**2*d**3/e**4 + A*b**3*d**2/e**3 - 3*A*b**2*c*d**3/e**4 + 3*A*b*c**2*d**4/e**5 - A*c**3*d**5/e**6 + B*a**3/e - 3*B*a**2*b*d/e**2 + 3*B*a**2*c*d**2/e**3 + 3*B*a*b**2*d**2/e**3 - 6*B*a*b*c*d**3/e**4 + 3*B*a*c**2*d**4/e**5 - B*b**3*d**3/e**4 + 3*B*b**2*c*d**4/e**5 - 3*B*b*c**2*d**5/e**6 + B*c**3*d**6/e**7) - (-A*e + B*d)*(a*e**2 - b*d*e + c*d**2)**3*log(d + e*x)/e**8","A",0
2340,1,1056,0,10.135606," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**2,x)","\frac{B c^{3} x^{6}}{6 e^{2}} + x^{5} \left(\frac{A c^{3}}{5 e^{2}} + \frac{3 B b c^{2}}{5 e^{2}} - \frac{2 B c^{3} d}{5 e^{3}}\right) + x^{4} \left(\frac{3 A b c^{2}}{4 e^{2}} - \frac{A c^{3} d}{2 e^{3}} + \frac{3 B a c^{2}}{4 e^{2}} + \frac{3 B b^{2} c}{4 e^{2}} - \frac{3 B b c^{2} d}{2 e^{3}} + \frac{3 B c^{3} d^{2}}{4 e^{4}}\right) + x^{3} \left(\frac{A a c^{2}}{e^{2}} + \frac{A b^{2} c}{e^{2}} - \frac{2 A b c^{2} d}{e^{3}} + \frac{A c^{3} d^{2}}{e^{4}} + \frac{2 B a b c}{e^{2}} - \frac{2 B a c^{2} d}{e^{3}} + \frac{B b^{3}}{3 e^{2}} - \frac{2 B b^{2} c d}{e^{3}} + \frac{3 B b c^{2} d^{2}}{e^{4}} - \frac{4 B c^{3} d^{3}}{3 e^{5}}\right) + x^{2} \left(\frac{3 A a b c}{e^{2}} - \frac{3 A a c^{2} d}{e^{3}} + \frac{A b^{3}}{2 e^{2}} - \frac{3 A b^{2} c d}{e^{3}} + \frac{9 A b c^{2} d^{2}}{2 e^{4}} - \frac{2 A c^{3} d^{3}}{e^{5}} + \frac{3 B a^{2} c}{2 e^{2}} + \frac{3 B a b^{2}}{2 e^{2}} - \frac{6 B a b c d}{e^{3}} + \frac{9 B a c^{2} d^{2}}{2 e^{4}} - \frac{B b^{3} d}{e^{3}} + \frac{9 B b^{2} c d^{2}}{2 e^{4}} - \frac{6 B b c^{2} d^{3}}{e^{5}} + \frac{5 B c^{3} d^{4}}{2 e^{6}}\right) + x \left(\frac{3 A a^{2} c}{e^{2}} + \frac{3 A a b^{2}}{e^{2}} - \frac{12 A a b c d}{e^{3}} + \frac{9 A a c^{2} d^{2}}{e^{4}} - \frac{2 A b^{3} d}{e^{3}} + \frac{9 A b^{2} c d^{2}}{e^{4}} - \frac{12 A b c^{2} d^{3}}{e^{5}} + \frac{5 A c^{3} d^{4}}{e^{6}} + \frac{3 B a^{2} b}{e^{2}} - \frac{6 B a^{2} c d}{e^{3}} - \frac{6 B a b^{2} d}{e^{3}} + \frac{18 B a b c d^{2}}{e^{4}} - \frac{12 B a c^{2} d^{3}}{e^{5}} + \frac{3 B b^{3} d^{2}}{e^{4}} - \frac{12 B b^{2} c d^{3}}{e^{5}} + \frac{15 B b c^{2} d^{4}}{e^{6}} - \frac{6 B c^{3} d^{5}}{e^{7}}\right) + \frac{- A a^{3} e^{7} + 3 A a^{2} b d e^{6} - 3 A a^{2} c d^{2} e^{5} - 3 A a b^{2} d^{2} e^{5} + 6 A a b c d^{3} e^{4} - 3 A a c^{2} d^{4} e^{3} + A b^{3} d^{3} e^{4} - 3 A b^{2} c d^{4} e^{3} + 3 A b c^{2} d^{5} e^{2} - A c^{3} d^{6} e + B a^{3} d e^{6} - 3 B a^{2} b d^{2} e^{5} + 3 B a^{2} c d^{3} e^{4} + 3 B a b^{2} d^{3} e^{4} - 6 B a b c d^{4} e^{3} + 3 B a c^{2} d^{5} e^{2} - B b^{3} d^{4} e^{3} + 3 B b^{2} c d^{5} e^{2} - 3 B b c^{2} d^{6} e + B c^{3} d^{7}}{d e^{8} + e^{9} x} + \frac{\left(a e^{2} - b d e + c d^{2}\right)^{2} \left(3 A b e^{2} - 6 A c d e + B a e^{2} - 4 B b d e + 7 B c d^{2}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"B*c**3*x**6/(6*e**2) + x**5*(A*c**3/(5*e**2) + 3*B*b*c**2/(5*e**2) - 2*B*c**3*d/(5*e**3)) + x**4*(3*A*b*c**2/(4*e**2) - A*c**3*d/(2*e**3) + 3*B*a*c**2/(4*e**2) + 3*B*b**2*c/(4*e**2) - 3*B*b*c**2*d/(2*e**3) + 3*B*c**3*d**2/(4*e**4)) + x**3*(A*a*c**2/e**2 + A*b**2*c/e**2 - 2*A*b*c**2*d/e**3 + A*c**3*d**2/e**4 + 2*B*a*b*c/e**2 - 2*B*a*c**2*d/e**3 + B*b**3/(3*e**2) - 2*B*b**2*c*d/e**3 + 3*B*b*c**2*d**2/e**4 - 4*B*c**3*d**3/(3*e**5)) + x**2*(3*A*a*b*c/e**2 - 3*A*a*c**2*d/e**3 + A*b**3/(2*e**2) - 3*A*b**2*c*d/e**3 + 9*A*b*c**2*d**2/(2*e**4) - 2*A*c**3*d**3/e**5 + 3*B*a**2*c/(2*e**2) + 3*B*a*b**2/(2*e**2) - 6*B*a*b*c*d/e**3 + 9*B*a*c**2*d**2/(2*e**4) - B*b**3*d/e**3 + 9*B*b**2*c*d**2/(2*e**4) - 6*B*b*c**2*d**3/e**5 + 5*B*c**3*d**4/(2*e**6)) + x*(3*A*a**2*c/e**2 + 3*A*a*b**2/e**2 - 12*A*a*b*c*d/e**3 + 9*A*a*c**2*d**2/e**4 - 2*A*b**3*d/e**3 + 9*A*b**2*c*d**2/e**4 - 12*A*b*c**2*d**3/e**5 + 5*A*c**3*d**4/e**6 + 3*B*a**2*b/e**2 - 6*B*a**2*c*d/e**3 - 6*B*a*b**2*d/e**3 + 18*B*a*b*c*d**2/e**4 - 12*B*a*c**2*d**3/e**5 + 3*B*b**3*d**2/e**4 - 12*B*b**2*c*d**3/e**5 + 15*B*b*c**2*d**4/e**6 - 6*B*c**3*d**5/e**7) + (-A*a**3*e**7 + 3*A*a**2*b*d*e**6 - 3*A*a**2*c*d**2*e**5 - 3*A*a*b**2*d**2*e**5 + 6*A*a*b*c*d**3*e**4 - 3*A*a*c**2*d**4*e**3 + A*b**3*d**3*e**4 - 3*A*b**2*c*d**4*e**3 + 3*A*b*c**2*d**5*e**2 - A*c**3*d**6*e + B*a**3*d*e**6 - 3*B*a**2*b*d**2*e**5 + 3*B*a**2*c*d**3*e**4 + 3*B*a*b**2*d**3*e**4 - 6*B*a*b*c*d**4*e**3 + 3*B*a*c**2*d**5*e**2 - B*b**3*d**4*e**3 + 3*B*b**2*c*d**5*e**2 - 3*B*b*c**2*d**6*e + B*c**3*d**7)/(d*e**8 + e**9*x) + (a*e**2 - b*d*e + c*d**2)**2*(3*A*b*e**2 - 6*A*c*d*e + B*a*e**2 - 4*B*b*d*e + 7*B*c*d**2)*log(d + e*x)/e**8","B",0
2341,1,1149,0,86.430127," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**3,x)","\frac{B c^{3} x^{5}}{5 e^{3}} + x^{4} \left(\frac{A c^{3}}{4 e^{3}} + \frac{3 B b c^{2}}{4 e^{3}} - \frac{3 B c^{3} d}{4 e^{4}}\right) + x^{3} \left(\frac{A b c^{2}}{e^{3}} - \frac{A c^{3} d}{e^{4}} + \frac{B a c^{2}}{e^{3}} + \frac{B b^{2} c}{e^{3}} - \frac{3 B b c^{2} d}{e^{4}} + \frac{2 B c^{3} d^{2}}{e^{5}}\right) + x^{2} \left(\frac{3 A a c^{2}}{2 e^{3}} + \frac{3 A b^{2} c}{2 e^{3}} - \frac{9 A b c^{2} d}{2 e^{4}} + \frac{3 A c^{3} d^{2}}{e^{5}} + \frac{3 B a b c}{e^{3}} - \frac{9 B a c^{2} d}{2 e^{4}} + \frac{B b^{3}}{2 e^{3}} - \frac{9 B b^{2} c d}{2 e^{4}} + \frac{9 B b c^{2} d^{2}}{e^{5}} - \frac{5 B c^{3} d^{3}}{e^{6}}\right) + x \left(\frac{6 A a b c}{e^{3}} - \frac{9 A a c^{2} d}{e^{4}} + \frac{A b^{3}}{e^{3}} - \frac{9 A b^{2} c d}{e^{4}} + \frac{18 A b c^{2} d^{2}}{e^{5}} - \frac{10 A c^{3} d^{3}}{e^{6}} + \frac{3 B a^{2} c}{e^{3}} + \frac{3 B a b^{2}}{e^{3}} - \frac{18 B a b c d}{e^{4}} + \frac{18 B a c^{2} d^{2}}{e^{5}} - \frac{3 B b^{3} d}{e^{4}} + \frac{18 B b^{2} c d^{2}}{e^{5}} - \frac{30 B b c^{2} d^{3}}{e^{6}} + \frac{15 B c^{3} d^{4}}{e^{7}}\right) + \frac{- A a^{3} e^{7} - 3 A a^{2} b d e^{6} + 9 A a^{2} c d^{2} e^{5} + 9 A a b^{2} d^{2} e^{5} - 30 A a b c d^{3} e^{4} + 21 A a c^{2} d^{4} e^{3} - 5 A b^{3} d^{3} e^{4} + 21 A b^{2} c d^{4} e^{3} - 27 A b c^{2} d^{5} e^{2} + 11 A c^{3} d^{6} e - B a^{3} d e^{6} + 9 B a^{2} b d^{2} e^{5} - 15 B a^{2} c d^{3} e^{4} - 15 B a b^{2} d^{3} e^{4} + 42 B a b c d^{4} e^{3} - 27 B a c^{2} d^{5} e^{2} + 7 B b^{3} d^{4} e^{3} - 27 B b^{2} c d^{5} e^{2} + 33 B b c^{2} d^{6} e - 13 B c^{3} d^{7} + x \left(- 6 A a^{2} b e^{7} + 12 A a^{2} c d e^{6} + 12 A a b^{2} d e^{6} - 36 A a b c d^{2} e^{5} + 24 A a c^{2} d^{3} e^{4} - 6 A b^{3} d^{2} e^{5} + 24 A b^{2} c d^{3} e^{4} - 30 A b c^{2} d^{4} e^{3} + 12 A c^{3} d^{5} e^{2} - 2 B a^{3} e^{7} + 12 B a^{2} b d e^{6} - 18 B a^{2} c d^{2} e^{5} - 18 B a b^{2} d^{2} e^{5} + 48 B a b c d^{3} e^{4} - 30 B a c^{2} d^{4} e^{3} + 8 B b^{3} d^{3} e^{4} - 30 B b^{2} c d^{4} e^{3} + 36 B b c^{2} d^{5} e^{2} - 14 B c^{3} d^{6} e\right)}{2 d^{2} e^{8} + 4 d e^{9} x + 2 e^{10} x^{2}} + \frac{3 \left(a e^{2} - b d e + c d^{2}\right) \left(A a c e^{3} + A b^{2} e^{3} - 5 A b c d e^{2} + 5 A c^{2} d^{2} e + B a b e^{3} - 3 B a c d e^{2} - 2 B b^{2} d e^{2} + 8 B b c d^{2} e - 7 B c^{2} d^{3}\right) \log{\left(d + e x \right)}}{e^{8}}"," ",0,"B*c**3*x**5/(5*e**3) + x**4*(A*c**3/(4*e**3) + 3*B*b*c**2/(4*e**3) - 3*B*c**3*d/(4*e**4)) + x**3*(A*b*c**2/e**3 - A*c**3*d/e**4 + B*a*c**2/e**3 + B*b**2*c/e**3 - 3*B*b*c**2*d/e**4 + 2*B*c**3*d**2/e**5) + x**2*(3*A*a*c**2/(2*e**3) + 3*A*b**2*c/(2*e**3) - 9*A*b*c**2*d/(2*e**4) + 3*A*c**3*d**2/e**5 + 3*B*a*b*c/e**3 - 9*B*a*c**2*d/(2*e**4) + B*b**3/(2*e**3) - 9*B*b**2*c*d/(2*e**4) + 9*B*b*c**2*d**2/e**5 - 5*B*c**3*d**3/e**6) + x*(6*A*a*b*c/e**3 - 9*A*a*c**2*d/e**4 + A*b**3/e**3 - 9*A*b**2*c*d/e**4 + 18*A*b*c**2*d**2/e**5 - 10*A*c**3*d**3/e**6 + 3*B*a**2*c/e**3 + 3*B*a*b**2/e**3 - 18*B*a*b*c*d/e**4 + 18*B*a*c**2*d**2/e**5 - 3*B*b**3*d/e**4 + 18*B*b**2*c*d**2/e**5 - 30*B*b*c**2*d**3/e**6 + 15*B*c**3*d**4/e**7) + (-A*a**3*e**7 - 3*A*a**2*b*d*e**6 + 9*A*a**2*c*d**2*e**5 + 9*A*a*b**2*d**2*e**5 - 30*A*a*b*c*d**3*e**4 + 21*A*a*c**2*d**4*e**3 - 5*A*b**3*d**3*e**4 + 21*A*b**2*c*d**4*e**3 - 27*A*b*c**2*d**5*e**2 + 11*A*c**3*d**6*e - B*a**3*d*e**6 + 9*B*a**2*b*d**2*e**5 - 15*B*a**2*c*d**3*e**4 - 15*B*a*b**2*d**3*e**4 + 42*B*a*b*c*d**4*e**3 - 27*B*a*c**2*d**5*e**2 + 7*B*b**3*d**4*e**3 - 27*B*b**2*c*d**5*e**2 + 33*B*b*c**2*d**6*e - 13*B*c**3*d**7 + x*(-6*A*a**2*b*e**7 + 12*A*a**2*c*d*e**6 + 12*A*a*b**2*d*e**6 - 36*A*a*b*c*d**2*e**5 + 24*A*a*c**2*d**3*e**4 - 6*A*b**3*d**2*e**5 + 24*A*b**2*c*d**3*e**4 - 30*A*b*c**2*d**4*e**3 + 12*A*c**3*d**5*e**2 - 2*B*a**3*e**7 + 12*B*a**2*b*d*e**6 - 18*B*a**2*c*d**2*e**5 - 18*B*a*b**2*d**2*e**5 + 48*B*a*b*c*d**3*e**4 - 30*B*a*c**2*d**4*e**3 + 8*B*b**3*d**3*e**4 - 30*B*b**2*c*d**4*e**3 + 36*B*b*c**2*d**5*e**2 - 14*B*c**3*d**6*e))/(2*d**2*e**8 + 4*d*e**9*x + 2*e**10*x**2) + 3*(a*e**2 - b*d*e + c*d**2)*(A*a*c*e**3 + A*b**2*e**3 - 5*A*b*c*d*e**2 + 5*A*c**2*d**2*e + B*a*b*e**3 - 3*B*a*c*d*e**2 - 2*B*b**2*d*e**2 + 8*B*b*c*d**2*e - 7*B*c**2*d**3)*log(d + e*x)/e**8","B",0
2342,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2343,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2344,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2345,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2346,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2347,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2348,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2349,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+b*x+a)**3/(e*x+d)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2350,1,3267,0,3.379000," ","integrate(x*(e*x+d)**m*(c*x**2+b*x+a),x)","\begin{cases} d^{m} \left(\frac{a x^{2}}{2} + \frac{b x^{3}}{3} + \frac{c x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{a d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 a e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 b d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 b d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 b e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 c d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 c d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{a d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 a e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 b d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 b d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 b e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 c d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 c e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\\frac{2 a d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 a d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 a e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 b d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 b e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 c d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{c e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\- \frac{a d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{a x}{e} + \frac{b d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{b d x}{e^{2}} + \frac{b x^{2}}{2 e} - \frac{c d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{c d^{2} x}{e^{3}} - \frac{c d x^{2}}{2 e^{2}} + \frac{c x^{3}}{3 e} & \text{for}\: m = -1 \\- \frac{a d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 a d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 a d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 a d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 a d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 a e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 a e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 a e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 b d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 b d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 b d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 b d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 b d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 b d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 b e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 b e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 b e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 c d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 c d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 c d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{c d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 c d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 c d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{c e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 c e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a*x**2/2 + b*x**3/3 + c*x**4/4), Eq(e, 0)), (-a*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*a*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*b*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*b*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*b*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*c*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*c*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-a*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*a*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*b*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*b*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*b*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*b*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*b*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*c*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*c*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (2*a*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*a*d*e**2/(2*d*e**4 + 2*e**5*x) + 2*a*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*b*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*b*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*b*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*b*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 6*c*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*c*d**3/(2*d*e**4 + 2*e**5*x) + 6*c*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*c*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + c*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (-a*d*log(d/e + x)/e**2 + a*x/e + b*d**2*log(d/e + x)/e**3 - b*d*x/e**2 + b*x**2/(2*e) - c*d**3*log(d/e + x)/e**4 + c*d**2*x/e**3 - c*d*x**2/(2*e**2) + c*x**3/(3*e), Eq(m, -1)), (-a*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*a*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*a*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*a*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*a*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*a*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*a*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*a*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*b*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*b*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*b*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*b*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*b*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*b*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*b*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*b*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*b*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*c*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*c*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*c*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + c*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*c*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*c*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + c*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*c*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
2351,1,192,0,0.096139," ","integrate(x*(e*x+d)**5*(c*x**2+b*x+a),x)","\frac{a d^{5} x^{2}}{2} + \frac{c e^{5} x^{9}}{9} + x^{8} \left(\frac{b e^{5}}{8} + \frac{5 c d e^{4}}{8}\right) + x^{7} \left(\frac{a e^{5}}{7} + \frac{5 b d e^{4}}{7} + \frac{10 c d^{2} e^{3}}{7}\right) + x^{6} \left(\frac{5 a d e^{4}}{6} + \frac{5 b d^{2} e^{3}}{3} + \frac{5 c d^{3} e^{2}}{3}\right) + x^{5} \left(2 a d^{2} e^{3} + 2 b d^{3} e^{2} + c d^{4} e\right) + x^{4} \left(\frac{5 a d^{3} e^{2}}{2} + \frac{5 b d^{4} e}{4} + \frac{c d^{5}}{4}\right) + x^{3} \left(\frac{5 a d^{4} e}{3} + \frac{b d^{5}}{3}\right)"," ",0,"a*d**5*x**2/2 + c*e**5*x**9/9 + x**8*(b*e**5/8 + 5*c*d*e**4/8) + x**7*(a*e**5/7 + 5*b*d*e**4/7 + 10*c*d**2*e**3/7) + x**6*(5*a*d*e**4/6 + 5*b*d**2*e**3/3 + 5*c*d**3*e**2/3) + x**5*(2*a*d**2*e**3 + 2*b*d**3*e**2 + c*d**4*e) + x**4*(5*a*d**3*e**2/2 + 5*b*d**4*e/4 + c*d**5/4) + x**3*(5*a*d**4*e/3 + b*d**5/3)","B",0
2352,1,153,0,0.087891," ","integrate(x*(e*x+d)**4*(c*x**2+b*x+a),x)","\frac{a d^{4} x^{2}}{2} + \frac{c e^{4} x^{8}}{8} + x^{7} \left(\frac{b e^{4}}{7} + \frac{4 c d e^{3}}{7}\right) + x^{6} \left(\frac{a e^{4}}{6} + \frac{2 b d e^{3}}{3} + c d^{2} e^{2}\right) + x^{5} \left(\frac{4 a d e^{3}}{5} + \frac{6 b d^{2} e^{2}}{5} + \frac{4 c d^{3} e}{5}\right) + x^{4} \left(\frac{3 a d^{2} e^{2}}{2} + b d^{3} e + \frac{c d^{4}}{4}\right) + x^{3} \left(\frac{4 a d^{3} e}{3} + \frac{b d^{4}}{3}\right)"," ",0,"a*d**4*x**2/2 + c*e**4*x**8/8 + x**7*(b*e**4/7 + 4*c*d*e**3/7) + x**6*(a*e**4/6 + 2*b*d*e**3/3 + c*d**2*e**2) + x**5*(4*a*d*e**3/5 + 6*b*d**2*e**2/5 + 4*c*d**3*e/5) + x**4*(3*a*d**2*e**2/2 + b*d**3*e + c*d**4/4) + x**3*(4*a*d**3*e/3 + b*d**4/3)","A",0
2353,1,116,0,0.082311," ","integrate(x*(e*x+d)**3*(c*x**2+b*x+a),x)","\frac{a d^{3} x^{2}}{2} + \frac{c e^{3} x^{7}}{7} + x^{6} \left(\frac{b e^{3}}{6} + \frac{c d e^{2}}{2}\right) + x^{5} \left(\frac{a e^{3}}{5} + \frac{3 b d e^{2}}{5} + \frac{3 c d^{2} e}{5}\right) + x^{4} \left(\frac{3 a d e^{2}}{4} + \frac{3 b d^{2} e}{4} + \frac{c d^{3}}{4}\right) + x^{3} \left(a d^{2} e + \frac{b d^{3}}{3}\right)"," ",0,"a*d**3*x**2/2 + c*e**3*x**7/7 + x**6*(b*e**3/6 + c*d*e**2/2) + x**5*(a*e**3/5 + 3*b*d*e**2/5 + 3*c*d**2*e/5) + x**4*(3*a*d*e**2/4 + 3*b*d**2*e/4 + c*d**3/4) + x**3*(a*d**2*e + b*d**3/3)","A",0
2354,1,80,0,0.075170," ","integrate(x*(e*x+d)**2*(c*x**2+b*x+a),x)","\frac{a d^{2} x^{2}}{2} + \frac{c e^{2} x^{6}}{6} + x^{5} \left(\frac{b e^{2}}{5} + \frac{2 c d e}{5}\right) + x^{4} \left(\frac{a e^{2}}{4} + \frac{b d e}{2} + \frac{c d^{2}}{4}\right) + x^{3} \left(\frac{2 a d e}{3} + \frac{b d^{2}}{3}\right)"," ",0,"a*d**2*x**2/2 + c*e**2*x**6/6 + x**5*(b*e**2/5 + 2*c*d*e/5) + x**4*(a*e**2/4 + b*d*e/2 + c*d**2/4) + x**3*(2*a*d*e/3 + b*d**2/3)","A",0
2355,1,42,0,0.065979," ","integrate(x*(e*x+d)*(c*x**2+b*x+a),x)","\frac{a d x^{2}}{2} + \frac{c e x^{5}}{5} + x^{4} \left(\frac{b e}{4} + \frac{c d}{4}\right) + x^{3} \left(\frac{a e}{3} + \frac{b d}{3}\right)"," ",0,"a*d*x**2/2 + c*e*x**5/5 + x**4*(b*e/4 + c*d/4) + x**3*(a*e/3 + b*d/3)","A",0
2356,1,19,0,0.058092," ","integrate(x*(c*x**2+b*x+a),x)","\frac{a x^{2}}{2} + \frac{b x^{3}}{3} + \frac{c x^{4}}{4}"," ",0,"a*x**2/2 + b*x**3/3 + c*x**4/4","A",0
2357,1,71,0,0.237781," ","integrate(x*(c*x**2+b*x+a)/(e*x+d),x)","\frac{c x^{3}}{3 e} - \frac{d \left(a e^{2} - b d e + c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}} + x^{2} \left(\frac{b}{2 e} - \frac{c d}{2 e^{2}}\right) + x \left(\frac{a}{e} - \frac{b d}{e^{2}} + \frac{c d^{2}}{e^{3}}\right)"," ",0,"c*x**3/(3*e) - d*(a*e**2 - b*d*e + c*d**2)*log(d + e*x)/e**4 + x**2*(b/(2*e) - c*d/(2*e**2)) + x*(a/e - b*d/e**2 + c*d**2/e**3)","A",0
2358,1,82,0,0.419421," ","integrate(x*(c*x**2+b*x+a)/(e*x+d)**2,x)","\frac{c x^{2}}{2 e^{2}} + x \left(\frac{b}{e^{2}} - \frac{2 c d}{e^{3}}\right) + \frac{a d e^{2} - b d^{2} e + c d^{3}}{d e^{4} + e^{5} x} + \frac{\left(a e^{2} - 2 b d e + 3 c d^{2}\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"c*x**2/(2*e**2) + x*(b/e**2 - 2*c*d/e**3) + (a*d*e**2 - b*d**2*e + c*d**3)/(d*e**4 + e**5*x) + (a*e**2 - 2*b*d*e + 3*c*d**2)*log(d + e*x)/e**4","A",0
2359,1,97,0,0.758812," ","integrate(x*(c*x**2+b*x+a)/(e*x+d)**3,x)","\frac{c x}{e^{3}} + \frac{- a d e^{2} + 3 b d^{2} e - 5 c d^{3} + x \left(- 2 a e^{3} + 4 b d e^{2} - 6 c d^{2} e\right)}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{\left(b e - 3 c d\right) \log{\left(d + e x \right)}}{e^{4}}"," ",0,"c*x/e**3 + (-a*d*e**2 + 3*b*d**2*e - 5*c*d**3 + x*(-2*a*e**3 + 4*b*d*e**2 - 6*c*d**2*e))/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + (b*e - 3*c*d)*log(d + e*x)/e**4","A",0
2360,1,114,0,1.330068," ","integrate(x*(c*x**2+b*x+a)/(e*x+d)**4,x)","\frac{c \log{\left(d + e x \right)}}{e^{4}} + \frac{- a d e^{2} - 2 b d^{2} e + 11 c d^{3} + x^{2} \left(- 6 b e^{3} + 18 c d e^{2}\right) + x \left(- 3 a e^{3} - 6 b d e^{2} + 27 c d^{2} e\right)}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}}"," ",0,"c*log(d + e*x)/e**4 + (-a*d*e**2 - 2*b*d**2*e + 11*c*d**3 + x**2*(-6*b*e**3 + 18*c*d*e**2) + x*(-3*a*e**3 - 6*b*d*e**2 + 27*c*d**2*e))/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3)","A",0
2361,1,126,0,2.213512," ","integrate(x*(c*x**2+b*x+a)/(e*x+d)**5,x)","\frac{- a d e^{2} - b d^{2} e - 3 c d^{3} - 12 c e^{3} x^{3} + x^{2} \left(- 6 b e^{3} - 18 c d e^{2}\right) + x \left(- 4 a e^{3} - 4 b d e^{2} - 12 c d^{2} e\right)}{12 d^{4} e^{4} + 48 d^{3} e^{5} x + 72 d^{2} e^{6} x^{2} + 48 d e^{7} x^{3} + 12 e^{8} x^{4}}"," ",0,"(-a*d*e**2 - b*d**2*e - 3*c*d**3 - 12*c*e**3*x**3 + x**2*(-6*b*e**3 - 18*c*d*e**2) + x*(-4*a*e**3 - 4*b*d*e**2 - 12*c*d**2*e))/(12*d**4*e**4 + 48*d**3*e**5*x + 72*d**2*e**6*x**2 + 48*d*e**7*x**3 + 12*e**8*x**4)","A",0
2362,1,141,0,3.659224," ","integrate(x*(c*x**2+b*x+a)/(e*x+d)**6,x)","\frac{- 3 a d e^{2} - 2 b d^{2} e - 3 c d^{3} - 30 c e^{3} x^{3} + x^{2} \left(- 20 b e^{3} - 30 c d e^{2}\right) + x \left(- 15 a e^{3} - 10 b d e^{2} - 15 c d^{2} e\right)}{60 d^{5} e^{4} + 300 d^{4} e^{5} x + 600 d^{3} e^{6} x^{2} + 600 d^{2} e^{7} x^{3} + 300 d e^{8} x^{4} + 60 e^{9} x^{5}}"," ",0,"(-3*a*d*e**2 - 2*b*d**2*e - 3*c*d**3 - 30*c*e**3*x**3 + x**2*(-20*b*e**3 - 30*c*d*e**2) + x*(-15*a*e**3 - 10*b*d*e**2 - 15*c*d**2*e))/(60*d**5*e**4 + 300*d**4*e**5*x + 600*d**3*e**6*x**2 + 600*d**2*e**7*x**3 + 300*d*e**8*x**4 + 60*e**9*x**5)","A",0
2363,1,150,0,5.832769," ","integrate(x*(c*x**2+b*x+a)/(e*x+d)**7,x)","\frac{- 2 a d e^{2} - b d^{2} e - c d^{3} - 20 c e^{3} x^{3} + x^{2} \left(- 15 b e^{3} - 15 c d e^{2}\right) + x \left(- 12 a e^{3} - 6 b d e^{2} - 6 c d^{2} e\right)}{60 d^{6} e^{4} + 360 d^{5} e^{5} x + 900 d^{4} e^{6} x^{2} + 1200 d^{3} e^{7} x^{3} + 900 d^{2} e^{8} x^{4} + 360 d e^{9} x^{5} + 60 e^{10} x^{6}}"," ",0,"(-2*a*d*e**2 - b*d**2*e - c*d**3 - 20*c*e**3*x**3 + x**2*(-15*b*e**3 - 15*c*d*e**2) + x*(-12*a*e**3 - 6*b*d*e**2 - 6*c*d**2*e))/(60*d**6*e**4 + 360*d**5*e**5*x + 900*d**4*e**6*x**2 + 1200*d**3*e**7*x**3 + 900*d**2*e**8*x**4 + 360*d*e**9*x**5 + 60*e**10*x**6)","A",0
2364,1,2759,0,25.808670," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x+a),x)","\frac{B e^{3} x^{3}}{3 c} + x^{2} \left(\frac{A e^{3}}{2 c} - \frac{B b e^{3}}{2 c^{2}} + \frac{3 B d e^{2}}{2 c}\right) + x \left(- \frac{A b e^{3}}{c^{2}} + \frac{3 A d e^{2}}{c} - \frac{B a e^{3}}{c^{2}} + \frac{B b^{2} e^{3}}{c^{3}} - \frac{3 B b d e^{2}}{c^{2}} + \frac{3 B d^{2} e}{c}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{- A a c^{2} e^{3} + A b^{2} c e^{3} - 3 A b c^{2} d e^{2} + 3 A c^{3} d^{2} e + 2 B a b c e^{3} - 3 B a c^{2} d e^{2} - B b^{3} e^{3} + 3 B b^{2} c d e^{2} - 3 B b c^{2} d^{2} e + B c^{3} d^{3}}{2 c^{4}}\right) \log{\left(x + \frac{2 A a^{2} c^{2} e^{3} - A a b^{2} c e^{3} + 3 A a b c^{2} d e^{2} - 6 A a c^{3} d^{2} e + A b c^{3} d^{3} - 3 B a^{2} b c e^{3} + 6 B a^{2} c^{2} d e^{2} + B a b^{3} e^{3} - 3 B a b^{2} c d e^{2} + 3 B a b c^{2} d^{2} e - 2 B a c^{3} d^{3} + 4 a c^{4} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{- A a c^{2} e^{3} + A b^{2} c e^{3} - 3 A b c^{2} d e^{2} + 3 A c^{3} d^{2} e + 2 B a b c e^{3} - 3 B a c^{2} d e^{2} - B b^{3} e^{3} + 3 B b^{2} c d e^{2} - 3 B b c^{2} d^{2} e + B c^{3} d^{3}}{2 c^{4}}\right) - b^{2} c^{3} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{- A a c^{2} e^{3} + A b^{2} c e^{3} - 3 A b c^{2} d e^{2} + 3 A c^{3} d^{2} e + 2 B a b c e^{3} - 3 B a c^{2} d e^{2} - B b^{3} e^{3} + 3 B b^{2} c d e^{2} - 3 B b c^{2} d^{2} e + B c^{3} d^{3}}{2 c^{4}}\right)}{3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{- A a c^{2} e^{3} + A b^{2} c e^{3} - 3 A b c^{2} d e^{2} + 3 A c^{3} d^{2} e + 2 B a b c e^{3} - 3 B a c^{2} d e^{2} - B b^{3} e^{3} + 3 B b^{2} c d e^{2} - 3 B b c^{2} d^{2} e + B c^{3} d^{3}}{2 c^{4}}\right) \log{\left(x + \frac{2 A a^{2} c^{2} e^{3} - A a b^{2} c e^{3} + 3 A a b c^{2} d e^{2} - 6 A a c^{3} d^{2} e + A b c^{3} d^{3} - 3 B a^{2} b c e^{3} + 6 B a^{2} c^{2} d e^{2} + B a b^{3} e^{3} - 3 B a b^{2} c d e^{2} + 3 B a b c^{2} d^{2} e - 2 B a c^{3} d^{3} + 4 a c^{4} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{- A a c^{2} e^{3} + A b^{2} c e^{3} - 3 A b c^{2} d e^{2} + 3 A c^{3} d^{2} e + 2 B a b c e^{3} - 3 B a c^{2} d e^{2} - B b^{3} e^{3} + 3 B b^{2} c d e^{2} - 3 B b c^{2} d^{2} e + B c^{3} d^{3}}{2 c^{4}}\right) - b^{2} c^{3} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{- A a c^{2} e^{3} + A b^{2} c e^{3} - 3 A b c^{2} d e^{2} + 3 A c^{3} d^{2} e + 2 B a b c e^{3} - 3 B a c^{2} d e^{2} - B b^{3} e^{3} + 3 B b^{2} c d e^{2} - 3 B b c^{2} d^{2} e + B c^{3} d^{3}}{2 c^{4}}\right)}{3 A a b c^{2} e^{3} - 6 A a c^{3} d e^{2} - A b^{3} c e^{3} + 3 A b^{2} c^{2} d e^{2} - 3 A b c^{3} d^{2} e + 2 A c^{4} d^{3} + 2 B a^{2} c^{2} e^{3} - 4 B a b^{2} c e^{3} + 9 B a b c^{2} d e^{2} - 6 B a c^{3} d^{2} e + B b^{4} e^{3} - 3 B b^{3} c d e^{2} + 3 B b^{2} c^{2} d^{2} e - B b c^{3} d^{3}} \right)}"," ",0,"B*e**3*x**3/(3*c) + x**2*(A*e**3/(2*c) - B*b*e**3/(2*c**2) + 3*B*d*e**2/(2*c)) + x*(-A*b*e**3/c**2 + 3*A*d*e**2/c - B*a*e**3/c**2 + B*b**2*e**3/c**3 - 3*B*b*d*e**2/c**2 + 3*B*d**2*e/c) + (-sqrt(-4*a*c + b**2)*(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)/(2*c**4*(4*a*c - b**2)) + (-A*a*c**2*e**3 + A*b**2*c*e**3 - 3*A*b*c**2*d*e**2 + 3*A*c**3*d**2*e + 2*B*a*b*c*e**3 - 3*B*a*c**2*d*e**2 - B*b**3*e**3 + 3*B*b**2*c*d*e**2 - 3*B*b*c**2*d**2*e + B*c**3*d**3)/(2*c**4))*log(x + (2*A*a**2*c**2*e**3 - A*a*b**2*c*e**3 + 3*A*a*b*c**2*d*e**2 - 6*A*a*c**3*d**2*e + A*b*c**3*d**3 - 3*B*a**2*b*c*e**3 + 6*B*a**2*c**2*d*e**2 + B*a*b**3*e**3 - 3*B*a*b**2*c*d*e**2 + 3*B*a*b*c**2*d**2*e - 2*B*a*c**3*d**3 + 4*a*c**4*(-sqrt(-4*a*c + b**2)*(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)/(2*c**4*(4*a*c - b**2)) + (-A*a*c**2*e**3 + A*b**2*c*e**3 - 3*A*b*c**2*d*e**2 + 3*A*c**3*d**2*e + 2*B*a*b*c*e**3 - 3*B*a*c**2*d*e**2 - B*b**3*e**3 + 3*B*b**2*c*d*e**2 - 3*B*b*c**2*d**2*e + B*c**3*d**3)/(2*c**4)) - b**2*c**3*(-sqrt(-4*a*c + b**2)*(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)/(2*c**4*(4*a*c - b**2)) + (-A*a*c**2*e**3 + A*b**2*c*e**3 - 3*A*b*c**2*d*e**2 + 3*A*c**3*d**2*e + 2*B*a*b*c*e**3 - 3*B*a*c**2*d*e**2 - B*b**3*e**3 + 3*B*b**2*c*d*e**2 - 3*B*b*c**2*d**2*e + B*c**3*d**3)/(2*c**4)))/(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)) + (sqrt(-4*a*c + b**2)*(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)/(2*c**4*(4*a*c - b**2)) + (-A*a*c**2*e**3 + A*b**2*c*e**3 - 3*A*b*c**2*d*e**2 + 3*A*c**3*d**2*e + 2*B*a*b*c*e**3 - 3*B*a*c**2*d*e**2 - B*b**3*e**3 + 3*B*b**2*c*d*e**2 - 3*B*b*c**2*d**2*e + B*c**3*d**3)/(2*c**4))*log(x + (2*A*a**2*c**2*e**3 - A*a*b**2*c*e**3 + 3*A*a*b*c**2*d*e**2 - 6*A*a*c**3*d**2*e + A*b*c**3*d**3 - 3*B*a**2*b*c*e**3 + 6*B*a**2*c**2*d*e**2 + B*a*b**3*e**3 - 3*B*a*b**2*c*d*e**2 + 3*B*a*b*c**2*d**2*e - 2*B*a*c**3*d**3 + 4*a*c**4*(sqrt(-4*a*c + b**2)*(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)/(2*c**4*(4*a*c - b**2)) + (-A*a*c**2*e**3 + A*b**2*c*e**3 - 3*A*b*c**2*d*e**2 + 3*A*c**3*d**2*e + 2*B*a*b*c*e**3 - 3*B*a*c**2*d*e**2 - B*b**3*e**3 + 3*B*b**2*c*d*e**2 - 3*B*b*c**2*d**2*e + B*c**3*d**3)/(2*c**4)) - b**2*c**3*(sqrt(-4*a*c + b**2)*(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3)/(2*c**4*(4*a*c - b**2)) + (-A*a*c**2*e**3 + A*b**2*c*e**3 - 3*A*b*c**2*d*e**2 + 3*A*c**3*d**2*e + 2*B*a*b*c*e**3 - 3*B*a*c**2*d*e**2 - B*b**3*e**3 + 3*B*b**2*c*d*e**2 - 3*B*b*c**2*d**2*e + B*c**3*d**3)/(2*c**4)))/(3*A*a*b*c**2*e**3 - 6*A*a*c**3*d*e**2 - A*b**3*c*e**3 + 3*A*b**2*c**2*d*e**2 - 3*A*b*c**3*d**2*e + 2*A*c**4*d**3 + 2*B*a**2*c**2*e**3 - 4*B*a*b**2*c*e**3 + 9*B*a*b*c**2*d*e**2 - 6*B*a*c**3*d**2*e + B*b**4*e**3 - 3*B*b**3*c*d*e**2 + 3*B*b**2*c**2*d**2*e - B*b*c**3*d**3))","B",0
2365,1,1532,0,11.087727," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x+a),x)","\frac{B e^{2} x^{2}}{2 c} + x \left(\frac{A e^{2}}{c} - \frac{B b e^{2}}{c^{2}} + \frac{2 B d e}{c}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{A b c e^{2} - 2 A c^{2} d e + B a c e^{2} - B b^{2} e^{2} + 2 B b c d e - B c^{2} d^{2}}{2 c^{3}}\right) \log{\left(x + \frac{A a b c e^{2} - 4 A a c^{2} d e + A b c^{2} d^{2} + 2 B a^{2} c e^{2} - B a b^{2} e^{2} + 2 B a b c d e - 2 B a c^{2} d^{2} + 4 a c^{3} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{A b c e^{2} - 2 A c^{2} d e + B a c e^{2} - B b^{2} e^{2} + 2 B b c d e - B c^{2} d^{2}}{2 c^{3}}\right) - b^{2} c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{A b c e^{2} - 2 A c^{2} d e + B a c e^{2} - B b^{2} e^{2} + 2 B b c d e - B c^{2} d^{2}}{2 c^{3}}\right)}{- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{A b c e^{2} - 2 A c^{2} d e + B a c e^{2} - B b^{2} e^{2} + 2 B b c d e - B c^{2} d^{2}}{2 c^{3}}\right) \log{\left(x + \frac{A a b c e^{2} - 4 A a c^{2} d e + A b c^{2} d^{2} + 2 B a^{2} c e^{2} - B a b^{2} e^{2} + 2 B a b c d e - 2 B a c^{2} d^{2} + 4 a c^{3} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{A b c e^{2} - 2 A c^{2} d e + B a c e^{2} - B b^{2} e^{2} + 2 B b c d e - B c^{2} d^{2}}{2 c^{3}}\right) - b^{2} c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{A b c e^{2} - 2 A c^{2} d e + B a c e^{2} - B b^{2} e^{2} + 2 B b c d e - B c^{2} d^{2}}{2 c^{3}}\right)}{- 2 A a c^{2} e^{2} + A b^{2} c e^{2} - 2 A b c^{2} d e + 2 A c^{3} d^{2} + 3 B a b c e^{2} - 4 B a c^{2} d e - B b^{3} e^{2} + 2 B b^{2} c d e - B b c^{2} d^{2}} \right)}"," ",0,"B*e**2*x**2/(2*c) + x*(A*e**2/c - B*b*e**2/c**2 + 2*B*d*e/c) + (-sqrt(-4*a*c + b**2)*(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)/(2*c**3*(4*a*c - b**2)) - (A*b*c*e**2 - 2*A*c**2*d*e + B*a*c*e**2 - B*b**2*e**2 + 2*B*b*c*d*e - B*c**2*d**2)/(2*c**3))*log(x + (A*a*b*c*e**2 - 4*A*a*c**2*d*e + A*b*c**2*d**2 + 2*B*a**2*c*e**2 - B*a*b**2*e**2 + 2*B*a*b*c*d*e - 2*B*a*c**2*d**2 + 4*a*c**3*(-sqrt(-4*a*c + b**2)*(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)/(2*c**3*(4*a*c - b**2)) - (A*b*c*e**2 - 2*A*c**2*d*e + B*a*c*e**2 - B*b**2*e**2 + 2*B*b*c*d*e - B*c**2*d**2)/(2*c**3)) - b**2*c**2*(-sqrt(-4*a*c + b**2)*(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)/(2*c**3*(4*a*c - b**2)) - (A*b*c*e**2 - 2*A*c**2*d*e + B*a*c*e**2 - B*b**2*e**2 + 2*B*b*c*d*e - B*c**2*d**2)/(2*c**3)))/(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)) + (sqrt(-4*a*c + b**2)*(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)/(2*c**3*(4*a*c - b**2)) - (A*b*c*e**2 - 2*A*c**2*d*e + B*a*c*e**2 - B*b**2*e**2 + 2*B*b*c*d*e - B*c**2*d**2)/(2*c**3))*log(x + (A*a*b*c*e**2 - 4*A*a*c**2*d*e + A*b*c**2*d**2 + 2*B*a**2*c*e**2 - B*a*b**2*e**2 + 2*B*a*b*c*d*e - 2*B*a*c**2*d**2 + 4*a*c**3*(sqrt(-4*a*c + b**2)*(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)/(2*c**3*(4*a*c - b**2)) - (A*b*c*e**2 - 2*A*c**2*d*e + B*a*c*e**2 - B*b**2*e**2 + 2*B*b*c*d*e - B*c**2*d**2)/(2*c**3)) - b**2*c**2*(sqrt(-4*a*c + b**2)*(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2)/(2*c**3*(4*a*c - b**2)) - (A*b*c*e**2 - 2*A*c**2*d*e + B*a*c*e**2 - B*b**2*e**2 + 2*B*b*c*d*e - B*c**2*d**2)/(2*c**3)))/(-2*A*a*c**2*e**2 + A*b**2*c*e**2 - 2*A*b*c**2*d*e + 2*A*c**3*d**2 + 3*B*a*b*c*e**2 - 4*B*a*c**2*d*e - B*b**3*e**2 + 2*B*b**2*c*d*e - B*b*c**2*d**2))","B",0
2366,1,677,0,3.444980," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x+a),x)","\frac{B e x}{c} + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{- A c e + B b e - B c d}{2 c^{2}}\right) \log{\left(x + \frac{2 A a c e - A b c d - B a b e + 2 B a c d - 4 a c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{- A c e + B b e - B c d}{2 c^{2}}\right) + b^{2} c \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{- A c e + B b e - B c d}{2 c^{2}}\right)}{A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{- A c e + B b e - B c d}{2 c^{2}}\right) \log{\left(x + \frac{2 A a c e - A b c d - B a b e + 2 B a c d - 4 a c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{- A c e + B b e - B c d}{2 c^{2}}\right) + b^{2} c \left(\frac{\sqrt{- 4 a c + b^{2}} \left(A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{- A c e + B b e - B c d}{2 c^{2}}\right)}{A b c e - 2 A c^{2} d + 2 B a c e - B b^{2} e + B b c d} \right)}"," ",0,"B*e*x/c + (-sqrt(-4*a*c + b**2)*(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)/(2*c**2*(4*a*c - b**2)) - (-A*c*e + B*b*e - B*c*d)/(2*c**2))*log(x + (2*A*a*c*e - A*b*c*d - B*a*b*e + 2*B*a*c*d - 4*a*c**2*(-sqrt(-4*a*c + b**2)*(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)/(2*c**2*(4*a*c - b**2)) - (-A*c*e + B*b*e - B*c*d)/(2*c**2)) + b**2*c*(-sqrt(-4*a*c + b**2)*(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)/(2*c**2*(4*a*c - b**2)) - (-A*c*e + B*b*e - B*c*d)/(2*c**2)))/(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)) + (sqrt(-4*a*c + b**2)*(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)/(2*c**2*(4*a*c - b**2)) - (-A*c*e + B*b*e - B*c*d)/(2*c**2))*log(x + (2*A*a*c*e - A*b*c*d - B*a*b*e + 2*B*a*c*d - 4*a*c**2*(sqrt(-4*a*c + b**2)*(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)/(2*c**2*(4*a*c - b**2)) - (-A*c*e + B*b*e - B*c*d)/(2*c**2)) + b**2*c*(sqrt(-4*a*c + b**2)*(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d)/(2*c**2*(4*a*c - b**2)) - (-A*c*e + B*b*e - B*c*d)/(2*c**2)))/(A*b*c*e - 2*A*c**2*d + 2*B*a*c*e - B*b**2*e + B*b*c*d))","B",0
2367,1,280,0,0.689913," ","integrate((B*x+A)/(c*x**2+b*x+a),x)","\left(\frac{B}{2 c} - \frac{\left(- 2 A c + B b\right) \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- A b + 2 B a - 4 a c \left(\frac{B}{2 c} - \frac{\left(- 2 A c + B b\right) \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)}\right) + b^{2} \left(\frac{B}{2 c} - \frac{\left(- 2 A c + B b\right) \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)}\right)}{- 2 A c + B b} \right)} + \left(\frac{B}{2 c} + \frac{\left(- 2 A c + B b\right) \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- A b + 2 B a - 4 a c \left(\frac{B}{2 c} + \frac{\left(- 2 A c + B b\right) \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)}\right) + b^{2} \left(\frac{B}{2 c} + \frac{\left(- 2 A c + B b\right) \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)}\right)}{- 2 A c + B b} \right)}"," ",0,"(B/(2*c) - (-2*A*c + B*b)*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)))*log(x + (-A*b + 2*B*a - 4*a*c*(B/(2*c) - (-2*A*c + B*b)*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2))) + b**2*(B/(2*c) - (-2*A*c + B*b)*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2))))/(-2*A*c + B*b)) + (B/(2*c) + (-2*A*c + B*b)*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)))*log(x + (-A*b + 2*B*a - 4*a*c*(B/(2*c) + (-2*A*c + B*b)*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2))) + b**2*(B/(2*c) + (-2*A*c + B*b)*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2))))/(-2*A*c + B*b))","B",0
2368,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2369,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2370,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2371,-1,0,0,0.000000," ","integrate((e*x+d)**4*(g*x+f)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2372,-1,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2373,1,2076,0,128.603366," ","integrate((e*x+d)**2*(g*x+f)/(c*x**2+b*x+a)**3,x)","\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) \log{\left(x + \frac{- 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) + 3 a b^{2} e^{2} g - 4 a b c d e g - 2 a b c e^{2} f + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) - 2 b^{3} d e g - b^{3} e^{2} f + 3 b^{2} c d^{2} g + 6 b^{2} c d e f - 6 b c^{2} d^{2} f}{6 a b c e^{2} g - 8 a c^{2} d e g - 4 a c^{2} e^{2} f - 4 b^{2} c d e g - 2 b^{2} c e^{2} f + 6 b c^{2} d^{2} g + 12 b c^{2} d e f - 12 c^{3} d^{2} f} \right)} - \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) \log{\left(x + \frac{64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) + 3 a b^{2} e^{2} g - 4 a b c d e g - 2 a b c e^{2} f - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(3 a b e^{2} g - 4 a c d e g - 2 a c e^{2} f - 2 b^{2} d e g - b^{2} e^{2} f + 3 b c d^{2} g + 6 b c d e f - 6 c^{2} d^{2} f\right) - 2 b^{3} d e g - b^{3} e^{2} f + 3 b^{2} c d^{2} g + 6 b^{2} c d e f - 6 b c^{2} d^{2} f}{6 a b c e^{2} g - 8 a c^{2} d e g - 4 a c^{2} e^{2} f - 4 b^{2} c d e g - 2 b^{2} c e^{2} f + 6 b c^{2} d^{2} g + 12 b c^{2} d e f - 12 c^{3} d^{2} f} \right)} + \frac{- 8 a^{3} c e^{2} g - a^{2} b^{2} e^{2} g + 12 a^{2} b c d e g + 6 a^{2} b c e^{2} f - 8 a^{2} c^{2} d^{2} g - 16 a^{2} c^{2} d e f - a b^{2} c d^{2} g - 2 a b^{2} c d e f + 10 a b c^{2} d^{2} f - b^{3} c d^{2} f + x^{3} \left(- 6 a b c^{2} e^{2} g + 8 a c^{3} d e g + 4 a c^{3} e^{2} f + 4 b^{2} c^{2} d e g + 2 b^{2} c^{2} e^{2} f - 6 b c^{3} d^{2} g - 12 b c^{3} d e f + 12 c^{4} d^{2} f\right) + x^{2} \left(- 16 a^{2} c^{2} e^{2} g - a b^{2} c e^{2} g + 12 a b c^{2} d e g + 6 a b c^{2} e^{2} f - b^{4} e^{2} g + 6 b^{3} c d e g + 3 b^{3} c e^{2} f - 9 b^{2} c^{2} d^{2} g - 18 b^{2} c^{2} d e f + 18 b c^{3} d^{2} f\right) + x \left(- 10 a^{2} b c e^{2} g - 8 a^{2} c^{2} d e g - 4 a^{2} c^{2} e^{2} f - 2 a b^{3} e^{2} g + 20 a b^{2} c d e g + 10 a b^{2} c e^{2} f - 10 a b c^{2} d^{2} g - 20 a b c^{2} d e f + 20 a c^{3} d^{2} f - 2 b^{3} c d^{2} g - 4 b^{3} c d e f + 4 b^{2} c^{2} d^{2} f\right)}{32 a^{4} c^{3} - 16 a^{3} b^{2} c^{2} + 2 a^{2} b^{4} c + x^{4} \left(32 a^{2} c^{5} - 16 a b^{2} c^{4} + 2 b^{4} c^{3}\right) + x^{3} \left(64 a^{2} b c^{4} - 32 a b^{3} c^{3} + 4 b^{5} c^{2}\right) + x^{2} \left(64 a^{3} c^{4} - 12 a b^{4} c^{2} + 2 b^{6} c\right) + x \left(64 a^{3} b c^{3} - 32 a^{2} b^{3} c^{2} + 4 a b^{5} c\right)}"," ",0,"sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f)*log(x + (-64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) + 3*a*b**2*e**2*g - 4*a*b*c*d*e*g - 2*a*b*c*e**2*f + b**6*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) - 2*b**3*d*e*g - b**3*e**2*f + 3*b**2*c*d**2*g + 6*b**2*c*d*e*f - 6*b*c**2*d**2*f)/(6*a*b*c*e**2*g - 8*a*c**2*d*e*g - 4*a*c**2*e**2*f - 4*b**2*c*d*e*g - 2*b**2*c*e**2*f + 6*b*c**2*d**2*g + 12*b*c**2*d*e*f - 12*c**3*d**2*f)) - sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f)*log(x + (64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) + 3*a*b**2*e**2*g - 4*a*b*c*d*e*g - 2*a*b*c*e**2*f - b**6*sqrt(-1/(4*a*c - b**2)**5)*(3*a*b*e**2*g - 4*a*c*d*e*g - 2*a*c*e**2*f - 2*b**2*d*e*g - b**2*e**2*f + 3*b*c*d**2*g + 6*b*c*d*e*f - 6*c**2*d**2*f) - 2*b**3*d*e*g - b**3*e**2*f + 3*b**2*c*d**2*g + 6*b**2*c*d*e*f - 6*b*c**2*d**2*f)/(6*a*b*c*e**2*g - 8*a*c**2*d*e*g - 4*a*c**2*e**2*f - 4*b**2*c*d*e*g - 2*b**2*c*e**2*f + 6*b*c**2*d**2*g + 12*b*c**2*d*e*f - 12*c**3*d**2*f)) + (-8*a**3*c*e**2*g - a**2*b**2*e**2*g + 12*a**2*b*c*d*e*g + 6*a**2*b*c*e**2*f - 8*a**2*c**2*d**2*g - 16*a**2*c**2*d*e*f - a*b**2*c*d**2*g - 2*a*b**2*c*d*e*f + 10*a*b*c**2*d**2*f - b**3*c*d**2*f + x**3*(-6*a*b*c**2*e**2*g + 8*a*c**3*d*e*g + 4*a*c**3*e**2*f + 4*b**2*c**2*d*e*g + 2*b**2*c**2*e**2*f - 6*b*c**3*d**2*g - 12*b*c**3*d*e*f + 12*c**4*d**2*f) + x**2*(-16*a**2*c**2*e**2*g - a*b**2*c*e**2*g + 12*a*b*c**2*d*e*g + 6*a*b*c**2*e**2*f - b**4*e**2*g + 6*b**3*c*d*e*g + 3*b**3*c*e**2*f - 9*b**2*c**2*d**2*g - 18*b**2*c**2*d*e*f + 18*b*c**3*d**2*f) + x*(-10*a**2*b*c*e**2*g - 8*a**2*c**2*d*e*g - 4*a**2*c**2*e**2*f - 2*a*b**3*e**2*g + 20*a*b**2*c*d*e*g + 10*a*b**2*c*e**2*f - 10*a*b*c**2*d**2*g - 20*a*b*c**2*d*e*f + 20*a*c**3*d**2*f - 2*b**3*c*d**2*g - 4*b**3*c*d*e*f + 4*b**2*c**2*d**2*f))/(32*a**4*c**3 - 16*a**3*b**2*c**2 + 2*a**2*b**4*c + x**4*(32*a**2*c**5 - 16*a*b**2*c**4 + 2*b**4*c**3) + x**3*(64*a**2*b*c**4 - 32*a*b**3*c**3 + 4*b**5*c**2) + x**2*(64*a**3*c**4 - 12*a*b**4*c**2 + 2*b**6*c) + x*(64*a**3*b*c**3 - 32*a**2*b**3*c**2 + 4*a*b**5*c))","B",0
2374,1,1234,0,15.169992," ","integrate((e*x+d)*(g*x+f)/(c*x**2+b*x+a)**3,x)","- \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) \log{\left(x + \frac{- 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) + 2 a b c e g + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) + b^{3} e g - 3 b^{2} c d g - 3 b^{2} c e f + 6 b c^{2} d f}{4 a c^{2} e g + 2 b^{2} c e g - 6 b c^{2} d g - 6 b c^{2} e f + 12 c^{3} d f} \right)} + \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) \log{\left(x + \frac{64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) + 2 a b c e g - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c e g + b^{2} e g - 3 b c d g - 3 b c e f + 6 c^{2} d f\right) + b^{3} e g - 3 b^{2} c d g - 3 b^{2} c e f + 6 b c^{2} d f}{4 a c^{2} e g + 2 b^{2} c e g - 6 b c^{2} d g - 6 b c^{2} e f + 12 c^{3} d f} \right)} + \frac{6 a^{2} b e g - 8 a^{2} c d g - 8 a^{2} c e f - a b^{2} d g - a b^{2} e f + 10 a b c d f - b^{3} d f + x^{3} \left(4 a c^{2} e g + 2 b^{2} c e g - 6 b c^{2} d g - 6 b c^{2} e f + 12 c^{3} d f\right) + x^{2} \left(6 a b c e g + 3 b^{3} e g - 9 b^{2} c d g - 9 b^{2} c e f + 18 b c^{2} d f\right) + x \left(- 4 a^{2} c e g + 10 a b^{2} e g - 10 a b c d g - 10 a b c e f + 20 a c^{2} d f - 2 b^{3} d g - 2 b^{3} e f + 4 b^{2} c d f\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f)*log(x + (-64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) + 2*a*b*c*e*g + b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) + b**3*e*g - 3*b**2*c*d*g - 3*b**2*c*e*f + 6*b*c**2*d*f)/(4*a*c**2*e*g + 2*b**2*c*e*g - 6*b*c**2*d*g - 6*b*c**2*e*f + 12*c**3*d*f)) + sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f)*log(x + (64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) + 2*a*b*c*e*g - b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c*e*g + b**2*e*g - 3*b*c*d*g - 3*b*c*e*f + 6*c**2*d*f) + b**3*e*g - 3*b**2*c*d*g - 3*b**2*c*e*f + 6*b*c**2*d*f)/(4*a*c**2*e*g + 2*b**2*c*e*g - 6*b*c**2*d*g - 6*b*c**2*e*f + 12*c**3*d*f)) + (6*a**2*b*e*g - 8*a**2*c*d*g - 8*a**2*c*e*f - a*b**2*d*g - a*b**2*e*f + 10*a*b*c*d*f - b**3*d*f + x**3*(4*a*c**2*e*g + 2*b**2*c*e*g - 6*b*c**2*d*g - 6*b*c**2*e*f + 12*c**3*d*f) + x**2*(6*a*b*c*e*g + 3*b**3*e*g - 9*b**2*c*d*g - 9*b**2*c*e*f + 18*b*c**2*d*f) + x*(-4*a**2*c*e*g + 10*a*b**2*e*g - 10*a*b*c*d*g - 10*a*b*c*e*f + 20*a*c**2*d*f - 2*b**3*d*g - 2*b**3*e*f + 4*b**2*c*d*f))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
2375,1,651,0,1.680777," ","integrate((g*x+f)/(c*x**2+b*x+a)**3,x)","3 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) \log{\left(x + \frac{- 192 a^{3} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) + 144 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) - 36 a b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) + 3 b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) + 3 b^{2} c g - 6 b c^{2} f}{6 b c^{2} g - 12 c^{3} f} \right)} - 3 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) \log{\left(x + \frac{192 a^{3} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) - 144 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) + 36 a b^{4} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) - 3 b^{6} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(b g - 2 c f\right) + 3 b^{2} c g - 6 b c^{2} f}{6 b c^{2} g - 12 c^{3} f} \right)} + \frac{- 8 a^{2} c g - a b^{2} g + 10 a b c f - b^{3} f + x^{3} \left(- 6 b c^{2} g + 12 c^{3} f\right) + x^{2} \left(- 9 b^{2} c g + 18 b c^{2} f\right) + x \left(- 10 a b c g + 20 a c^{2} f - 2 b^{3} g + 4 b^{2} c f\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"3*c*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f)*log(x + (-192*a**3*c**4*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) + 144*a**2*b**2*c**3*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) - 36*a*b**4*c**2*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) + 3*b**6*c*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) + 3*b**2*c*g - 6*b*c**2*f)/(6*b*c**2*g - 12*c**3*f)) - 3*c*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f)*log(x + (192*a**3*c**4*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) - 144*a**2*b**2*c**3*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) + 36*a*b**4*c**2*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) - 3*b**6*c*sqrt(-1/(4*a*c - b**2)**5)*(b*g - 2*c*f) + 3*b**2*c*g - 6*b*c**2*f)/(6*b*c**2*g - 12*c**3*f)) + (-8*a**2*c*g - a*b**2*g + 10*a*b*c*f - b**3*f + x**3*(-6*b*c**2*g + 12*c**3*f) + x**2*(-9*b**2*c*g + 18*b*c**2*f) + x*(-10*a*b*c*g + 20*a*c**2*f - 2*b**3*g + 4*b**2*c*f))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
2376,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2377,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)**2/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2378,1,41,0,0.131523," ","integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2),x)","- \frac{4 x^{4}}{3} + \frac{32 x^{3}}{27} + \frac{1156 x^{2}}{27} + \frac{11576 x}{81} + \frac{10625 \log{\left(x + \frac{2}{3} \right)}}{243} - 6 \log{\left(x + 1 \right)}"," ",0,"-4*x**4/3 + 32*x**3/27 + 1156*x**2/27 + 11576*x/81 + 10625*log(x + 2/3)/243 - 6*log(x + 1)","A",0
2379,1,34,0,0.125254," ","integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2),x)","- \frac{8 x^{3}}{9} + \frac{26 x^{2}}{9} + \frac{922 x}{27} + \frac{2125 \log{\left(x + \frac{2}{3} \right)}}{81} - 6 \log{\left(x + 1 \right)}"," ",0,"-8*x**3/9 + 26*x**2/9 + 922*x/27 + 2125*log(x + 2/3)/81 - 6*log(x + 1)","A",0
2380,1,27,0,0.122555," ","integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2),x)","- \frac{2 x^{2}}{3} + \frac{44 x}{9} + \frac{425 \log{\left(x + \frac{2}{3} \right)}}{27} - 6 \log{\left(x + 1 \right)}"," ",0,"-2*x**2/3 + 44*x/9 + 425*log(x + 2/3)/27 - 6*log(x + 1)","A",0
2381,1,20,0,0.115217," ","integrate((5-x)*(3+2*x)/(3*x**2+5*x+2),x)","- \frac{2 x}{3} + \frac{85 \log{\left(x + \frac{2}{3} \right)}}{9} - 6 \log{\left(x + 1 \right)}"," ",0,"-2*x/3 + 85*log(x + 2/3)/9 - 6*log(x + 1)","A",0
2382,1,15,0,0.104219," ","integrate((5-x)/(3*x**2+5*x+2),x)","\frac{17 \log{\left(x + \frac{2}{3} \right)}}{3} - 6 \log{\left(x + 1 \right)}"," ",0,"17*log(x + 2/3)/3 - 6*log(x + 1)","A",0
2383,1,26,0,0.137035," ","integrate((5-x)/(3+2*x)/(3*x**2+5*x+2),x)","\frac{17 \log{\left(x + \frac{2}{3} \right)}}{5} - 6 \log{\left(x + 1 \right)} + \frac{13 \log{\left(x + \frac{3}{2} \right)}}{5}"," ",0,"17*log(x + 2/3)/5 - 6*log(x + 1) + 13*log(x + 3/2)/5","A",0
2384,1,32,0,0.163076," ","integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2),x)","\frac{51 \log{\left(x + \frac{2}{3} \right)}}{25} - 6 \log{\left(x + 1 \right)} + \frac{99 \log{\left(x + \frac{3}{2} \right)}}{25} - \frac{13}{10 x + 15}"," ",0,"51*log(x + 2/3)/25 - 6*log(x + 1) + 99*log(x + 3/2)/25 - 13/(10*x + 15)","A",0
2385,1,41,0,0.181094," ","integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2),x)","- \frac{396 x + 659}{200 x^{2} + 600 x + 450} + \frac{153 \log{\left(x + \frac{2}{3} \right)}}{125} - 6 \log{\left(x + 1 \right)} + \frac{597 \log{\left(x + \frac{3}{2} \right)}}{125}"," ",0,"-(396*x + 659)/(200*x**2 + 600*x + 450) + 153*log(x + 2/3)/125 - 6*log(x + 1) + 597*log(x + 3/2)/125","A",0
2386,1,51,0,0.198241," ","integrate((5-x)/(3+2*x)**4/(3*x**2+5*x+2),x)","- \frac{14328 x^{2} + 45954 x + 37343}{6000 x^{3} + 27000 x^{2} + 40500 x + 20250} + \frac{459 \log{\left(x + \frac{2}{3} \right)}}{625} - 6 \log{\left(x + 1 \right)} + \frac{3291 \log{\left(x + \frac{3}{2} \right)}}{625}"," ",0,"-(14328*x**2 + 45954*x + 37343)/(6000*x**3 + 27000*x**2 + 40500*x + 20250) + 459*log(x + 2/3)/625 - 6*log(x + 1) + 3291*log(x + 3/2)/625","A",0
2387,1,42,0,0.162829," ","integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**2,x)","- \frac{8 x^{2}}{9} + \frac{112 x}{27} - \frac{12083 x + 11597}{243 x^{2} + 405 x + 162} - \frac{1625 \log{\left(x + \frac{2}{3} \right)}}{27} + 83 \log{\left(x + 1 \right)}"," ",0,"-8*x**2/9 + 112*x/27 - (12083*x + 11597)/(243*x**2 + 405*x + 162) - 1625*log(x + 2/3)/27 + 83*log(x + 1)","A",0
2388,1,36,0,0.157987," ","integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**2,x)","- \frac{8 x}{9} - \frac{2611 x + 2449}{81 x^{2} + 135 x + 54} - \frac{1825 \log{\left(x + \frac{2}{3} \right)}}{27} + 71 \log{\left(x + 1 \right)}"," ",0,"-8*x/9 - (2611*x + 2449)/(81*x**2 + 135*x + 54) - 1825*log(x + 2/3)/27 + 71*log(x + 1)","A",0
2389,1,31,0,0.151655," ","integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**2,x)","- \frac{587 x + 533}{27 x^{2} + 45 x + 18} - \frac{535 \log{\left(x + \frac{2}{3} \right)}}{9} + 59 \log{\left(x + 1 \right)}"," ",0,"-(587*x + 533)/(27*x**2 + 45*x + 18) - 535*log(x + 2/3)/9 + 59*log(x + 1)","A",0
2390,1,29,0,0.133510," ","integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**2,x)","- \frac{139 x + 121}{9 x^{2} + 15 x + 6} - 47 \log{\left(x + \frac{2}{3} \right)} + 47 \log{\left(x + 1 \right)}"," ",0,"-(139*x + 121)/(9*x**2 + 15*x + 6) - 47*log(x + 2/3) + 47*log(x + 1)","A",0
2391,1,29,0,0.125621," ","integrate((5-x)/(3*x**2+5*x+2)**2,x)","- \frac{35 x + 29}{3 x^{2} + 5 x + 2} - 35 \log{\left(x + \frac{2}{3} \right)} + 35 \log{\left(x + 1 \right)}"," ",0,"-(35*x + 29)/(3*x**2 + 5*x + 2) - 35*log(x + 2/3) + 35*log(x + 1)","A",0
2392,1,41,0,0.181884," ","integrate((5-x)/(3+2*x)/(3*x**2+5*x+2)**2,x)","- \frac{141 x + 111}{15 x^{2} + 25 x + 10} - \frac{627 \log{\left(x + \frac{2}{3} \right)}}{25} + 23 \log{\left(x + 1 \right)} + \frac{52 \log{\left(x + \frac{3}{2} \right)}}{25}"," ",0,"-(141*x + 111)/(15*x**2 + 25*x + 10) - 627*log(x + 2/3)/25 + 23*log(x + 1) + 52*log(x + 3/2)/25","A",0
2393,1,51,0,0.188695," ","integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**2,x)","- \frac{1362 x^{2} + 2975 x + 1463}{150 x^{3} + 475 x^{2} + 475 x + 150} - \frac{2187 \log{\left(x + \frac{2}{3} \right)}}{125} + 11 \log{\left(x + 1 \right)} + \frac{812 \log{\left(x + \frac{3}{2} \right)}}{125}"," ",0,"-(1362*x**2 + 2975*x + 1463)/(150*x**3 + 475*x**2 + 475*x + 150) - 2187*log(x + 2/3)/125 + 11*log(x + 1) + 812*log(x + 3/2)/125","A",0
2394,1,60,0,0.211059," ","integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**2,x)","- \frac{15708 x^{3} + 56162 x^{2} + 63967 x + 22763}{1500 x^{4} + 7000 x^{3} + 11875 x^{2} + 8625 x + 2250} - \frac{7479 \log{\left(x + \frac{2}{3} \right)}}{625} - \log{\left(x + 1 \right)} + \frac{8104 \log{\left(x + \frac{3}{2} \right)}}{625}"," ",0,"-(15708*x**3 + 56162*x**2 + 63967*x + 22763)/(1500*x**4 + 7000*x**3 + 11875*x**2 + 8625*x + 2250) - 7479*log(x + 2/3)/625 - log(x + 1) + 8104*log(x + 3/2)/625","A",0
2395,1,71,0,0.233680," ","integrate((5-x)/(3+2*x)**4/(3*x**2+5*x+2)**2,x)","- \frac{594792 x^{4} + 2974776 x^{3} + 5433540 x^{2} + 4260599 x + 1195793}{45000 x^{5} + 277500 x^{4} + 671250 x^{3} + 793125 x^{2} + 455625 x + 101250} - \frac{25191 \log{\left(x + \frac{2}{3} \right)}}{3125} - 13 \log{\left(x + 1 \right)} + \frac{65816 \log{\left(x + \frac{3}{2} \right)}}{3125}"," ",0,"-(594792*x**4 + 2974776*x**3 + 5433540*x**2 + 4260599*x + 1195793)/(45000*x**5 + 277500*x**4 + 671250*x**3 + 793125*x**2 + 455625*x + 101250) - 25191*log(x + 2/3)/3125 - 13*log(x + 1) + 65816*log(x + 3/2)/3125","A",0
2396,1,58,0,0.194897," ","integrate((5-x)*(3+2*x)**5/(3*x**2+5*x+2)**3,x)","- \frac{32 x}{27} - \frac{- 502254 x^{3} - 1235675 x^{2} - 979978 x - 247043}{1458 x^{4} + 4860 x^{3} + 5994 x^{2} + 3240 x + 648} + \frac{29375 \log{\left(x + \frac{2}{3} \right)}}{27} - 1085 \log{\left(x + 1 \right)}"," ",0,"-32*x/27 - (-502254*x**3 - 1235675*x**2 - 979978*x - 247043)/(1458*x**4 + 4860*x**3 + 5994*x**2 + 3240*x + 648) + 29375*log(x + 2/3)/27 - 1085*log(x + 1)","A",0
2397,1,53,0,0.190236," ","integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**3,x)","- \frac{- 47362 x^{3} - 117789 x^{2} - 94986 x - 24613}{162 x^{4} + 540 x^{3} + 666 x^{2} + 360 x + 72} + \frac{23825 \log{\left(x + \frac{2}{3} \right)}}{27} - 883 \log{\left(x + 1 \right)}"," ",0,"-(-47362*x**3 - 117789*x**2 - 94986*x - 24613)/(162*x**4 + 540*x**3 + 666*x**2 + 360*x + 72) + 23825*log(x + 2/3)/27 - 883*log(x + 1)","A",0
2398,1,51,0,0.172204," ","integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**3,x)","- \frac{- 38118 x^{3} - 95203 x^{2} - 77330 x - 20299}{162 x^{4} + 540 x^{3} + 666 x^{2} + 360 x + 72} + 705 \log{\left(x + \frac{2}{3} \right)} - 705 \log{\left(x + 1 \right)}"," ",0,"-(-38118*x**3 - 95203*x**2 - 77330*x - 20299)/(162*x**4 + 540*x**3 + 666*x**2 + 360*x + 72) + 705*log(x + 2/3) - 705*log(x + 1)","A",0
2399,1,51,0,0.167895," ","integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**3,x)","- \frac{- 9918 x^{3} - 24799 x^{2} - 20198 x - 5335}{54 x^{4} + 180 x^{3} + 222 x^{2} + 120 x + 24} + 551 \log{\left(x + \frac{2}{3} \right)} - 551 \log{\left(x + 1 \right)}"," ",0,"-(-9918*x**3 - 24799*x**2 - 20198*x - 5335)/(54*x**4 + 180*x**3 + 222*x**2 + 120*x + 24) + 551*log(x + 2/3) - 551*log(x + 1)","A",0
2400,1,51,0,0.162229," ","integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**3,x)","- \frac{- 2526 x^{3} - 6315 x^{2} - 5146 x - 1363}{18 x^{4} + 60 x^{3} + 74 x^{2} + 40 x + 8} + 421 \log{\left(x + \frac{2}{3} \right)} - 421 \log{\left(x + 1 \right)}"," ",0,"-(-2526*x**3 - 6315*x**2 - 5146*x - 1363)/(18*x**4 + 60*x**3 + 74*x**2 + 40*x + 8) + 421*log(x + 2/3) - 421*log(x + 1)","A",0
2401,1,51,0,0.154670," ","integrate((5-x)/(3*x**2+5*x+2)**3,x)","- \frac{- 1890 x^{3} - 4725 x^{2} - 3850 x - 1021}{18 x^{4} + 60 x^{3} + 74 x^{2} + 40 x + 8} + 315 \log{\left(x + \frac{2}{3} \right)} - 315 \log{\left(x + 1 \right)}"," ",0,"-(-1890*x**3 - 4725*x**2 - 3850*x - 1021)/(18*x**4 + 60*x**3 + 74*x**2 + 40*x + 8) + 315*log(x + 2/3) - 315*log(x + 1)","A",0
2402,1,63,0,0.213503," ","integrate((5-x)/(3+2*x)/(3*x**2+5*x+2)**3,x)","- \frac{- 34326 x^{3} - 85971 x^{2} - 70114 x - 18619}{450 x^{4} + 1500 x^{3} + 1850 x^{2} + 1000 x + 200} + \frac{28917 \log{\left(x + \frac{2}{3} \right)}}{125} - 233 \log{\left(x + 1 \right)} + \frac{208 \log{\left(x + \frac{3}{2} \right)}}{125}"," ",0,"-(-34326*x**3 - 85971*x**2 - 70114*x - 18619)/(450*x**4 + 1500*x**3 + 1850*x**2 + 1000*x + 200) + 28917*log(x + 2/3)/125 - 233*log(x + 1) + 208*log(x + 3/2)/125","A",0
2403,1,73,0,0.230004," ","integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**3,x)","- \frac{- 233028 x^{4} - 939480 x^{3} - 1368599 x^{2} - 855120 x - 193723}{4500 x^{5} + 21750 x^{4} + 41000 x^{3} + 37750 x^{2} + 17000 x + 3000} + \frac{104463 \log{\left(x + \frac{2}{3} \right)}}{625} - 175 \log{\left(x + 1 \right)} + \frac{4912 \log{\left(x + \frac{3}{2} \right)}}{625}"," ",0,"-(-233028*x**4 - 939480*x**3 - 1368599*x**2 - 855120*x - 193723)/(4500*x**5 + 21750*x**4 + 41000*x**3 + 37750*x**2 + 17000*x + 3000) + 104463*log(x + 2/3)/625 - 175*log(x + 1) + 4912*log(x + 3/2)/625","A",0
2404,1,83,0,0.237966," ","integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**3,x)","- \frac{- 1291896 x^{5} - 7311204 x^{4} - 16096458 x^{3} - 17180967 x^{2} - 8871646 x - 1771579}{45000 x^{6} + 285000 x^{5} + 736250 x^{4} + 992500 x^{3} + 736250 x^{2} + 285000 x + 45000} + \frac{372033 \log{\left(x + \frac{2}{3} \right)}}{3125} - 141 \log{\left(x + 1 \right)} + \frac{68592 \log{\left(x + \frac{3}{2} \right)}}{3125}"," ",0,"-(-1291896*x**5 - 7311204*x**4 - 16096458*x**3 - 17180967*x**2 - 8871646*x - 1771579)/(45000*x**6 + 285000*x**5 + 736250*x**4 + 992500*x**3 + 736250*x**2 + 285000*x + 45000) + 372033*log(x + 2/3)/3125 - 141*log(x + 1) + 68592*log(x + 3/2)/3125","A",0
2405,1,31,0,0.121048," ","integrate(x*(1+x)**2/(x**2+x+1)**3,x)","\frac{- 3 x^{2} - 4 x - 2}{6 x^{4} + 12 x^{3} + 18 x^{2} + 12 x + 6}"," ",0,"(-3*x**2 - 4*x - 2)/(6*x**4 + 12*x**3 + 18*x**2 + 12*x + 6)","A",0
2406,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 999 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 864 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 264 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 16 x^{4} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 16 x^{5} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 405 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-999*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-864*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-264*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(16*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(16*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-405*sqrt(3*x**2 + 5*x + 2), x)","F",0
2407,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 243 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 126 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 4 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 8 x^{4} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 135 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-243*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-126*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-4*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(8*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-135*sqrt(3*x**2 + 5*x + 2), x)","F",0
2408,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 51 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 8 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 4 x^{3} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 45 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-51*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-8*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(4*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-45*sqrt(3*x**2 + 5*x + 2), x)","F",0
2409,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 7 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 2 x^{2} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 15 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-7*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(2*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-15*sqrt(3*x**2 + 5*x + 2), x)","F",0
2410,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2),x)","- \int x \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 5 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-5*sqrt(3*x**2 + 5*x + 2), x)","F",0
2411,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x)","F",0
2412,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**2,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x)","F",0
2413,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**3,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x)","F",0
2414,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**4,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x)","F",0
2415,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**5,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x)","F",0
2416,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**6,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x)","F",0
2417,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**7,x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x)","F",0
2418,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 4023 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 7938 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 7845 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3880 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 680 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 128 x^{6} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 48 x^{7} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 810 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-4023*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-7938*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-7845*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3880*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-680*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(128*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(48*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(-810*sqrt(3*x**2 + 5*x + 2), x)","F",0
2419,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 1161 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1872 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1367 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 382 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 28 x^{5} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 24 x^{6} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 270 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-1161*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1872*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1367*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-382*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(28*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(24*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(-270*sqrt(3*x**2 + 5*x + 2), x)","F",0
2420,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 327 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 406 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 185 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 4 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 12 x^{5} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 90 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-327*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-406*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-185*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-4*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(12*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-90*sqrt(3*x**2 + 5*x + 2), x)","F",0
2421,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 89 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 76 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 11 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 6 x^{4} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 30 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-89*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-76*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-11*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(6*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-30*sqrt(3*x**2 + 5*x + 2), x)","F",0
2422,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 23 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 10 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 3 x^{3} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 10 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-23*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-10*sqrt(3*x**2 + 5*x + 2), x)","F",0
2423,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x)","F",0
2424,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**2,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x)","F",0
2425,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**3,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x)","F",0
2426,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**4,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x)","F",0
2427,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**5,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x)","F",0
2428,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**6,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x)","F",0
2429,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**7,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x)","F",0
2430,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**8,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x)","F",0
2431,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**9,x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x)","F",0
2432,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 12096 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 38421 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 67449 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 70799 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 44295 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 14784 x^{6} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1304 x^{7} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 624 x^{8} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 144 x^{9} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 1620 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-12096*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-38421*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-67449*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-70799*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-44295*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-14784*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1304*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(624*x**8*sqrt(3*x**2 + 5*x + 2), x) - Integral(144*x**9*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1620*sqrt(3*x**2 + 5*x + 2), x)","F",0
2433,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 3672 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 10359 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 15577 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 13215 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 5955 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 958 x^{6} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 204 x^{7} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 72 x^{8} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 540 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-3672*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-10359*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-15577*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-13215*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-5955*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-958*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(204*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(72*x**8*sqrt(3*x**2 + 5*x + 2), x) - Integral(-540*sqrt(3*x**2 + 5*x + 2), x)","F",0
2434,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 1104 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 2717 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3381 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 2151 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 551 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 48 x^{6} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 36 x^{7} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 180 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-1104*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-2717*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3381*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-2151*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-551*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(48*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(36*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(-180*sqrt(3*x**2 + 5*x + 2), x)","F",0
2435,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 328 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 687 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 669 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 271 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 18 x^{6} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 60 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-328*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-687*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-669*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-271*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(18*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(-60*sqrt(3*x**2 + 5*x + 2), x)","F",0
2436,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 96 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 165 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 113 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 15 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 9 x^{5} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 20 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-96*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-20*sqrt(3*x**2 + 5*x + 2), x)","F",0
2437,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x),x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x)","F",0
2438,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**2,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x)","F",0
2439,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**3,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x)","F",0
2440,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**4,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x)","F",0
2441,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**5,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x)","F",0
2442,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**6,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x)","F",0
2443,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**7,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x)","F",0
2444,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**8,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x)","F",0
2445,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**9,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x)","F",0
2446,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**10,x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x)","F",0
2447,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4*(3*x**2+5*x+2)**(7/2),x)","- \int \left(- 32292 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 142182 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 363291 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 594106 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 644932 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 463440 x^{6} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 209413 x^{7} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 49624 x^{8} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 504 x^{9} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 2592 x^{10} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 432 x^{11} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 3240 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-32292*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-142182*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-363291*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-594106*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-644932*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-463440*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(-209413*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(-49624*x**8*sqrt(3*x**2 + 5*x + 2), x) - Integral(-504*x**9*sqrt(3*x**2 + 5*x + 2), x) - Integral(2592*x**10*sqrt(3*x**2 + 5*x + 2), x) - Integral(432*x**11*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3240*sqrt(3*x**2 + 5*x + 2), x)","F",0
2448,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3*(3*x**2+5*x+2)**(7/2),x)","- \int \left(- 10044 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 40698 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 93965 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 135392 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 124716 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 71336 x^{6} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 22247 x^{7} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1710 x^{8} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 972 x^{9} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 216 x^{10} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 1080 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-10044*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-40698*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-93965*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-135392*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-124716*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-71336*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(-22247*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1710*x**8*sqrt(3*x**2 + 5*x + 2), x) - Integral(972*x**9*sqrt(3*x**2 + 5*x + 2), x) - Integral(216*x**10*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1080*sqrt(3*x**2 + 5*x + 2), x)","F",0
2449,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2*(3*x**2+5*x+2)**(7/2),x)","- \int \left(- 3108 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 11494 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 23659 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 29358 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 22000 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 9112 x^{6} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1341 x^{7} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 324 x^{8} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 108 x^{9} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 360 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-3108*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-11494*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-23659*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-29358*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-22000*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-9112*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1341*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(324*x**8*sqrt(3*x**2 + 5*x + 2), x) - Integral(108*x**9*sqrt(3*x**2 + 5*x + 2), x) - Integral(-360*sqrt(3*x**2 + 5*x + 2), x)","F",0
2450,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)*(3*x**2+5*x+2)**(7/2),x)","- \int \left(- 956 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3194 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 5757 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 5948 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3368 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 792 x^{6} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 81 x^{7} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 54 x^{8} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 120 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-956*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3194*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-5757*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-5948*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3368*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(-792*x**6*sqrt(3*x**2 + 5*x + 2), x) - Integral(81*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(54*x**8*sqrt(3*x**2 + 5*x + 2), x) - Integral(-120*sqrt(3*x**2 + 5*x + 2), x)","F",0
2451,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2),x)","- \int \left(- 292 x \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 870 x^{2} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 396 x^{5} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 27 x^{7} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int \left(- 40 \sqrt{3 x^{2} + 5 x + 2}\right)\, dx"," ",0,"-Integral(-292*x*sqrt(3*x**2 + 5*x + 2), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2), x) - Integral(-40*sqrt(3*x**2 + 5*x + 2), x)","F",0
2452,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x),x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{2 x + 3}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(2*x + 3), x)","F",0
2453,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**2,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} + 12 x + 9}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(4*x**2 + 12*x + 9), x)","F",0
2454,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**3,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} + 36 x^{2} + 54 x + 27}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(8*x**3 + 36*x**2 + 54*x + 27), x)","F",0
2455,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**4,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81), x)","F",0
2456,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**5,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} + 240 x^{4} + 720 x^{3} + 1080 x^{2} + 810 x + 243}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(32*x**5 + 240*x**4 + 720*x**3 + 1080*x**2 + 810*x + 243), x)","F",0
2457,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**6,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{64 x^{6} + 576 x^{5} + 2160 x^{4} + 4320 x^{3} + 4860 x^{2} + 2916 x + 729}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(64*x**6 + 576*x**5 + 2160*x**4 + 4320*x**3 + 4860*x**2 + 2916*x + 729), x)","F",0
2458,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**7,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{128 x^{7} + 1344 x^{6} + 6048 x^{5} + 15120 x^{4} + 22680 x^{3} + 20412 x^{2} + 10206 x + 2187}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(128*x**7 + 1344*x**6 + 6048*x**5 + 15120*x**4 + 22680*x**3 + 20412*x**2 + 10206*x + 2187), x)","F",0
2459,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**8,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 90720*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x)","F",0
2460,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**9,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(512*x**9 + 6912*x**8 + 41472*x**7 + 145152*x**6 + 326592*x**5 + 489888*x**4 + 489888*x**3 + 314928*x**2 + 118098*x + 19683), x)","F",0
2461,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**10,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{1024 x^{10} + 15360 x^{9} + 103680 x^{8} + 414720 x^{7} + 1088640 x^{6} + 1959552 x^{5} + 2449440 x^{4} + 2099520 x^{3} + 1180980 x^{2} + 393660 x + 59049}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(1024*x**10 + 15360*x**9 + 103680*x**8 + 414720*x**7 + 1088640*x**6 + 1959552*x**5 + 2449440*x**4 + 2099520*x**3 + 1180980*x**2 + 393660*x + 59049), x)","F",0
2462,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**11,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{2048 x^{11} + 33792 x^{10} + 253440 x^{9} + 1140480 x^{8} + 3421440 x^{7} + 7185024 x^{6} + 10777536 x^{5} + 11547360 x^{4} + 8660520 x^{3} + 4330260 x^{2} + 1299078 x + 177147}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(2048*x**11 + 33792*x**10 + 253440*x**9 + 1140480*x**8 + 3421440*x**7 + 7185024*x**6 + 10777536*x**5 + 11547360*x**4 + 8660520*x**3 + 4330260*x**2 + 1299078*x + 177147), x)","F",0
2463,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**12,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{4096 x^{12} + 73728 x^{11} + 608256 x^{10} + 3041280 x^{9} + 10264320 x^{8} + 24634368 x^{7} + 43110144 x^{6} + 55427328 x^{5} + 51963120 x^{4} + 34642080 x^{3} + 15588936 x^{2} + 4251528 x + 531441}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(4096*x**12 + 73728*x**11 + 608256*x**10 + 3041280*x**9 + 10264320*x**8 + 24634368*x**7 + 43110144*x**6 + 55427328*x**5 + 51963120*x**4 + 34642080*x**3 + 15588936*x**2 + 4251528*x + 531441), x)","F",0
2464,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**13,x)","- \int \left(- \frac{40 \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\right)\, dx - \int \left(- \frac{292 x \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\right)\, dx - \int \left(- \frac{870 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\right)\, dx - \int \left(- \frac{1339 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\right)\, dx - \int \left(- \frac{1090 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\right)\, dx - \int \left(- \frac{396 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\right)\, dx - \int \frac{27 x^{7} \sqrt{3 x^{2} + 5 x + 2}}{8192 x^{13} + 159744 x^{12} + 1437696 x^{11} + 7907328 x^{10} + 29652480 x^{9} + 80061696 x^{8} + 160123392 x^{7} + 240185088 x^{6} + 270208224 x^{5} + 225173520 x^{4} + 135104112 x^{3} + 55269864 x^{2} + 13817466 x + 1594323}\, dx"," ",0,"-Integral(-40*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x) - Integral(-292*x*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x) - Integral(-870*x**2*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x) - Integral(-1339*x**3*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x) - Integral(-1090*x**4*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x) - Integral(-396*x**5*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x) - Integral(27*x**7*sqrt(3*x**2 + 5*x + 2)/(8192*x**13 + 159744*x**12 + 1437696*x**11 + 7907328*x**10 + 29652480*x**9 + 80061696*x**8 + 160123392*x**7 + 240185088*x**6 + 270208224*x**5 + 225173520*x**4 + 135104112*x**3 + 55269864*x**2 + 13817466*x + 1594323), x)","F",0
2465,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/sqrt(a + b*x + c*x**2), x)","F",0
2466,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/sqrt(a + b*x + c*x**2), x)","F",0
2467,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/sqrt(a + b*x + c*x**2), x)","F",0
2468,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/sqrt(a + b*x + c*x**2), x)","F",0
2469,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
2470,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**2*sqrt(a + b*x + c*x**2)), x)","F",0
2471,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**3*sqrt(a + b*x + c*x**2)), x)","F",0
2472,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**4/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{4} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**4*sqrt(a + b*x + c*x**2)), x)","F",0
2473,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{3}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**3/(a + b*x + c*x**2)**(3/2), x)","F",0
2474,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{2}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**2/(a + b*x + c*x**2)**(3/2), x)","F",0
2475,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
2476,0,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + B x}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
2477,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + B x}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
2478,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2479,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**3/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2480,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2481,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2482,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2483,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2484,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2485,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2486,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**2/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2487,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**6/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2488,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**5/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2489,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**4/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2490,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**3/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2491,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**2/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2492,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2493,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2494,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2495,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{999 x}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{864 x^{2}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{264 x^{3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{16 x^{4}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \frac{16 x^{5}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{405}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-999*x/sqrt(3*x**2 + 5*x + 2), x) - Integral(-864*x**2/sqrt(3*x**2 + 5*x + 2), x) - Integral(-264*x**3/sqrt(3*x**2 + 5*x + 2), x) - Integral(16*x**4/sqrt(3*x**2 + 5*x + 2), x) - Integral(16*x**5/sqrt(3*x**2 + 5*x + 2), x) - Integral(-405/sqrt(3*x**2 + 5*x + 2), x)","F",0
2496,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{243 x}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{126 x^{2}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{4 x^{3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{8 x^{4}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{135}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-243*x/sqrt(3*x**2 + 5*x + 2), x) - Integral(-126*x**2/sqrt(3*x**2 + 5*x + 2), x) - Integral(-4*x**3/sqrt(3*x**2 + 5*x + 2), x) - Integral(8*x**4/sqrt(3*x**2 + 5*x + 2), x) - Integral(-135/sqrt(3*x**2 + 5*x + 2), x)","F",0
2497,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{51 x}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{8 x^{2}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{4 x^{3}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{45}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-51*x/sqrt(3*x**2 + 5*x + 2), x) - Integral(-8*x**2/sqrt(3*x**2 + 5*x + 2), x) - Integral(4*x**3/sqrt(3*x**2 + 5*x + 2), x) - Integral(-45/sqrt(3*x**2 + 5*x + 2), x)","F",0
2498,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{7 x}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{2 x^{2}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{15}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-7*x/sqrt(3*x**2 + 5*x + 2), x) - Integral(2*x**2/sqrt(3*x**2 + 5*x + 2), x) - Integral(-15/sqrt(3*x**2 + 5*x + 2), x)","F",0
2499,0,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{\sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/sqrt(3*x**2 + 5*x + 2), x) - Integral(-5/sqrt(3*x**2 + 5*x + 2), x)","F",0
2500,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{2 x \sqrt{3 x^{2} + 5 x + 2} + 3 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{2 x \sqrt{3 x^{2} + 5 x + 2} + 3 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(2*x*sqrt(3*x**2 + 5*x + 2) + 3*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(2*x*sqrt(3*x**2 + 5*x + 2) + 3*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2501,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{4 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 12 x \sqrt{3 x^{2} + 5 x + 2} + 9 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{4 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 12 x \sqrt{3 x^{2} + 5 x + 2} + 9 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(4*x**2*sqrt(3*x**2 + 5*x + 2) + 12*x*sqrt(3*x**2 + 5*x + 2) + 9*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(4*x**2*sqrt(3*x**2 + 5*x + 2) + 12*x*sqrt(3*x**2 + 5*x + 2) + 9*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2502,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{8 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 36 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 54 x \sqrt{3 x^{2} + 5 x + 2} + 27 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{8 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 36 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 54 x \sqrt{3 x^{2} + 5 x + 2} + 27 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(8*x**3*sqrt(3*x**2 + 5*x + 2) + 36*x**2*sqrt(3*x**2 + 5*x + 2) + 54*x*sqrt(3*x**2 + 5*x + 2) + 27*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(8*x**3*sqrt(3*x**2 + 5*x + 2) + 36*x**2*sqrt(3*x**2 + 5*x + 2) + 54*x*sqrt(3*x**2 + 5*x + 2) + 27*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2503,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**4/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{16 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 96 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 216 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 216 x \sqrt{3 x^{2} + 5 x + 2} + 81 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{16 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 96 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 216 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 216 x \sqrt{3 x^{2} + 5 x + 2} + 81 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(16*x**4*sqrt(3*x**2 + 5*x + 2) + 96*x**3*sqrt(3*x**2 + 5*x + 2) + 216*x**2*sqrt(3*x**2 + 5*x + 2) + 216*x*sqrt(3*x**2 + 5*x + 2) + 81*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(16*x**4*sqrt(3*x**2 + 5*x + 2) + 96*x**3*sqrt(3*x**2 + 5*x + 2) + 216*x**2*sqrt(3*x**2 + 5*x + 2) + 216*x*sqrt(3*x**2 + 5*x + 2) + 81*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2504,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**5/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{32 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 240 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 720 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 1080 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 810 x \sqrt{3 x^{2} + 5 x + 2} + 243 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{32 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 240 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 720 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 1080 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 810 x \sqrt{3 x^{2} + 5 x + 2} + 243 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(32*x**5*sqrt(3*x**2 + 5*x + 2) + 240*x**4*sqrt(3*x**2 + 5*x + 2) + 720*x**3*sqrt(3*x**2 + 5*x + 2) + 1080*x**2*sqrt(3*x**2 + 5*x + 2) + 810*x*sqrt(3*x**2 + 5*x + 2) + 243*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(32*x**5*sqrt(3*x**2 + 5*x + 2) + 240*x**4*sqrt(3*x**2 + 5*x + 2) + 720*x**3*sqrt(3*x**2 + 5*x + 2) + 1080*x**2*sqrt(3*x**2 + 5*x + 2) + 810*x*sqrt(3*x**2 + 5*x + 2) + 243*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2505,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**6/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{64 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 576 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 2160 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 4320 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 4860 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 2916 x \sqrt{3 x^{2} + 5 x + 2} + 729 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{64 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 576 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 2160 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 4320 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 4860 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 2916 x \sqrt{3 x^{2} + 5 x + 2} + 729 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(64*x**6*sqrt(3*x**2 + 5*x + 2) + 576*x**5*sqrt(3*x**2 + 5*x + 2) + 2160*x**4*sqrt(3*x**2 + 5*x + 2) + 4320*x**3*sqrt(3*x**2 + 5*x + 2) + 4860*x**2*sqrt(3*x**2 + 5*x + 2) + 2916*x*sqrt(3*x**2 + 5*x + 2) + 729*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(64*x**6*sqrt(3*x**2 + 5*x + 2) + 576*x**5*sqrt(3*x**2 + 5*x + 2) + 2160*x**4*sqrt(3*x**2 + 5*x + 2) + 4320*x**3*sqrt(3*x**2 + 5*x + 2) + 4860*x**2*sqrt(3*x**2 + 5*x + 2) + 2916*x*sqrt(3*x**2 + 5*x + 2) + 729*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2506,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{999 x}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{864 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{264 x^{3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{16 x^{4}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \frac{16 x^{5}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{405}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-999*x/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-864*x**2/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-264*x**3/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(16*x**4/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(16*x**5/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-405/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2507,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{243 x}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{126 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{4 x^{3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{8 x^{4}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{135}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-243*x/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-126*x**2/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-4*x**3/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(8*x**4/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-135/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2508,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{51 x}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{8 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{4 x^{3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{45}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-51*x/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-8*x**2/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(4*x**3/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-45/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2509,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{7 x}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{2 x^{2}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{15}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-7*x/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(2*x**2/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-15/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2510,0,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2511,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{6 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 19 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 19 x \sqrt{3 x^{2} + 5 x + 2} + 6 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{6 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 19 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 19 x \sqrt{3 x^{2} + 5 x + 2} + 6 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(6*x**3*sqrt(3*x**2 + 5*x + 2) + 19*x**2*sqrt(3*x**2 + 5*x + 2) + 19*x*sqrt(3*x**2 + 5*x + 2) + 6*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(6*x**3*sqrt(3*x**2 + 5*x + 2) + 19*x**2*sqrt(3*x**2 + 5*x + 2) + 19*x*sqrt(3*x**2 + 5*x + 2) + 6*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2512,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{12 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 56 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 95 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 69 x \sqrt{3 x^{2} + 5 x + 2} + 18 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{12 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 56 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 95 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 69 x \sqrt{3 x^{2} + 5 x + 2} + 18 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(12*x**4*sqrt(3*x**2 + 5*x + 2) + 56*x**3*sqrt(3*x**2 + 5*x + 2) + 95*x**2*sqrt(3*x**2 + 5*x + 2) + 69*x*sqrt(3*x**2 + 5*x + 2) + 18*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(12*x**4*sqrt(3*x**2 + 5*x + 2) + 56*x**3*sqrt(3*x**2 + 5*x + 2) + 95*x**2*sqrt(3*x**2 + 5*x + 2) + 69*x*sqrt(3*x**2 + 5*x + 2) + 18*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2513,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{24 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 148 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 358 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 423 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 243 x \sqrt{3 x^{2} + 5 x + 2} + 54 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{24 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 148 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 358 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 423 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 243 x \sqrt{3 x^{2} + 5 x + 2} + 54 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(24*x**5*sqrt(3*x**2 + 5*x + 2) + 148*x**4*sqrt(3*x**2 + 5*x + 2) + 358*x**3*sqrt(3*x**2 + 5*x + 2) + 423*x**2*sqrt(3*x**2 + 5*x + 2) + 243*x*sqrt(3*x**2 + 5*x + 2) + 54*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(24*x**5*sqrt(3*x**2 + 5*x + 2) + 148*x**4*sqrt(3*x**2 + 5*x + 2) + 358*x**3*sqrt(3*x**2 + 5*x + 2) + 423*x**2*sqrt(3*x**2 + 5*x + 2) + 243*x*sqrt(3*x**2 + 5*x + 2) + 54*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2514,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**4/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{48 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 368 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 1160 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 1920 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 1755 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 837 x \sqrt{3 x^{2} + 5 x + 2} + 162 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{48 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 368 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 1160 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 1920 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 1755 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 837 x \sqrt{3 x^{2} + 5 x + 2} + 162 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(48*x**6*sqrt(3*x**2 + 5*x + 2) + 368*x**5*sqrt(3*x**2 + 5*x + 2) + 1160*x**4*sqrt(3*x**2 + 5*x + 2) + 1920*x**3*sqrt(3*x**2 + 5*x + 2) + 1755*x**2*sqrt(3*x**2 + 5*x + 2) + 837*x*sqrt(3*x**2 + 5*x + 2) + 162*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(48*x**6*sqrt(3*x**2 + 5*x + 2) + 368*x**5*sqrt(3*x**2 + 5*x + 2) + 1160*x**4*sqrt(3*x**2 + 5*x + 2) + 1920*x**3*sqrt(3*x**2 + 5*x + 2) + 1755*x**2*sqrt(3*x**2 + 5*x + 2) + 837*x*sqrt(3*x**2 + 5*x + 2) + 162*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2515,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**5/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{96 x^{7} \sqrt{3 x^{2} + 5 x + 2} + 880 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 3424 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 7320 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 9270 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 6939 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 2835 x \sqrt{3 x^{2} + 5 x + 2} + 486 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{96 x^{7} \sqrt{3 x^{2} + 5 x + 2} + 880 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 3424 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 7320 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 9270 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 6939 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 2835 x \sqrt{3 x^{2} + 5 x + 2} + 486 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(96*x**7*sqrt(3*x**2 + 5*x + 2) + 880*x**6*sqrt(3*x**2 + 5*x + 2) + 3424*x**5*sqrt(3*x**2 + 5*x + 2) + 7320*x**4*sqrt(3*x**2 + 5*x + 2) + 9270*x**3*sqrt(3*x**2 + 5*x + 2) + 6939*x**2*sqrt(3*x**2 + 5*x + 2) + 2835*x*sqrt(3*x**2 + 5*x + 2) + 486*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(96*x**7*sqrt(3*x**2 + 5*x + 2) + 880*x**6*sqrt(3*x**2 + 5*x + 2) + 3424*x**5*sqrt(3*x**2 + 5*x + 2) + 7320*x**4*sqrt(3*x**2 + 5*x + 2) + 9270*x**3*sqrt(3*x**2 + 5*x + 2) + 6939*x**2*sqrt(3*x**2 + 5*x + 2) + 2835*x*sqrt(3*x**2 + 5*x + 2) + 486*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2516,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{999 x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{864 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{264 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{16 x^{4}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \frac{16 x^{5}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{405}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-999*x/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-864*x**2/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-264*x**3/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(16*x**4/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(16*x**5/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-405/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2517,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{243 x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{126 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{4 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{8 x^{4}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{135}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-243*x/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-126*x**2/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-4*x**3/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(8*x**4/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-135/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2518,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{51 x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{8 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{4 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{45}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-51*x/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-8*x**2/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(4*x**3/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-45/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2519,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{7 x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{2 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{15}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(-7*x/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(2*x**2/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-15/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2520,0,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**(5/2),x)","- \int \frac{x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2521,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)/(3*x**2+5*x+2)**(5/2),x)","- \int \frac{x}{18 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 87 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 164 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 151 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 68 x \sqrt{3 x^{2} + 5 x + 2} + 12 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{18 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 87 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 164 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 151 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 68 x \sqrt{3 x^{2} + 5 x + 2} + 12 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(18*x**5*sqrt(3*x**2 + 5*x + 2) + 87*x**4*sqrt(3*x**2 + 5*x + 2) + 164*x**3*sqrt(3*x**2 + 5*x + 2) + 151*x**2*sqrt(3*x**2 + 5*x + 2) + 68*x*sqrt(3*x**2 + 5*x + 2) + 12*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(18*x**5*sqrt(3*x**2 + 5*x + 2) + 87*x**4*sqrt(3*x**2 + 5*x + 2) + 164*x**3*sqrt(3*x**2 + 5*x + 2) + 151*x**2*sqrt(3*x**2 + 5*x + 2) + 68*x*sqrt(3*x**2 + 5*x + 2) + 12*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2522,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**(5/2),x)","- \int \frac{x}{36 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 228 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 589 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 794 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 589 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 228 x \sqrt{3 x^{2} + 5 x + 2} + 36 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{36 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 228 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 589 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 794 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 589 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 228 x \sqrt{3 x^{2} + 5 x + 2} + 36 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(36*x**6*sqrt(3*x**2 + 5*x + 2) + 228*x**5*sqrt(3*x**2 + 5*x + 2) + 589*x**4*sqrt(3*x**2 + 5*x + 2) + 794*x**3*sqrt(3*x**2 + 5*x + 2) + 589*x**2*sqrt(3*x**2 + 5*x + 2) + 228*x*sqrt(3*x**2 + 5*x + 2) + 36*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(36*x**6*sqrt(3*x**2 + 5*x + 2) + 228*x**5*sqrt(3*x**2 + 5*x + 2) + 589*x**4*sqrt(3*x**2 + 5*x + 2) + 794*x**3*sqrt(3*x**2 + 5*x + 2) + 589*x**2*sqrt(3*x**2 + 5*x + 2) + 228*x*sqrt(3*x**2 + 5*x + 2) + 36*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2523,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**(5/2),x)","- \int \frac{x}{72 x^{7} \sqrt{3 x^{2} + 5 x + 2} + 564 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 1862 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 3355 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 3560 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 2223 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 756 x \sqrt{3 x^{2} + 5 x + 2} + 108 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{72 x^{7} \sqrt{3 x^{2} + 5 x + 2} + 564 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 1862 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 3355 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 3560 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 2223 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 756 x \sqrt{3 x^{2} + 5 x + 2} + 108 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(72*x**7*sqrt(3*x**2 + 5*x + 2) + 564*x**6*sqrt(3*x**2 + 5*x + 2) + 1862*x**5*sqrt(3*x**2 + 5*x + 2) + 3355*x**4*sqrt(3*x**2 + 5*x + 2) + 3560*x**3*sqrt(3*x**2 + 5*x + 2) + 2223*x**2*sqrt(3*x**2 + 5*x + 2) + 756*x*sqrt(3*x**2 + 5*x + 2) + 108*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(72*x**7*sqrt(3*x**2 + 5*x + 2) + 564*x**6*sqrt(3*x**2 + 5*x + 2) + 1862*x**5*sqrt(3*x**2 + 5*x + 2) + 3355*x**4*sqrt(3*x**2 + 5*x + 2) + 3560*x**3*sqrt(3*x**2 + 5*x + 2) + 2223*x**2*sqrt(3*x**2 + 5*x + 2) + 756*x*sqrt(3*x**2 + 5*x + 2) + 108*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2524,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**4/(3*x**2+5*x+2)**(5/2),x)","- \int \frac{x}{144 x^{8} \sqrt{3 x^{2} + 5 x + 2} + 1344 x^{7} \sqrt{3 x^{2} + 5 x + 2} + 5416 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 12296 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 17185 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 15126 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 8181 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 2484 x \sqrt{3 x^{2} + 5 x + 2} + 324 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{144 x^{8} \sqrt{3 x^{2} + 5 x + 2} + 1344 x^{7} \sqrt{3 x^{2} + 5 x + 2} + 5416 x^{6} \sqrt{3 x^{2} + 5 x + 2} + 12296 x^{5} \sqrt{3 x^{2} + 5 x + 2} + 17185 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 15126 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 8181 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 2484 x \sqrt{3 x^{2} + 5 x + 2} + 324 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(144*x**8*sqrt(3*x**2 + 5*x + 2) + 1344*x**7*sqrt(3*x**2 + 5*x + 2) + 5416*x**6*sqrt(3*x**2 + 5*x + 2) + 12296*x**5*sqrt(3*x**2 + 5*x + 2) + 17185*x**4*sqrt(3*x**2 + 5*x + 2) + 15126*x**3*sqrt(3*x**2 + 5*x + 2) + 8181*x**2*sqrt(3*x**2 + 5*x + 2) + 2484*x*sqrt(3*x**2 + 5*x + 2) + 324*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(144*x**8*sqrt(3*x**2 + 5*x + 2) + 1344*x**7*sqrt(3*x**2 + 5*x + 2) + 5416*x**6*sqrt(3*x**2 + 5*x + 2) + 12296*x**5*sqrt(3*x**2 + 5*x + 2) + 17185*x**4*sqrt(3*x**2 + 5*x + 2) + 15126*x**3*sqrt(3*x**2 + 5*x + 2) + 8181*x**2*sqrt(3*x**2 + 5*x + 2) + 2484*x*sqrt(3*x**2 + 5*x + 2) + 324*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2525,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x**2+x+1)**(1/2),x)","\int \frac{x - 1}{\left(x + 1\right) \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral((x - 1)/((x + 1)*sqrt(x**2 + x + 1)), x)","F",0
2526,1,116,0,3.784098," ","integrate((5-x)*(3+2*x)**(7/2)*(3*x**2+5*x+2),x)","- \frac{16 x^{7} \sqrt{2 x + 3}}{5} - \frac{304 x^{6} \sqrt{2 x + 3}}{65} + \frac{49672 x^{5} \sqrt{2 x + 3}}{715} + \frac{405824 x^{4} \sqrt{2 x + 3}}{1287} + \frac{248887 x^{3} \sqrt{2 x + 3}}{429} + \frac{388473 x^{2} \sqrt{2 x + 3}}{715} + \frac{181869 x \sqrt{2 x + 3}}{715} + \frac{33543 \sqrt{2 x + 3}}{715}"," ",0,"-16*x**7*sqrt(2*x + 3)/5 - 304*x**6*sqrt(2*x + 3)/65 + 49672*x**5*sqrt(2*x + 3)/715 + 405824*x**4*sqrt(2*x + 3)/1287 + 248887*x**3*sqrt(2*x + 3)/429 + 388473*x**2*sqrt(2*x + 3)/715 + 181869*x*sqrt(2*x + 3)/715 + 33543*sqrt(2*x + 3)/715","B",0
2527,1,100,0,1.849756," ","integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2),x)","- \frac{24 x^{6} \sqrt{2 x + 3}}{13} + \frac{68 x^{5} \sqrt{2 x + 3}}{143} + \frac{53606 x^{4} \sqrt{2 x + 3}}{1287} + \frac{372019 x^{3} \sqrt{2 x + 3}}{3003} + \frac{151563 x^{2} \sqrt{2 x + 3}}{1001} + \frac{84261 x \sqrt{2 x + 3}}{1001} + \frac{17487 \sqrt{2 x + 3}}{1001}"," ",0,"-24*x**6*sqrt(2*x + 3)/13 + 68*x**5*sqrt(2*x + 3)/143 + 53606*x**4*sqrt(2*x + 3)/1287 + 372019*x**3*sqrt(2*x + 3)/3003 + 151563*x**2*sqrt(2*x + 3)/1001 + 84261*x*sqrt(2*x + 3)/1001 + 17487*sqrt(2*x + 3)/1001","B",0
2528,1,46,0,13.957310," ","integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2),x)","- \frac{3 \left(2 x + 3\right)^{\frac{11}{2}}}{88} + \frac{47 \left(2 x + 3\right)^{\frac{9}{2}}}{72} - \frac{109 \left(2 x + 3\right)^{\frac{7}{2}}}{56} + \frac{13 \left(2 x + 3\right)^{\frac{5}{2}}}{8}"," ",0,"-3*(2*x + 3)**(11/2)/88 + 47*(2*x + 3)**(9/2)/72 - 109*(2*x + 3)**(7/2)/56 + 13*(2*x + 3)**(5/2)/8","A",0
2529,1,44,0,2.695415," ","integrate((5-x)*(3*x**2+5*x+2)*(3+2*x)**(1/2),x)","- \frac{\left(2 x + 3\right)^{\frac{9}{2}}}{24} + \frac{47 \left(2 x + 3\right)^{\frac{7}{2}}}{56} - \frac{109 \left(2 x + 3\right)^{\frac{5}{2}}}{40} + \frac{65 \left(2 x + 3\right)^{\frac{3}{2}}}{24}"," ",0,"-(2*x + 3)**(9/2)/24 + 47*(2*x + 3)**(7/2)/56 - 109*(2*x + 3)**(5/2)/40 + 65*(2*x + 3)**(3/2)/24","A",0
2530,1,46,0,41.280592," ","integrate((5-x)*(3*x**2+5*x+2)/(3+2*x)**(1/2),x)","- \frac{3 \left(2 x + 3\right)^{\frac{7}{2}}}{56} + \frac{47 \left(2 x + 3\right)^{\frac{5}{2}}}{40} - \frac{109 \left(2 x + 3\right)^{\frac{3}{2}}}{24} + \frac{65 \sqrt{2 x + 3}}{8}"," ",0,"-3*(2*x + 3)**(7/2)/56 + 47*(2*x + 3)**(5/2)/40 - 109*(2*x + 3)**(3/2)/24 + 65*sqrt(2*x + 3)/8","A",0
2531,1,46,0,19.149656," ","integrate((5-x)*(3*x**2+5*x+2)/(3+2*x)**(3/2),x)","- \frac{3 \left(2 x + 3\right)^{\frac{5}{2}}}{40} + \frac{47 \left(2 x + 3\right)^{\frac{3}{2}}}{24} - \frac{109 \sqrt{2 x + 3}}{8} - \frac{65}{8 \sqrt{2 x + 3}}"," ",0,"-3*(2*x + 3)**(5/2)/40 + 47*(2*x + 3)**(3/2)/24 - 109*sqrt(2*x + 3)/8 - 65/(8*sqrt(2*x + 3))","A",0
2532,1,102,0,0.659828," ","integrate((5-x)*(3*x**2+5*x+2)/(3+2*x)**(5/2),x)","- \frac{3 x^{3}}{6 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}} + \frac{57 x^{2}}{6 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}} + \frac{273 x}{6 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}} + \frac{263}{6 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}"," ",0,"-3*x**3/(6*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)) + 57*x**2/(6*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)) + 273*x/(6*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)) + 263/(6*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3))","B",0
2533,1,158,0,1.373044," ","integrate((5-x)*(3*x**2+5*x+2)/(3+2*x)**(7/2),x)","- \frac{9 x^{3}}{12 x^{2} \sqrt{2 x + 3} + 36 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}} - \frac{111 x^{2}}{12 x^{2} \sqrt{2 x + 3} + 36 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}} - \frac{245 x}{12 x^{2} \sqrt{2 x + 3} + 36 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}} - \frac{153}{12 x^{2} \sqrt{2 x + 3} + 36 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}"," ",0,"-9*x**3/(12*x**2*sqrt(2*x + 3) + 36*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)) - 111*x**2/(12*x**2*sqrt(2*x + 3) + 36*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)) - 245*x/(12*x**2*sqrt(2*x + 3) + 36*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)) - 153/(12*x**2*sqrt(2*x + 3) + 36*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3))","B",0
2534,1,146,0,5.884907," ","integrate((5-x)*(3+2*x)**(7/2)*(3*x**2+5*x+2)**2,x)","- \frac{144 x^{9} \sqrt{2 x + 3}}{19} - \frac{7968 x^{8} \sqrt{2 x + 3}}{323} + \frac{612424 x^{7} \sqrt{2 x + 3}}{4845} + \frac{19589192 x^{6} \sqrt{2 x + 3}}{20995} + \frac{577368069 x^{5} \sqrt{2 x + 3}}{230945} + \frac{1538030804 x^{4} \sqrt{2 x + 3}}{415701} + \frac{456297481 x^{3} \sqrt{2 x + 3}}{138567} + \frac{405735126 x^{2} \sqrt{2 x + 3}}{230945} + \frac{119699988 x \sqrt{2 x + 3}}{230945} + \frac{15030936 \sqrt{2 x + 3}}{230945}"," ",0,"-144*x**9*sqrt(2*x + 3)/19 - 7968*x**8*sqrt(2*x + 3)/323 + 612424*x**7*sqrt(2*x + 3)/4845 + 19589192*x**6*sqrt(2*x + 3)/20995 + 577368069*x**5*sqrt(2*x + 3)/230945 + 1538030804*x**4*sqrt(2*x + 3)/415701 + 456297481*x**3*sqrt(2*x + 3)/138567 + 405735126*x**2*sqrt(2*x + 3)/230945 + 119699988*x*sqrt(2*x + 3)/230945 + 15030936*sqrt(2*x + 3)/230945","B",0
2535,1,70,0,29.675316," ","integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**2,x)","- \frac{9 \left(2 x + 3\right)^{\frac{17}{2}}}{544} + \frac{11 \left(2 x + 3\right)^{\frac{15}{2}}}{32} - \frac{359 \left(2 x + 3\right)^{\frac{13}{2}}}{208} + \frac{651 \left(2 x + 3\right)^{\frac{11}{2}}}{176} - \frac{355 \left(2 x + 3\right)^{\frac{9}{2}}}{96} + \frac{325 \left(2 x + 3\right)^{\frac{7}{2}}}{224}"," ",0,"-9*(2*x + 3)**(17/2)/544 + 11*(2*x + 3)**(15/2)/32 - 359*(2*x + 3)**(13/2)/208 + 651*(2*x + 3)**(11/2)/176 - 355*(2*x + 3)**(9/2)/96 + 325*(2*x + 3)**(7/2)/224","A",0
2536,1,70,0,23.804126," ","integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**2,x)","- \frac{3 \left(2 x + 3\right)^{\frac{15}{2}}}{160} + \frac{165 \left(2 x + 3\right)^{\frac{13}{2}}}{416} - \frac{359 \left(2 x + 3\right)^{\frac{11}{2}}}{176} + \frac{217 \left(2 x + 3\right)^{\frac{9}{2}}}{48} - \frac{1065 \left(2 x + 3\right)^{\frac{7}{2}}}{224} + \frac{65 \left(2 x + 3\right)^{\frac{5}{2}}}{32}"," ",0,"-3*(2*x + 3)**(15/2)/160 + 165*(2*x + 3)**(13/2)/416 - 359*(2*x + 3)**(11/2)/176 + 217*(2*x + 3)**(9/2)/48 - 1065*(2*x + 3)**(7/2)/224 + 65*(2*x + 3)**(5/2)/32","A",0
2537,1,70,0,3.559822," ","integrate((5-x)*(3*x**2+5*x+2)**2*(3+2*x)**(1/2),x)","- \frac{9 \left(2 x + 3\right)^{\frac{13}{2}}}{416} + \frac{15 \left(2 x + 3\right)^{\frac{11}{2}}}{32} - \frac{359 \left(2 x + 3\right)^{\frac{9}{2}}}{144} + \frac{93 \left(2 x + 3\right)^{\frac{7}{2}}}{16} - \frac{213 \left(2 x + 3\right)^{\frac{5}{2}}}{32} + \frac{325 \left(2 x + 3\right)^{\frac{3}{2}}}{96}"," ",0,"-9*(2*x + 3)**(13/2)/416 + 15*(2*x + 3)**(11/2)/32 - 359*(2*x + 3)**(9/2)/144 + 93*(2*x + 3)**(7/2)/16 - 213*(2*x + 3)**(5/2)/32 + 325*(2*x + 3)**(3/2)/96","A",0
2538,1,70,0,85.806288," ","integrate((5-x)*(3*x**2+5*x+2)**2/(3+2*x)**(1/2),x)","- \frac{9 \left(2 x + 3\right)^{\frac{11}{2}}}{352} + \frac{55 \left(2 x + 3\right)^{\frac{9}{2}}}{96} - \frac{359 \left(2 x + 3\right)^{\frac{7}{2}}}{112} + \frac{651 \left(2 x + 3\right)^{\frac{5}{2}}}{80} - \frac{355 \left(2 x + 3\right)^{\frac{3}{2}}}{32} + \frac{325 \sqrt{2 x + 3}}{32}"," ",0,"-9*(2*x + 3)**(11/2)/352 + 55*(2*x + 3)**(9/2)/96 - 359*(2*x + 3)**(7/2)/112 + 651*(2*x + 3)**(5/2)/80 - 355*(2*x + 3)**(3/2)/32 + 325*sqrt(2*x + 3)/32","A",0
2539,1,68,0,35.236416," ","integrate((5-x)*(3*x**2+5*x+2)**2/(3+2*x)**(3/2),x)","- \frac{\left(2 x + 3\right)^{\frac{9}{2}}}{32} + \frac{165 \left(2 x + 3\right)^{\frac{7}{2}}}{224} - \frac{359 \left(2 x + 3\right)^{\frac{5}{2}}}{80} + \frac{217 \left(2 x + 3\right)^{\frac{3}{2}}}{16} - \frac{1065 \sqrt{2 x + 3}}{32} - \frac{325}{32 \sqrt{2 x + 3}}"," ",0,"-(2*x + 3)**(9/2)/32 + 165*(2*x + 3)**(7/2)/224 - 359*(2*x + 3)**(5/2)/80 + 217*(2*x + 3)**(3/2)/16 - 1065*sqrt(2*x + 3)/32 - 325/(32*sqrt(2*x + 3))","A",0
2540,1,70,0,43.539975," ","integrate((5-x)*(3*x**2+5*x+2)**2/(3+2*x)**(5/2),x)","- \frac{9 \left(2 x + 3\right)^{\frac{7}{2}}}{224} + \frac{33 \left(2 x + 3\right)^{\frac{5}{2}}}{32} - \frac{359 \left(2 x + 3\right)^{\frac{3}{2}}}{48} + \frac{651 \sqrt{2 x + 3}}{16} + \frac{1065}{32 \sqrt{2 x + 3}} - \frac{325}{96 \left(2 x + 3\right)^{\frac{3}{2}}}"," ",0,"-9*(2*x + 3)**(7/2)/224 + 33*(2*x + 3)**(5/2)/32 - 359*(2*x + 3)**(3/2)/48 + 651*sqrt(2*x + 3)/16 + 1065/(32*sqrt(2*x + 3)) - 325/(96*(2*x + 3)**(3/2))","A",0
2541,1,238,0,1.563295," ","integrate((5-x)*(3*x**2+5*x+2)**2/(3+2*x)**(7/2),x)","- \frac{9 x^{5}}{20 x^{2} \sqrt{2 x + 3} + 60 x \sqrt{2 x + 3} + 45 \sqrt{2 x + 3}} + \frac{70 x^{4}}{20 x^{2} \sqrt{2 x + 3} + 60 x \sqrt{2 x + 3} + 45 \sqrt{2 x + 3}} - \frac{275 x^{3}}{20 x^{2} \sqrt{2 x + 3} + 60 x \sqrt{2 x + 3} + 45 \sqrt{2 x + 3}} - \frac{3300 x^{2}}{20 x^{2} \sqrt{2 x + 3} + 60 x \sqrt{2 x + 3} + 45 \sqrt{2 x + 3}} - \frac{6760 x}{20 x^{2} \sqrt{2 x + 3} + 60 x \sqrt{2 x + 3} + 45 \sqrt{2 x + 3}} - \frac{4076}{20 x^{2} \sqrt{2 x + 3} + 60 x \sqrt{2 x + 3} + 45 \sqrt{2 x + 3}}"," ",0,"-9*x**5/(20*x**2*sqrt(2*x + 3) + 60*x*sqrt(2*x + 3) + 45*sqrt(2*x + 3)) + 70*x**4/(20*x**2*sqrt(2*x + 3) + 60*x*sqrt(2*x + 3) + 45*sqrt(2*x + 3)) - 275*x**3/(20*x**2*sqrt(2*x + 3) + 60*x*sqrt(2*x + 3) + 45*sqrt(2*x + 3)) - 3300*x**2/(20*x**2*sqrt(2*x + 3) + 60*x*sqrt(2*x + 3) + 45*sqrt(2*x + 3)) - 6760*x/(20*x**2*sqrt(2*x + 3) + 60*x*sqrt(2*x + 3) + 45*sqrt(2*x + 3)) - 4076/(20*x**2*sqrt(2*x + 3) + 60*x*sqrt(2*x + 3) + 45*sqrt(2*x + 3))","B",0
2542,1,94,0,49.990354," ","integrate((5-x)*(3+2*x)**(7/2)*(3*x**2+5*x+2)**3,x)","- \frac{27 \left(2 x + 3\right)^{\frac{23}{2}}}{2944} + \frac{27 \left(2 x + 3\right)^{\frac{21}{2}}}{128} - \frac{3519 \left(2 x + 3\right)^{\frac{19}{2}}}{2432} + \frac{10475 \left(2 x + 3\right)^{\frac{17}{2}}}{2176} - \frac{17201 \left(2 x + 3\right)^{\frac{15}{2}}}{1920} + \frac{16005 \left(2 x + 3\right)^{\frac{13}{2}}}{1664} - \frac{7925 \left(2 x + 3\right)^{\frac{11}{2}}}{1408} + \frac{1625 \left(2 x + 3\right)^{\frac{9}{2}}}{1152}"," ",0,"-27*(2*x + 3)**(23/2)/2944 + 27*(2*x + 3)**(21/2)/128 - 3519*(2*x + 3)**(19/2)/2432 + 10475*(2*x + 3)**(17/2)/2176 - 17201*(2*x + 3)**(15/2)/1920 + 16005*(2*x + 3)**(13/2)/1664 - 7925*(2*x + 3)**(11/2)/1408 + 1625*(2*x + 3)**(9/2)/1152","A",0
2543,1,94,0,42.098084," ","integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**3,x)","- \frac{9 \left(2 x + 3\right)^{\frac{21}{2}}}{896} + \frac{567 \left(2 x + 3\right)^{\frac{19}{2}}}{2432} - \frac{207 \left(2 x + 3\right)^{\frac{17}{2}}}{128} + \frac{2095 \left(2 x + 3\right)^{\frac{15}{2}}}{384} - \frac{17201 \left(2 x + 3\right)^{\frac{13}{2}}}{1664} + \frac{1455 \left(2 x + 3\right)^{\frac{11}{2}}}{128} - \frac{7925 \left(2 x + 3\right)^{\frac{9}{2}}}{1152} + \frac{1625 \left(2 x + 3\right)^{\frac{7}{2}}}{896}"," ",0,"-9*(2*x + 3)**(21/2)/896 + 567*(2*x + 3)**(19/2)/2432 - 207*(2*x + 3)**(17/2)/128 + 2095*(2*x + 3)**(15/2)/384 - 17201*(2*x + 3)**(13/2)/1664 + 1455*(2*x + 3)**(11/2)/128 - 7925*(2*x + 3)**(9/2)/1152 + 1625*(2*x + 3)**(7/2)/896","A",0
2544,1,94,0,35.462844," ","integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**3,x)","- \frac{27 \left(2 x + 3\right)^{\frac{19}{2}}}{2432} + \frac{567 \left(2 x + 3\right)^{\frac{17}{2}}}{2176} - \frac{1173 \left(2 x + 3\right)^{\frac{15}{2}}}{640} + \frac{10475 \left(2 x + 3\right)^{\frac{13}{2}}}{1664} - \frac{17201 \left(2 x + 3\right)^{\frac{11}{2}}}{1408} + \frac{5335 \left(2 x + 3\right)^{\frac{9}{2}}}{384} - \frac{7925 \left(2 x + 3\right)^{\frac{7}{2}}}{896} + \frac{325 \left(2 x + 3\right)^{\frac{5}{2}}}{128}"," ",0,"-27*(2*x + 3)**(19/2)/2432 + 567*(2*x + 3)**(17/2)/2176 - 1173*(2*x + 3)**(15/2)/640 + 10475*(2*x + 3)**(13/2)/1664 - 17201*(2*x + 3)**(11/2)/1408 + 5335*(2*x + 3)**(9/2)/384 - 7925*(2*x + 3)**(7/2)/896 + 325*(2*x + 3)**(5/2)/128","A",0
2545,1,94,0,4.017110," ","integrate((5-x)*(3*x**2+5*x+2)**3*(3+2*x)**(1/2),x)","- \frac{27 \left(2 x + 3\right)^{\frac{17}{2}}}{2176} + \frac{189 \left(2 x + 3\right)^{\frac{15}{2}}}{640} - \frac{3519 \left(2 x + 3\right)^{\frac{13}{2}}}{1664} + \frac{10475 \left(2 x + 3\right)^{\frac{11}{2}}}{1408} - \frac{17201 \left(2 x + 3\right)^{\frac{9}{2}}}{1152} + \frac{16005 \left(2 x + 3\right)^{\frac{7}{2}}}{896} - \frac{1585 \left(2 x + 3\right)^{\frac{5}{2}}}{128} + \frac{1625 \left(2 x + 3\right)^{\frac{3}{2}}}{384}"," ",0,"-27*(2*x + 3)**(17/2)/2176 + 189*(2*x + 3)**(15/2)/640 - 3519*(2*x + 3)**(13/2)/1664 + 10475*(2*x + 3)**(11/2)/1408 - 17201*(2*x + 3)**(9/2)/1152 + 16005*(2*x + 3)**(7/2)/896 - 1585*(2*x + 3)**(5/2)/128 + 1625*(2*x + 3)**(3/2)/384","A",0
2546,1,94,0,124.644396," ","integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(1/2),x)","- \frac{9 \left(2 x + 3\right)^{\frac{15}{2}}}{640} + \frac{567 \left(2 x + 3\right)^{\frac{13}{2}}}{1664} - \frac{3519 \left(2 x + 3\right)^{\frac{11}{2}}}{1408} + \frac{10475 \left(2 x + 3\right)^{\frac{9}{2}}}{1152} - \frac{17201 \left(2 x + 3\right)^{\frac{7}{2}}}{896} + \frac{3201 \left(2 x + 3\right)^{\frac{5}{2}}}{128} - \frac{7925 \left(2 x + 3\right)^{\frac{3}{2}}}{384} + \frac{1625 \sqrt{2 x + 3}}{128}"," ",0,"-9*(2*x + 3)**(15/2)/640 + 567*(2*x + 3)**(13/2)/1664 - 3519*(2*x + 3)**(11/2)/1408 + 10475*(2*x + 3)**(9/2)/1152 - 17201*(2*x + 3)**(7/2)/896 + 3201*(2*x + 3)**(5/2)/128 - 7925*(2*x + 3)**(3/2)/384 + 1625*sqrt(2*x + 3)/128","A",0
2547,1,94,0,46.036191," ","integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(3/2),x)","- \frac{27 \left(2 x + 3\right)^{\frac{13}{2}}}{1664} + \frac{567 \left(2 x + 3\right)^{\frac{11}{2}}}{1408} - \frac{391 \left(2 x + 3\right)^{\frac{9}{2}}}{128} + \frac{10475 \left(2 x + 3\right)^{\frac{7}{2}}}{896} - \frac{17201 \left(2 x + 3\right)^{\frac{5}{2}}}{640} + \frac{5335 \left(2 x + 3\right)^{\frac{3}{2}}}{128} - \frac{7925 \sqrt{2 x + 3}}{128} - \frac{1625}{128 \sqrt{2 x + 3}}"," ",0,"-27*(2*x + 3)**(13/2)/1664 + 567*(2*x + 3)**(11/2)/1408 - 391*(2*x + 3)**(9/2)/128 + 10475*(2*x + 3)**(7/2)/896 - 17201*(2*x + 3)**(5/2)/640 + 5335*(2*x + 3)**(3/2)/128 - 7925*sqrt(2*x + 3)/128 - 1625/(128*sqrt(2*x + 3))","A",0
2548,1,94,0,56.093819," ","integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(5/2),x)","- \frac{27 \left(2 x + 3\right)^{\frac{11}{2}}}{1408} + \frac{63 \left(2 x + 3\right)^{\frac{9}{2}}}{128} - \frac{3519 \left(2 x + 3\right)^{\frac{7}{2}}}{896} + \frac{2095 \left(2 x + 3\right)^{\frac{5}{2}}}{128} - \frac{17201 \left(2 x + 3\right)^{\frac{3}{2}}}{384} + \frac{16005 \sqrt{2 x + 3}}{128} + \frac{7925}{128 \sqrt{2 x + 3}} - \frac{1625}{384 \left(2 x + 3\right)^{\frac{3}{2}}}"," ",0,"-27*(2*x + 3)**(11/2)/1408 + 63*(2*x + 3)**(9/2)/128 - 3519*(2*x + 3)**(7/2)/896 + 2095*(2*x + 3)**(5/2)/128 - 17201*(2*x + 3)**(3/2)/384 + 16005*sqrt(2*x + 3)/128 + 7925/(128*sqrt(2*x + 3)) - 1625/(384*(2*x + 3)**(3/2))","A",0
2549,1,94,0,62.144177," ","integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(7/2),x)","- \frac{3 \left(2 x + 3\right)^{\frac{9}{2}}}{128} + \frac{81 \left(2 x + 3\right)^{\frac{7}{2}}}{128} - \frac{3519 \left(2 x + 3\right)^{\frac{5}{2}}}{640} + \frac{10475 \left(2 x + 3\right)^{\frac{3}{2}}}{384} - \frac{17201 \sqrt{2 x + 3}}{128} - \frac{16005}{128 \sqrt{2 x + 3}} + \frac{7925}{384 \left(2 x + 3\right)^{\frac{3}{2}}} - \frac{325}{128 \left(2 x + 3\right)^{\frac{5}{2}}}"," ",0,"-3*(2*x + 3)**(9/2)/128 + 81*(2*x + 3)**(7/2)/128 - 3519*(2*x + 3)**(5/2)/640 + 10475*(2*x + 3)**(3/2)/384 - 17201*sqrt(2*x + 3)/128 - 16005/(128*sqrt(2*x + 3)) + 7925/(384*(2*x + 3)**(3/2)) - 325/(128*(2*x + 3)**(5/2))","A",0
2550,1,138,0,113.476798," ","integrate((5-x)*(3+2*x)**(7/2)/(3*x**2+5*x+2),x)","- \frac{2 \left(2 x + 3\right)^{\frac{7}{2}}}{21} + \frac{62 \left(2 x + 3\right)^{\frac{5}{2}}}{45} + \frac{526 \left(2 x + 3\right)^{\frac{3}{2}}}{81} + \frac{3278 \sqrt{2 x + 3}}{81} + \frac{21250 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{81} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)}"," ",0,"-2*(2*x + 3)**(7/2)/21 + 62*(2*x + 3)**(5/2)/45 + 526*(2*x + 3)**(3/2)/81 + 3278*sqrt(2*x + 3)/81 + 21250*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/81 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1)","A",0
2551,1,126,0,83.327771," ","integrate((5-x)*(3+2*x)**(5/2)/(3*x**2+5*x+2),x)","- \frac{2 \left(2 x + 3\right)^{\frac{5}{2}}}{15} + \frac{62 \left(2 x + 3\right)^{\frac{3}{2}}}{27} + \frac{526 \sqrt{2 x + 3}}{27} + \frac{4250 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{27} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)}"," ",0,"-2*(2*x + 3)**(5/2)/15 + 62*(2*x + 3)**(3/2)/27 + 526*sqrt(2*x + 3)/27 + 4250*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/27 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1)","A",0
2552,1,114,0,59.214878," ","integrate((5-x)*(3+2*x)**(3/2)/(3*x**2+5*x+2),x)","- \frac{2 \left(2 x + 3\right)^{\frac{3}{2}}}{9} + \frac{62 \sqrt{2 x + 3}}{9} + \frac{850 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{9} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)}"," ",0,"-2*(2*x + 3)**(3/2)/9 + 62*sqrt(2*x + 3)/9 + 850*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/9 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1)","A",0
2553,1,102,0,8.204636," ","integrate((5-x)*(3+2*x)**(1/2)/(3*x**2+5*x+2),x)","- \frac{2 \sqrt{2 x + 3}}{3} + \frac{170 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{3} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)}"," ",0,"-2*sqrt(2*x + 3)/3 + 170*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/3 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1)","A",0
2554,1,95,0,82.714221," ","integrate((5-x)/(3*x**2+5*x+2)/(3+2*x)**(1/2),x)","34 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15}}{3 \sqrt{2 x + 3}} \right)}}{15} & \text{for}\: \frac{1}{2 x + 3} > \frac{3}{5} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15}}{3 \sqrt{2 x + 3}} \right)}}{15} & \text{for}\: \frac{1}{2 x + 3} < \frac{3}{5} \end{cases}\right) - 6 \log{\left(-1 + \frac{1}{\sqrt{2 x + 3}} \right)} + 6 \log{\left(1 + \frac{1}{\sqrt{2 x + 3}} \right)}"," ",0,"34*Piecewise((-sqrt(15)*acoth(sqrt(15)/(3*sqrt(2*x + 3)))/15, 1/(2*x + 3) > 3/5), (-sqrt(15)*atanh(sqrt(15)/(3*sqrt(2*x + 3)))/15, 1/(2*x + 3) < 3/5)) - 6*log(-1 + 1/sqrt(2*x + 3)) + 6*log(1 + 1/sqrt(2*x + 3))","A",0
2555,1,102,0,76.667014," ","integrate((5-x)/(3+2*x)**(3/2)/(3*x**2+5*x+2),x)","\frac{102 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{5} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)} - \frac{26}{5 \sqrt{2 x + 3}}"," ",0,"102*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/5 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1) - 26/(5*sqrt(2*x + 3))","A",0
2556,1,114,0,105.816995," ","integrate((5-x)/(3+2*x)**(5/2)/(3*x**2+5*x+2),x)","\frac{306 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{25} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)} - \frac{198}{25 \sqrt{2 x + 3}} - \frac{26}{15 \left(2 x + 3\right)^{\frac{3}{2}}}"," ",0,"306*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/25 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1) - 198/(25*sqrt(2*x + 3)) - 26/(15*(2*x + 3)**(3/2))","A",0
2557,1,126,0,94.034444," ","integrate((5-x)/(3+2*x)**(7/2)/(3*x**2+5*x+2),x)","\frac{918 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right)}{125} - 6 \log{\left(\sqrt{2 x + 3} - 1 \right)} + 6 \log{\left(\sqrt{2 x + 3} + 1 \right)} - \frac{1194}{125 \sqrt{2 x + 3}} - \frac{66}{25 \left(2 x + 3\right)^{\frac{3}{2}}} - \frac{26}{25 \left(2 x + 3\right)^{\frac{5}{2}}}"," ",0,"918*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3))/125 - 6*log(sqrt(2*x + 3) - 1) + 6*log(sqrt(2*x + 3) + 1) - 1194/(125*sqrt(2*x + 3)) - 66/(25*(2*x + 3)**(3/2)) - 26/(25*(2*x + 3)**(5/2))","A",0
2558,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(7/2)/(3*x**2+5*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2559,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)/(3*x**2+5*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2560,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)/(3*x**2+5*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2561,1,212,0,122.218706," ","integrate((5-x)*(3+2*x)**(1/2)/(3*x**2+5*x+2)**2,x)","340 \left(\begin{cases} \frac{\sqrt{15} \left(- \frac{\log{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} - 1 \right)}}{4} + \frac{\log{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} + 1 \right)}}{4} - \frac{1}{4 \left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} + 1\right)} - \frac{1}{4 \left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} - 1\right)}\right)}{75} & \text{for}\: x \geq - \frac{3}{2} \wedge x < - \frac{2}{3} \end{cases}\right) - 282 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{2 x + 3}}{5} \right)}}{15} & \text{for}\: 2 x + 3 < \frac{5}{3} \end{cases}\right) + 41 \log{\left(\sqrt{2 x + 3} - 1 \right)} - 41 \log{\left(\sqrt{2 x + 3} + 1 \right)} - \frac{6}{\sqrt{2 x + 3} + 1} - \frac{6}{\sqrt{2 x + 3} - 1}"," ",0,"340*Piecewise((sqrt(15)*(-log(sqrt(15)*sqrt(2*x + 3)/5 - 1)/4 + log(sqrt(15)*sqrt(2*x + 3)/5 + 1)/4 - 1/(4*(sqrt(15)*sqrt(2*x + 3)/5 + 1)) - 1/(4*(sqrt(15)*sqrt(2*x + 3)/5 - 1)))/75, (x >= -3/2) & (x < -2/3))) - 282*Piecewise((-sqrt(15)*acoth(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 > 5/3), (-sqrt(15)*atanh(sqrt(15)*sqrt(2*x + 3)/5)/15, 2*x + 3 < 5/3)) + 41*log(sqrt(2*x + 3) - 1) - 41*log(sqrt(2*x + 3) + 1) - 6/(sqrt(2*x + 3) + 1) - 6/(sqrt(2*x + 3) - 1)","A",0
2562,-1,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**2/(3+2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2563,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(3/2)/(3*x**2+5*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2564,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(5/2)/(3*x**2+5*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2565,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(7/2)/(3*x**2+5*x+2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2566,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(9/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2567,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(7/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2568,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2569,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2570,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(1/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2571,-1,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**3/(3+2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2572,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(3/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2573,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(5/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2574,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(7/2)/(3*x**2+5*x+2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2575,0,0,0,0.000000," ","integrate((5+10*x+35**(1/2))/(5*x**2+3*x+2)/(1+2*x)**(1/2),x)","\int \frac{10 x + 5 + \sqrt{35}}{\sqrt{2 x + 1} \left(5 x^{2} + 3 x + 2\right)}\, dx"," ",0,"Integral((10*x + 5 + sqrt(35))/(sqrt(2*x + 1)*(5*x**2 + 3*x + 2)), x)","F",0
2576,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 45 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 51 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 8 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 4 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-45*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-51*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-8*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(4*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2577,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 15 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 7 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 2 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-15*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-7*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(2*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2578,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(1/2)*(3*x**2+5*x+2)**(1/2),x)","- \int \left(- 5 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2579,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**(1/2),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{2 x + 3}}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/sqrt(2*x + 3), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/sqrt(2*x + 3), x)","F",0
2580,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**(3/2),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x)","F",0
2581,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**(5/2),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x)","F",0
2582,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**(7/2),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x)","F",0
2583,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(1/2)/(3+2*x)**(9/2),x)","- \int \left(- \frac{5 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \frac{x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-5*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(x*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x)","F",0
2584,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 90 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 327 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 406 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 185 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 4 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 12 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-90*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-327*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-406*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-185*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-4*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(12*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2585,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**(3/2),x)","- \int \left(- 30 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 89 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 76 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 11 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 6 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-30*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-89*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-76*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-11*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(6*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2586,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)*(3+2*x)**(1/2),x)","- \int \left(- 10 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 23 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 10 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 3 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-10*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-23*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-10*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(3*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2587,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(1/2),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{2 x + 3}}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{\sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/sqrt(2*x + 3), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/sqrt(2*x + 3), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/sqrt(2*x + 3), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/sqrt(2*x + 3), x)","F",0
2588,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(3/2),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x)","F",0
2589,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(5/2),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x)","F",0
2590,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(7/2),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x)","F",0
2591,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(9/2),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x)","F",0
2592,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(11/2),x)","- \int \left(- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} \sqrt{2 x + 3} + 240 x^{4} \sqrt{2 x + 3} + 720 x^{3} \sqrt{2 x + 3} + 1080 x^{2} \sqrt{2 x + 3} + 810 x \sqrt{2 x + 3} + 243 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} \sqrt{2 x + 3} + 240 x^{4} \sqrt{2 x + 3} + 720 x^{3} \sqrt{2 x + 3} + 1080 x^{2} \sqrt{2 x + 3} + 810 x \sqrt{2 x + 3} + 243 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} \sqrt{2 x + 3} + 240 x^{4} \sqrt{2 x + 3} + 720 x^{3} \sqrt{2 x + 3} + 1080 x^{2} \sqrt{2 x + 3} + 810 x \sqrt{2 x + 3} + 243 \sqrt{2 x + 3}}\right)\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{32 x^{5} \sqrt{2 x + 3} + 240 x^{4} \sqrt{2 x + 3} + 720 x^{3} \sqrt{2 x + 3} + 1080 x^{2} \sqrt{2 x + 3} + 810 x \sqrt{2 x + 3} + 243 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-10*sqrt(3*x**2 + 5*x + 2)/(32*x**5*sqrt(2*x + 3) + 240*x**4*sqrt(2*x + 3) + 720*x**3*sqrt(2*x + 3) + 1080*x**2*sqrt(2*x + 3) + 810*x*sqrt(2*x + 3) + 243*sqrt(2*x + 3)), x) - Integral(-23*x*sqrt(3*x**2 + 5*x + 2)/(32*x**5*sqrt(2*x + 3) + 240*x**4*sqrt(2*x + 3) + 720*x**3*sqrt(2*x + 3) + 1080*x**2*sqrt(2*x + 3) + 810*x*sqrt(2*x + 3) + 243*sqrt(2*x + 3)), x) - Integral(-10*x**2*sqrt(3*x**2 + 5*x + 2)/(32*x**5*sqrt(2*x + 3) + 240*x**4*sqrt(2*x + 3) + 720*x**3*sqrt(2*x + 3) + 1080*x**2*sqrt(2*x + 3) + 810*x*sqrt(2*x + 3) + 243*sqrt(2*x + 3)), x) - Integral(3*x**3*sqrt(3*x**2 + 5*x + 2)/(32*x**5*sqrt(2*x + 3) + 240*x**4*sqrt(2*x + 3) + 720*x**3*sqrt(2*x + 3) + 1080*x**2*sqrt(2*x + 3) + 810*x*sqrt(2*x + 3) + 243*sqrt(2*x + 3)), x)","F",0
2593,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2594,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 180 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 1104 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 2717 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3381 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 2151 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 551 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 48 x^{6} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx - \int 36 x^{7} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-180*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-1104*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-2717*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3381*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-2151*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-551*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(48*x**6*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(36*x**7*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2595,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**(5/2),x)","- \int \left(- 60 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 328 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 687 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 669 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 271 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 3 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 18 x^{6} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-60*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-328*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-687*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-669*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-271*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-3*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(18*x**6*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2596,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)*(3+2*x)**(1/2),x)","- \int \left(- 20 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 96 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 165 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 113 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int \left(- 15 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\right)\, dx - \int 9 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}\, dx"," ",0,"-Integral(-20*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-96*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-165*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-113*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(-15*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x) - Integral(9*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2), x)","F",0
2597,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2598,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(3/2),x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(2*x*sqrt(2*x + 3) + 3*sqrt(2*x + 3)), x)","F",0
2599,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(5/2),x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(4*x**2*sqrt(2*x + 3) + 12*x*sqrt(2*x + 3) + 9*sqrt(2*x + 3)), x)","F",0
2600,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(7/2),x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{8 x^{3} \sqrt{2 x + 3} + 36 x^{2} \sqrt{2 x + 3} + 54 x \sqrt{2 x + 3} + 27 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(8*x**3*sqrt(2*x + 3) + 36*x**2*sqrt(2*x + 3) + 54*x*sqrt(2*x + 3) + 27*sqrt(2*x + 3)), x)","F",0
2601,0,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(9/2),x)","- \int \left(- \frac{20 \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{96 x \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{165 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{113 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \left(- \frac{15 x^{4} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\right)\, dx - \int \frac{9 x^{5} \sqrt{3 x^{2} + 5 x + 2}}{16 x^{4} \sqrt{2 x + 3} + 96 x^{3} \sqrt{2 x + 3} + 216 x^{2} \sqrt{2 x + 3} + 216 x \sqrt{2 x + 3} + 81 \sqrt{2 x + 3}}\, dx"," ",0,"-Integral(-20*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(-96*x*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(-165*x**2*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(-113*x**3*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(-15*x**4*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x) - Integral(9*x**5*sqrt(3*x**2 + 5*x + 2)/(16*x**4*sqrt(2*x + 3) + 96*x**3*sqrt(2*x + 3) + 216*x**2*sqrt(2*x + 3) + 216*x*sqrt(2*x + 3) + 81*sqrt(2*x + 3)), x)","F",0
2602,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2603,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2604,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2605,-1,0,0,0.000000," ","integrate((5-x)*(3*x**2+5*x+2)**(5/2)/(3+2*x)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2606,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{45 \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{51 x \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{8 x^{2} \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{4 x^{3} \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-45*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x) - Integral(-51*x*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x) - Integral(-8*x**2*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x) - Integral(4*x**3*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x)","F",0
2607,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{15 \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{7 x \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{2 x^{2} \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-15*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x) - Integral(-7*x*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x) - Integral(2*x**2*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x)","F",0
2608,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(1/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{5 \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{x \sqrt{2 x + 3}}{\sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-5*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x) - Integral(x*sqrt(2*x + 3)/sqrt(3*x**2 + 5*x + 2), x)","F",0
2609,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(1/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \left(- \frac{5}{\sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{x}{\sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-5/(sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(x/(sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2610,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(3/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{2 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 3 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{2 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 3 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(2*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(2*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2611,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(5/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{4 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 12 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 9 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{4 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 12 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 9 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(4*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 12*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 9*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(4*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 12*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 9*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2612,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(7/2)/(3*x**2+5*x+2)**(1/2),x)","- \int \frac{x}{8 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 36 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 54 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 27 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{8 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 36 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 54 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 27 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(8*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 36*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 54*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 27*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(8*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 36*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 54*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 27*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2613,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(7/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{135 \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{243 x \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{126 x^{2} \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{4 x^{3} \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{8 x^{4} \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-135*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-243*x*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-126*x**2*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-4*x**3*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(8*x**4*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2614,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{45 \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{51 x \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{8 x^{2} \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{4 x^{3} \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-45*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-51*x*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-8*x**2*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(4*x**3*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2615,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{15 \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{7 x \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{2 x^{2} \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-15*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-7*x*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(2*x**2*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2616,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(1/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \left(- \frac{5 \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{x \sqrt{2 x + 3}}{3 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-5*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x) - Integral(x*sqrt(2*x + 3)/(3*x**2*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2617,0,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**(3/2)/(3+2*x)**(1/2),x)","- \int \frac{x}{3 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{3 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 5 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 2 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(3*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(3*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 5*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2618,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(3/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{6 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 19 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 19 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 6 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{6 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 19 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 19 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 6 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(6*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 19*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 19*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 6*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(6*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 19*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 19*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 6*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2619,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(5/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{12 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 56 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 95 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 69 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 18 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{12 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 56 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 95 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 69 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 18 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(12*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 56*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 95*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 69*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 18*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(12*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 56*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 95*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 69*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 18*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2620,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(7/2)/(3*x**2+5*x+2)**(3/2),x)","- \int \frac{x}{24 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 148 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 358 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 423 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 243 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 54 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{24 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 148 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 358 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 423 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 243 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 54 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(24*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 148*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 358*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 423*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 243*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 54*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(24*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 148*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 358*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 423*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 243*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 54*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2621,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(9/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2622,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(7/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2623,-1,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(5/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2624,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(3/2)/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{15 \sqrt{2 x + 3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \left(- \frac{7 x \sqrt{2 x + 3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{2 x^{2} \sqrt{2 x + 3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-15*sqrt(2*x + 3)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-7*x*sqrt(2*x + 3)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(2*x**2*sqrt(2*x + 3)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2625,0,0,0,0.000000," ","integrate((5-x)*(3+2*x)**(1/2)/(3*x**2+5*x+2)**(5/2),x)","- \int \left(- \frac{5 \sqrt{2 x + 3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx - \int \frac{x \sqrt{2 x + 3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx"," ",0,"-Integral(-5*sqrt(2*x + 3)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x) - Integral(x*sqrt(2*x + 3)/(9*x**4*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2626,0,0,0,0.000000," ","integrate((5-x)/(3*x**2+5*x+2)**(5/2)/(3+2*x)**(1/2),x)","- \int \frac{x}{9 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{9 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(9*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(9*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 30*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 37*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 20*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2627,0,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(3/2)/(3*x**2+5*x+2)**(5/2),x)","- \int \frac{x}{18 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 87 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 164 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 151 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 68 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 12 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left(- \frac{5}{18 x^{5} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 87 x^{4} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 164 x^{3} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 151 x^{2} \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 68 x \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2} + 12 \sqrt{2 x + 3} \sqrt{3 x^{2} + 5 x + 2}}\right)\, dx"," ",0,"-Integral(x/(18*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 87*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 164*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 151*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 68*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 12*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x) - Integral(-5/(18*x**5*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 87*x**4*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 164*x**3*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 151*x**2*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 68*x*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2) + 12*sqrt(2*x + 3)*sqrt(3*x**2 + 5*x + 2)), x)","F",0
2628,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(5/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2629,-1,0,0,0.000000," ","integrate((5-x)/(3+2*x)**(7/2)/(3*x**2+5*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2630,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{\frac{3}{2}}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**(3/2)/sqrt(a + b*x + c*x**2), x)","F",0
2631,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/sqrt(a + b*x + c*x**2), x)","F",0
2632,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\sqrt{d + e x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/(sqrt(d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
2633,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**(3/2)*sqrt(a + b*x + c*x**2)), x)","F",0
2634,0,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x}{\left(d + e x\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x)/((d + e*x)**(5/2)*sqrt(a + b*x + c*x**2)), x)","F",0
2635,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(5/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2636,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2637,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(A + B x\right) \sqrt{d + e x}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x)*sqrt(d + e*x)/(a + b*x + c*x**2)**(3/2), x)","F",0
2638,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2639,-1,0,0,0.000000," ","integrate((B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2640,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2641,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2642,1,5930,0,5.252377," ","integrate((B*x+A)*(e*x+d)**m*(c*x**2+b*x+a),x)","\begin{cases} d^{m} \left(A a x + \frac{A b x^{2}}{2} + \frac{A c x^{3}}{3} + \frac{B a x^{2}}{2} + \frac{B b x^{3}}{3} + \frac{B c x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{2 A a e^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{A b d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 A b e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 A c d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A c d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 A c e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{B a d e^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 B a e^{3} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 B b d^{2} e}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 B b d e^{2} x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 B b e^{3} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 B c d^{3}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 B c d^{2} e x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 B c d e^{2} x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 B c e^{3} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{A a e^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{A b d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 A b e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 A c d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 A c d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 A c e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{B a d e^{2}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 B a e^{3} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 B b d^{2} e}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 B b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 B b d e^{2} x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B b e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 B c d^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 B c d^{2} e x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 B c d e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 B c e^{3} x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\- \frac{2 A a e^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A b d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A b d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A b e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 A c d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 A c e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a d e^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a d e^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B a e^{3} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 B b d^{2} e \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 B b d^{2} e}{2 d e^{4} + 2 e^{5} x} - \frac{4 B b d e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 B b e^{3} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{3}}{2 d e^{4} + 2 e^{5} x} + \frac{6 B c d^{2} e x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 B c d e^{2} x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{B c e^{3} x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\\frac{A a \log{\left(\frac{d}{e} + x \right)}}{e} - \frac{A b d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{A b x}{e} + \frac{A c d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{A c d x}{e^{2}} + \frac{A c x^{2}}{2 e} - \frac{B a d \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{B a x}{e} + \frac{B b d^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{B b d x}{e^{2}} + \frac{B b x^{2}}{2 e} - \frac{B c d^{3} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{B c d^{2} x}{e^{3}} - \frac{B c d x^{2}}{2 e^{2}} + \frac{B c x^{3}}{3 e} & \text{for}\: m = -1 \\\frac{A a d e^{3} m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 A a d e^{3} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 A a d e^{3} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a d e^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A a e^{4} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 A a e^{4} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 A a e^{4} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 A a e^{4} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{A b d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 A b d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 A b d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A b d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 A b d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 A b d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A b e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A b e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 A b e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 A b e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 A c d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A c d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 A c d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 A c d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A c d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 A c d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 A c d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{A c e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 A c e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 A c e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 A c e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{B a d^{2} e^{2} m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 B a d^{2} e^{2} m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 B a d^{2} e^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B a d e^{3} m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 B a d e^{3} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 B a d e^{3} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B a e^{4} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B a e^{4} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 B a e^{4} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 B a e^{4} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B b d^{3} e m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B b d^{3} e \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 B b d^{2} e^{2} m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 B b d^{2} e^{2} m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B b d e^{3} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 B b d e^{3} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 B b d e^{3} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B b e^{4} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 B b e^{4} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 B b e^{4} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 B b e^{4} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 B c d^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c d^{3} e m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B c d^{2} e^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 B c d^{2} e^{2} m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B c d e^{3} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 B c d e^{3} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 B c d e^{3} m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{B c e^{4} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c e^{4} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 B c e^{4} m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 B c e^{4} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(A*a*x + A*b*x**2/2 + A*c*x**3/3 + B*a*x**2/2 + B*b*x**3/3 + B*c*x**4/4), Eq(e, 0)), (-2*A*a*e**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - A*b*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*A*b*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*A*c*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*c*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*A*c*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - B*a*d*e**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*B*a*e**3*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*B*b*d**2*e/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*B*b*d*e**2*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*B*b*e**3*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*c*d**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*B*c*d**3/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d**2*e*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*B*c*d**2*e*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d*e**2*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*B*c*d*e**2*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*B*c*e**3*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-A*a*e**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - A*b*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*A*b*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*c*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*A*c*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*c*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*A*c*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*A*c*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - B*a*d*e**2/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*B*a*e**3*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*b*d**2*e*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*B*b*d**2*e/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*B*b*d*e**2*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*B*b*d*e**2*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*b*e**3*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*c*d**3*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*B*c*d**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*c*d**2*e*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*B*c*d**2*e*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*B*c*d*e**2*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*B*c*e**3*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (-2*A*a*e**3/(2*d*e**4 + 2*e**5*x) + 2*A*b*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*A*b*d*e**2/(2*d*e**4 + 2*e**5*x) + 2*A*b*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*c*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*A*c*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*A*c*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*A*c*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 2*B*a*d*e**2*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*B*a*d*e**2/(2*d*e**4 + 2*e**5*x) + 2*B*a*e**3*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*B*b*d**2*e*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*B*b*d**2*e/(2*d*e**4 + 2*e**5*x) - 4*B*b*d*e**2*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*B*b*e**3*x**2/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**3*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**3/(2*d*e**4 + 2*e**5*x) + 6*B*c*d**2*e*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*B*c*d*e**2*x**2/(2*d*e**4 + 2*e**5*x) + B*c*e**3*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (A*a*log(d/e + x)/e - A*b*d*log(d/e + x)/e**2 + A*b*x/e + A*c*d**2*log(d/e + x)/e**3 - A*c*d*x/e**2 + A*c*x**2/(2*e) - B*a*d*log(d/e + x)/e**2 + B*a*x/e + B*b*d**2*log(d/e + x)/e**3 - B*b*d*x/e**2 + B*b*x**2/(2*e) - B*c*d**3*log(d/e + x)/e**4 + B*c*d**2*x/e**3 - B*c*d*x**2/(2*e**2) + B*c*x**3/(3*e), Eq(m, -1)), (A*a*d*e**3*m**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*A*a*d*e**3*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*A*a*d*e**3*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a*d*e**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*a*e**4*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*A*a*e**4*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*A*a*e**4*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*A*a*e**4*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - A*b*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*A*b*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*A*b*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*b*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*A*b*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*A*b*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*b*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*b*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*A*b*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*A*b*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*A*c*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*c*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*A*c*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*A*c*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*c*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*A*c*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*A*c*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + A*c*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*A*c*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*A*c*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*A*c*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - B*a*d**2*e**2*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*B*a*d**2*e**2*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*B*a*d**2*e**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*a*d*e**3*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*B*a*d*e**3*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*B*a*d*e**3*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*a*e**4*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*a*e**4*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*B*a*e**4*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*B*a*e**4*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*b*d**3*e*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*b*d**3*e*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*B*b*d**2*e**2*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*B*b*d**2*e**2*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*b*d*e**3*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*B*b*d*e**3*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*B*b*d*e**3*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*b*e**4*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*B*b*e**4*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*B*b*e**4*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*B*b*e**4*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*B*c*d**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*d**3*e*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*c*d**2*e**2*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*B*c*d**2*e**2*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*c*d*e**3*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*B*c*d*e**3*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*B*c*d*e**3*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + B*c*e**4*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*e**4*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*B*c*e**4*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*B*c*e**4*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
2643,0,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(c*x**2+b*x+a),x)","\int \frac{\left(A + B x\right) \left(d + e x\right)^{m}}{a + b x + c x^{2}}\, dx"," ",0,"Integral((A + B*x)*(d + e*x)**m/(a + b*x + c*x**2), x)","F",0
2644,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**m/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2645,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(1+m)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2646,-1,0,0,0.000000," ","integrate((B*x+A)*(e*x+d)**(-3-2*p)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
