Integrand size = 29, antiderivative size = 411 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx=\frac {2 (b e-a f)^2 (d e-c f)^2 (f g-e h) (e+f x)^{5/2}}{5 f^6}-\frac {2 (b e-a f) (d e-c f) (b d e (4 f g-5 e h)-b c f (2 f g-3 e h)-a f (2 d f g-3 d e h+c f h)) (e+f x)^{7/2}}{7 f^6}+\frac {2 \left (a^2 d f^2 (d f g-3 d e h+2 c f h)+2 a b f \left (c^2 f^2 h+2 c d f (f g-3 e h)-3 d^2 e (f g-2 e h)\right )+b^2 \left (2 d^2 e^2 (3 f g-5 e h)+c^2 f^2 (f g-3 e h)-6 c d e f (f g-2 e h)\right )\right ) (e+f x)^{9/2}}{9 f^6}+\frac {2 \left (a^2 d^2 f^2 h+2 a b d f (d f g-4 d e h+2 c f h)+b^2 \left (c^2 f^2 h-2 d^2 e (2 f g-5 e h)+2 c d f (f g-4 e h)\right )\right ) (e+f x)^{11/2}}{11 f^6}+\frac {2 b d (2 a d f h+b (d f g-5 d e h+2 c f h)) (e+f x)^{13/2}}{13 f^6}+\frac {2 b^2 d^2 h (e+f x)^{15/2}}{15 f^6} \] Output:
2/5*(-a*f+b*e)^2*(-c*f+d*e)^2*(-e*h+f*g)*(f*x+e)^(5/2)/f^6-2/7*(-a*f+b*e)* (-c*f+d*e)*(b*d*e*(-5*e*h+4*f*g)-b*c*f*(-3*e*h+2*f*g)-a*f*(c*f*h-3*d*e*h+2 *d*f*g))*(f*x+e)^(7/2)/f^6+2/9*(a^2*d*f^2*(2*c*f*h-3*d*e*h+d*f*g)+2*a*b*f* (c^2*f^2*h+2*c*d*f*(-3*e*h+f*g)-3*d^2*e*(-2*e*h+f*g))+b^2*(2*d^2*e^2*(-5*e *h+3*f*g)+c^2*f^2*(-3*e*h+f*g)-6*c*d*e*f*(-2*e*h+f*g)))*(f*x+e)^(9/2)/f^6+ 2/11*(a^2*d^2*f^2*h+2*a*b*d*f*(2*c*f*h-4*d*e*h+d*f*g)+b^2*(c^2*f^2*h-2*d^2 *e*(-5*e*h+2*f*g)+2*c*d*f*(-4*e*h+f*g)))*(f*x+e)^(11/2)/f^6+2/13*b*d*(2*a* d*f*h+b*(2*c*f*h-5*d*e*h+d*f*g))*(f*x+e)^(13/2)/f^6+2/15*b^2*d^2*h*(f*x+e) ^(15/2)/f^6
Time = 0.54 (sec) , antiderivative size = 554, normalized size of antiderivative = 1.35 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx=\frac {2 (e+f x)^{5/2} \left (13 a^2 f^2 \left (99 c^2 f^2 (7 f g-2 e h+5 f h x)+22 c d f \left (8 e^2 h+5 f^2 x (9 g+7 h x)-2 e f (9 g+10 h x)\right )+d^2 \left (-48 e^3 h+35 f^3 x^2 (11 g+9 h x)+8 e^2 f (11 g+15 h x)-10 e f^2 x (22 g+21 h x)\right )\right )+2 a b f \left (143 c^2 f^2 \left (8 e^2 h+5 f^2 x (9 g+7 h x)-2 e f (9 g+10 h x)\right )+3 d^2 \left (128 e^4 h+105 f^4 x^3 (13 g+11 h x)-70 e f^3 x^2 (13 g+12 h x)+40 e^2 f^2 x (13 g+14 h x)-16 e^3 f (13 g+20 h x)\right )+26 c d f \left (-48 e^3 h+35 f^3 x^2 (11 g+9 h x)+8 e^2 f (11 g+15 h x)-10 e f^2 x (22 g+21 h x)\right )\right )+b^2 \left (d^2 \left (-256 e^5 h+1680 e^2 f^3 x^2 (g+h x)+128 e^4 f (3 g+5 h x)-160 e^3 f^2 x (6 g+7 h x)-210 e f^4 x^3 (12 g+11 h x)+231 f^5 x^4 (15 g+13 h x)\right )+6 c d f \left (128 e^4 h+105 f^4 x^3 (13 g+11 h x)-70 e f^3 x^2 (13 g+12 h x)+40 e^2 f^2 x (13 g+14 h x)-16 e^3 f (13 g+20 h x)\right )+13 c^2 f^2 \left (-48 e^3 h+35 f^3 x^2 (11 g+9 h x)+8 e^2 f (11 g+15 h x)-10 e f^2 x (22 g+21 h x)\right )\right )\right )}{45045 f^6} \] Input:
Integrate[(a + b*x)^2*(c + d*x)^2*(e + f*x)^(3/2)*(g + h*x),x]
Output:
(2*(e + f*x)^(5/2)*(13*a^2*f^2*(99*c^2*f^2*(7*f*g - 2*e*h + 5*f*h*x) + 22* c*d*f*(8*e^2*h + 5*f^2*x*(9*g + 7*h*x) - 2*e*f*(9*g + 10*h*x)) + d^2*(-48* e^3*h + 35*f^3*x^2*(11*g + 9*h*x) + 8*e^2*f*(11*g + 15*h*x) - 10*e*f^2*x*( 22*g + 21*h*x))) + 2*a*b*f*(143*c^2*f^2*(8*e^2*h + 5*f^2*x*(9*g + 7*h*x) - 2*e*f*(9*g + 10*h*x)) + 3*d^2*(128*e^4*h + 105*f^4*x^3*(13*g + 11*h*x) - 70*e*f^3*x^2*(13*g + 12*h*x) + 40*e^2*f^2*x*(13*g + 14*h*x) - 16*e^3*f*(13 *g + 20*h*x)) + 26*c*d*f*(-48*e^3*h + 35*f^3*x^2*(11*g + 9*h*x) + 8*e^2*f* (11*g + 15*h*x) - 10*e*f^2*x*(22*g + 21*h*x))) + b^2*(d^2*(-256*e^5*h + 16 80*e^2*f^3*x^2*(g + h*x) + 128*e^4*f*(3*g + 5*h*x) - 160*e^3*f^2*x*(6*g + 7*h*x) - 210*e*f^4*x^3*(12*g + 11*h*x) + 231*f^5*x^4*(15*g + 13*h*x)) + 6* c*d*f*(128*e^4*h + 105*f^4*x^3*(13*g + 11*h*x) - 70*e*f^3*x^2*(13*g + 12*h *x) + 40*e^2*f^2*x*(13*g + 14*h*x) - 16*e^3*f*(13*g + 20*h*x)) + 13*c^2*f^ 2*(-48*e^3*h + 35*f^3*x^2*(11*g + 9*h*x) + 8*e^2*f*(11*g + 15*h*x) - 10*e* f^2*x*(22*g + 21*h*x)))))/(45045*f^6)
Time = 0.71 (sec) , antiderivative size = 411, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {165, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx\) |
| \(\Big \downarrow \) 165 |
| \(\displaystyle \int \left (\frac {(e+f x)^{7/2} \left (a^2 d f^2 (2 c f h-3 d e h+d f g)+2 a b f \left (c^2 f^2 h+2 c d f (f g-3 e h)-3 d^2 e (f g-2 e h)\right )+b^2 \left (c^2 f^2 (f g-3 e h)-6 c d e f (f g-2 e h)+2 d^2 e^2 (3 f g-5 e h)\right )\right )}{f^5}+\frac {(e+f x)^{9/2} \left (a^2 d^2 f^2 h+2 a b d f (2 c f h-4 d e h+d f g)+b^2 \left (c^2 f^2 h+2 c d f (f g-4 e h)-2 d^2 e (2 f g-5 e h)\right )\right )}{f^5}+\frac {b d (e+f x)^{11/2} (2 a d f h+b (2 c f h-5 d e h+d f g))}{f^5}+\frac {(e+f x)^{5/2} (b e-a f) (d e-c f) (a f (c f h-3 d e h+2 d f g)+b c f (2 f g-3 e h)-b d e (4 f g-5 e h))}{f^5}+\frac {(e+f x)^{3/2} (a f-b e)^2 (c f-d e)^2 (f g-e h)}{f^5}+\frac {b^2 d^2 h (e+f x)^{13/2}}{f^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {2 (e+f x)^{9/2} \left (a^2 d f^2 (2 c f h-3 d e h+d f g)+2 a b f \left (c^2 f^2 h+2 c d f (f g-3 e h)-3 d^2 e (f g-2 e h)\right )+b^2 \left (c^2 f^2 (f g-3 e h)-6 c d e f (f g-2 e h)+2 d^2 e^2 (3 f g-5 e h)\right )\right )}{9 f^6}+\frac {2 (e+f x)^{11/2} \left (a^2 d^2 f^2 h+2 a b d f (2 c f h-4 d e h+d f g)+b^2 \left (c^2 f^2 h+2 c d f (f g-4 e h)-2 d^2 e (2 f g-5 e h)\right )\right )}{11 f^6}+\frac {2 b d (e+f x)^{13/2} (2 a d f h+b (2 c f h-5 d e h+d f g))}{13 f^6}-\frac {2 (e+f x)^{7/2} (b e-a f) (d e-c f) (-a f (c f h-3 d e h+2 d f g)-b c f (2 f g-3 e h)+b d e (4 f g-5 e h))}{7 f^6}+\frac {2 (e+f x)^{5/2} (b e-a f)^2 (d e-c f)^2 (f g-e h)}{5 f^6}+\frac {2 b^2 d^2 h (e+f x)^{15/2}}{15 f^6}\) |
Input:
Int[(a + b*x)^2*(c + d*x)^2*(e + f*x)^(3/2)*(g + h*x),x]
Output:
(2*(b*e - a*f)^2*(d*e - c*f)^2*(f*g - e*h)*(e + f*x)^(5/2))/(5*f^6) - (2*( b*e - a*f)*(d*e - c*f)*(b*d*e*(4*f*g - 5*e*h) - b*c*f*(2*f*g - 3*e*h) - a* f*(2*d*f*g - 3*d*e*h + c*f*h))*(e + f*x)^(7/2))/(7*f^6) + (2*(a^2*d*f^2*(d *f*g - 3*d*e*h + 2*c*f*h) + 2*a*b*f*(c^2*f^2*h + 2*c*d*f*(f*g - 3*e*h) - 3 *d^2*e*(f*g - 2*e*h)) + b^2*(2*d^2*e^2*(3*f*g - 5*e*h) + c^2*f^2*(f*g - 3* e*h) - 6*c*d*e*f*(f*g - 2*e*h)))*(e + f*x)^(9/2))/(9*f^6) + (2*(a^2*d^2*f^ 2*h + 2*a*b*d*f*(d*f*g - 4*d*e*h + 2*c*f*h) + b^2*(c^2*f^2*h - 2*d^2*e*(2* f*g - 5*e*h) + 2*c*d*f*(f*g - 4*e*h)))*(e + f*x)^(11/2))/(11*f^6) + (2*b*d *(2*a*d*f*h + b*(d*f*g - 5*d*e*h + 2*c*f*h))*(e + f*x)^(13/2))/(13*f^6) + (2*b^2*d^2*h*(e + f*x)^(15/2))/(15*f^6)
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_)*((g_.) + (h_.)*(x_)), x_] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d* x)^n*(e + f*x)^p*(g + h*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, h, m}, x] && (IntegersQ[m, n, p] || (IGtQ[n, 0] && IGtQ[p, 0]))
Time = 1.04 (sec) , antiderivative size = 412, normalized size of antiderivative = 1.00
| method | result | size |
| derivativedivides | \(\frac {\frac {2 h \,b^{2} d^{2} \left (f x +e \right )^{\frac {15}{2}}}{15}+\frac {2 \left (\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) h +b^{2} d^{2} \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {13}{2}}}{13}+\frac {2 \left (\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) h +\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {11}{2}}}{11}+\frac {2 \left (\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) h +\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {9}{2}}}{9}+\frac {2 \left (\left (a f -b e \right )^{2} \left (c f -d e \right )^{2} h +\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {7}{2}}}{7}+\frac {2 \left (a f -b e \right )^{2} \left (c f -d e \right )^{2} \left (-e h +f g \right ) \left (f x +e \right )^{\frac {5}{2}}}{5}}{f^{6}}\) | \(412\) |
| default | \(\frac {\frac {2 h \,b^{2} d^{2} \left (f x +e \right )^{\frac {15}{2}}}{15}-\frac {2 \left (-\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) h +b^{2} d^{2} \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {13}{2}}}{13}-\frac {2 \left (-\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) h +\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {11}{2}}}{11}-\frac {2 \left (-\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) h +\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {9}{2}}}{9}-\frac {2 \left (-\left (a f -b e \right )^{2} \left (c f -d e \right )^{2} h +\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {7}{2}}}{7}-\frac {2 \left (a f -b e \right )^{2} \left (c f -d e \right )^{2} \left (e h -f g \right ) \left (f x +e \right )^{\frac {5}{2}}}{5}}{f^{6}}\) | \(416\) |
| pseudoelliptic | \(-\frac {4 \left (\left (-\frac {35 x^{2} \left (\left (\frac {3}{5} h \,x^{3}+\frac {9}{13} g \,x^{2}\right ) d^{2}+\frac {18 x c \left (\frac {11 h x}{13}+g \right ) d}{11}+c^{2} \left (\frac {9 h x}{11}+g \right )\right ) b^{2}}{18}-5 a x \left (\left (\frac {7}{13} h \,x^{3}+\frac {7}{11} g \,x^{2}\right ) d^{2}+\frac {14 x c \left (\frac {9 h x}{11}+g \right ) d}{9}+c^{2} \left (\frac {7 h x}{9}+g \right )\right ) b -\frac {7 a^{2} \left (\frac {5 x^{2} \left (\frac {9 h x}{11}+g \right ) d^{2}}{9}+\frac {10 x c \left (\frac {7 h x}{9}+g \right ) d}{7}+c^{2} \left (\frac {5 h x}{7}+g \right )\right )}{2}\right ) f^{5}+\left (\frac {10 x \left (\frac {126 x^{2} \left (\frac {11 h x}{12}+g \right ) d^{2}}{143}+\frac {21 x c \left (\frac {12 h x}{13}+g \right ) d}{11}+c^{2} \left (\frac {21 h x}{22}+g \right )\right ) b^{2}}{9}+2 a \left (\frac {35 x^{2} \left (\frac {12 h x}{13}+g \right ) d^{2}}{33}+\frac {20 x c \left (\frac {21 h x}{22}+g \right ) d}{9}+c^{2} \left (\frac {10 h x}{9}+g \right )\right ) b +a^{2} \left (\frac {10 x \left (\frac {21 h x}{22}+g \right ) d^{2}}{9}+2 c \left (\frac {10 h x}{9}+g \right ) d +h \,c^{2}\right )\right ) e \,f^{4}-\frac {8 \left (\left (\frac {105 x^{2} \left (h x +g \right ) d^{2}}{143}+\frac {15 \left (\frac {14 h x}{13}+g \right ) x c d}{11}+\frac {c^{2} \left (\frac {15 h x}{11}+g \right )}{2}\right ) b^{2}+a \left (\frac {15 \left (\frac {14 h x}{13}+g \right ) x \,d^{2}}{11}+2 c \left (\frac {15 h x}{11}+g \right ) d +h \,c^{2}\right ) b +a^{2} d \left (\left (\frac {15 h x}{22}+\frac {g}{2}\right ) d +c h \right )\right ) e^{2} f^{3}}{9}+\frac {8 e^{3} \left (\left (\frac {20 x \left (\frac {7 h x}{6}+g \right ) d^{2}}{13}+2 \left (\frac {20 h x}{13}+g \right ) c d +h \,c^{2}\right ) b^{2}+4 a \left (\left (\frac {10 h x}{13}+\frac {g}{2}\right ) d +c h \right ) d b +a^{2} d^{2} h \right ) f^{2}}{33}-\frac {128 d b \,e^{4} \left (\left (\left (\frac {5 h x}{6}+\frac {g}{2}\right ) d +c h \right ) b +a d h \right ) f}{429}+\frac {128 b^{2} d^{2} e^{5} h}{1287}\right ) \left (f x +e \right )^{\frac {5}{2}}}{35 f^{6}}\) | \(479\) |
| gosper | \(-\frac {2 \left (f x +e \right )^{\frac {5}{2}} \left (-3003 h \,b^{2} d^{2} x^{5} f^{5}-6930 a b \,d^{2} f^{5} h \,x^{4}-6930 b^{2} c d \,f^{5} h \,x^{4}+2310 b^{2} d^{2} e \,f^{4} h \,x^{4}-3465 b^{2} d^{2} f^{5} g \,x^{4}-4095 a^{2} d^{2} f^{5} h \,x^{3}-16380 a b c d \,f^{5} h \,x^{3}+5040 a b \,d^{2} e \,f^{4} h \,x^{3}-8190 a b \,d^{2} f^{5} g \,x^{3}-4095 b^{2} c^{2} f^{5} h \,x^{3}+5040 b^{2} c d e \,f^{4} h \,x^{3}-8190 b^{2} c d \,f^{5} g \,x^{3}-1680 b^{2} d^{2} e^{2} f^{3} h \,x^{3}+2520 b^{2} d^{2} e \,f^{4} g \,x^{3}-10010 a^{2} c d \,f^{5} h \,x^{2}+2730 a^{2} d^{2} e \,f^{4} h \,x^{2}-5005 a^{2} d^{2} f^{5} g \,x^{2}-10010 a b \,c^{2} f^{5} h \,x^{2}+10920 a b c d e \,f^{4} h \,x^{2}-20020 a b c d \,f^{5} g \,x^{2}-3360 a b \,d^{2} e^{2} f^{3} h \,x^{2}+5460 a b \,d^{2} e \,f^{4} g \,x^{2}+2730 b^{2} c^{2} e \,f^{4} h \,x^{2}-5005 b^{2} c^{2} f^{5} g \,x^{2}-3360 b^{2} c d \,e^{2} f^{3} h \,x^{2}+5460 b^{2} c d e \,f^{4} g \,x^{2}+1120 b^{2} d^{2} e^{3} f^{2} h \,x^{2}-1680 b^{2} d^{2} e^{2} f^{3} g \,x^{2}-6435 a^{2} c^{2} f^{5} h x +5720 a^{2} c d e \,f^{4} h x -12870 a^{2} c d \,f^{5} g x -1560 a^{2} d^{2} e^{2} f^{3} h x +2860 a^{2} d^{2} e \,f^{4} g x +5720 a b \,c^{2} e \,f^{4} h x -12870 a b \,c^{2} f^{5} g x -6240 a b c d \,e^{2} f^{3} h x +11440 a b c d e \,f^{4} g x +1920 a b \,d^{2} e^{3} f^{2} h x -3120 a b \,d^{2} e^{2} f^{3} g x -1560 b^{2} c^{2} e^{2} f^{3} h x +2860 b^{2} c^{2} e \,f^{4} g x +1920 b^{2} c d \,e^{3} f^{2} h x -3120 b^{2} c d \,e^{2} f^{3} g x -640 b^{2} d^{2} e^{4} f h x +960 b^{2} d^{2} e^{3} f^{2} g x +2574 a^{2} c^{2} e \,f^{4} h -9009 g \,a^{2} c^{2} f^{5}-2288 a^{2} c d \,e^{2} f^{3} h +5148 a^{2} c d e \,f^{4} g +624 a^{2} d^{2} e^{3} f^{2} h -1144 a^{2} d^{2} e^{2} f^{3} g -2288 a b \,c^{2} e^{2} f^{3} h +5148 a b \,c^{2} e \,f^{4} g +2496 a b c d \,e^{3} f^{2} h -4576 a b c d \,e^{2} f^{3} g -768 a b \,d^{2} e^{4} f h +1248 a b \,d^{2} e^{3} f^{2} g +624 b^{2} c^{2} e^{3} f^{2} h -1144 b^{2} c^{2} e^{2} f^{3} g -768 b^{2} c d \,e^{4} f h +1248 b^{2} c d \,e^{3} f^{2} g +256 b^{2} d^{2} e^{5} h -384 b^{2} d^{2} e^{4} f g \right )}{45045 f^{6}}\) | \(919\) |
| orering | \(-\frac {2 \left (f x +e \right )^{\frac {5}{2}} \left (-3003 h \,b^{2} d^{2} x^{5} f^{5}-6930 a b \,d^{2} f^{5} h \,x^{4}-6930 b^{2} c d \,f^{5} h \,x^{4}+2310 b^{2} d^{2} e \,f^{4} h \,x^{4}-3465 b^{2} d^{2} f^{5} g \,x^{4}-4095 a^{2} d^{2} f^{5} h \,x^{3}-16380 a b c d \,f^{5} h \,x^{3}+5040 a b \,d^{2} e \,f^{4} h \,x^{3}-8190 a b \,d^{2} f^{5} g \,x^{3}-4095 b^{2} c^{2} f^{5} h \,x^{3}+5040 b^{2} c d e \,f^{4} h \,x^{3}-8190 b^{2} c d \,f^{5} g \,x^{3}-1680 b^{2} d^{2} e^{2} f^{3} h \,x^{3}+2520 b^{2} d^{2} e \,f^{4} g \,x^{3}-10010 a^{2} c d \,f^{5} h \,x^{2}+2730 a^{2} d^{2} e \,f^{4} h \,x^{2}-5005 a^{2} d^{2} f^{5} g \,x^{2}-10010 a b \,c^{2} f^{5} h \,x^{2}+10920 a b c d e \,f^{4} h \,x^{2}-20020 a b c d \,f^{5} g \,x^{2}-3360 a b \,d^{2} e^{2} f^{3} h \,x^{2}+5460 a b \,d^{2} e \,f^{4} g \,x^{2}+2730 b^{2} c^{2} e \,f^{4} h \,x^{2}-5005 b^{2} c^{2} f^{5} g \,x^{2}-3360 b^{2} c d \,e^{2} f^{3} h \,x^{2}+5460 b^{2} c d e \,f^{4} g \,x^{2}+1120 b^{2} d^{2} e^{3} f^{2} h \,x^{2}-1680 b^{2} d^{2} e^{2} f^{3} g \,x^{2}-6435 a^{2} c^{2} f^{5} h x +5720 a^{2} c d e \,f^{4} h x -12870 a^{2} c d \,f^{5} g x -1560 a^{2} d^{2} e^{2} f^{3} h x +2860 a^{2} d^{2} e \,f^{4} g x +5720 a b \,c^{2} e \,f^{4} h x -12870 a b \,c^{2} f^{5} g x -6240 a b c d \,e^{2} f^{3} h x +11440 a b c d e \,f^{4} g x +1920 a b \,d^{2} e^{3} f^{2} h x -3120 a b \,d^{2} e^{2} f^{3} g x -1560 b^{2} c^{2} e^{2} f^{3} h x +2860 b^{2} c^{2} e \,f^{4} g x +1920 b^{2} c d \,e^{3} f^{2} h x -3120 b^{2} c d \,e^{2} f^{3} g x -640 b^{2} d^{2} e^{4} f h x +960 b^{2} d^{2} e^{3} f^{2} g x +2574 a^{2} c^{2} e \,f^{4} h -9009 g \,a^{2} c^{2} f^{5}-2288 a^{2} c d \,e^{2} f^{3} h +5148 a^{2} c d e \,f^{4} g +624 a^{2} d^{2} e^{3} f^{2} h -1144 a^{2} d^{2} e^{2} f^{3} g -2288 a b \,c^{2} e^{2} f^{3} h +5148 a b \,c^{2} e \,f^{4} g +2496 a b c d \,e^{3} f^{2} h -4576 a b c d \,e^{2} f^{3} g -768 a b \,d^{2} e^{4} f h +1248 a b \,d^{2} e^{3} f^{2} g +624 b^{2} c^{2} e^{3} f^{2} h -1144 b^{2} c^{2} e^{2} f^{3} g -768 b^{2} c d \,e^{4} f h +1248 b^{2} c d \,e^{3} f^{2} g +256 b^{2} d^{2} e^{5} h -384 b^{2} d^{2} e^{4} f g \right )}{45045 f^{6}}\) | \(919\) |
| trager | \(\text {Expression too large to display}\) | \(1539\) |
| risch | \(\text {Expression too large to display}\) | \(1539\) |
Input:
int((b*x+a)^2*(d*x+c)^2*(f*x+e)^(3/2)*(h*x+g),x,method=_RETURNVERBOSE)
Output:
2/f^6*(1/15*h*b^2*d^2*(f*x+e)^(15/2)+1/13*((2*b*(a*f-b*e)*d^2+2*b^2*d*(c*f -d*e))*h+b^2*d^2*(-e*h+f*g))*(f*x+e)^(13/2)+1/11*(((a*f-b*e)^2*d^2+4*b*(a* f-b*e)*d*(c*f-d*e)+b^2*(c*f-d*e)^2)*h+(2*b*(a*f-b*e)*d^2+2*b^2*d*(c*f-d*e) )*(-e*h+f*g))*(f*x+e)^(11/2)+1/9*((2*(a*f-b*e)^2*d*(c*f-d*e)+2*b*(a*f-b*e) *(c*f-d*e)^2)*h+((a*f-b*e)^2*d^2+4*b*(a*f-b*e)*d*(c*f-d*e)+b^2*(c*f-d*e)^2 )*(-e*h+f*g))*(f*x+e)^(9/2)+1/7*((a*f-b*e)^2*(c*f-d*e)^2*h+(2*(a*f-b*e)^2* d*(c*f-d*e)+2*b*(a*f-b*e)*(c*f-d*e)^2)*(-e*h+f*g))*(f*x+e)^(7/2)+1/5*(a*f- b*e)^2*(c*f-d*e)^2*(-e*h+f*g)*(f*x+e)^(5/2))
Leaf count of result is larger than twice the leaf count of optimal. 1128 vs. \(2 (387) = 774\).
Time = 0.10 (sec) , antiderivative size = 1128, normalized size of antiderivative = 2.74 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx=\text {Too large to display} \] Input:
integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^(3/2)*(h*x+g),x, algorithm="fricas")
Output:
2/45045*(3003*b^2*d^2*f^7*h*x^7 + 231*(15*b^2*d^2*f^7*g + 2*(8*b^2*d^2*e*f ^6 + 15*(b^2*c*d + a*b*d^2)*f^7)*h)*x^6 + 63*(10*(7*b^2*d^2*e*f^6 + 13*(b^ 2*c*d + a*b*d^2)*f^7)*g + (b^2*d^2*e^2*f^5 + 140*(b^2*c*d + a*b*d^2)*e*f^6 + 65*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^7)*h)*x^5 + 35*((3*b^2*d^2*e^2*f^5 + 312*(b^2*c*d + a*b*d^2)*e*f^6 + 143*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^7 )*g - 2*(b^2*d^2*e^3*f^4 - 3*(b^2*c*d + a*b*d^2)*e^2*f^5 - 78*(b^2*c^2 + 4 *a*b*c*d + a^2*d^2)*e*f^6 - 143*(a*b*c^2 + a^2*c*d)*f^7)*h)*x^4 - 5*(2*(12 *b^2*d^2*e^3*f^4 - 39*(b^2*c*d + a*b*d^2)*e^2*f^5 - 715*(b^2*c^2 + 4*a*b*c *d + a^2*d^2)*e*f^6 - 1287*(a*b*c^2 + a^2*c*d)*f^7)*g - (16*b^2*d^2*e^4*f^ 3 + 1287*a^2*c^2*f^7 - 48*(b^2*c*d + a*b*d^2)*e^3*f^4 + 39*(b^2*c^2 + 4*a* b*c*d + a^2*d^2)*e^2*f^5 + 2860*(a*b*c^2 + a^2*c*d)*e*f^6)*h)*x^3 + 3*((48 *b^2*d^2*e^4*f^3 + 3003*a^2*c^2*f^7 - 156*(b^2*c*d + a*b*d^2)*e^3*f^4 + 14 3*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^2*f^5 + 6864*(a*b*c^2 + a^2*c*d)*e*f^6 )*g - 2*(16*b^2*d^2*e^5*f^2 - 1716*a^2*c^2*e*f^6 - 48*(b^2*c*d + a*b*d^2)* e^4*f^3 + 39*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^3*f^4 - 143*(a*b*c^2 + a^2* c*d)*e^2*f^5)*h)*x^2 + (384*b^2*d^2*e^6*f + 9009*a^2*c^2*e^2*f^5 - 1248*(b ^2*c*d + a*b*d^2)*e^5*f^2 + 1144*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^4*f^3 - 5148*(a*b*c^2 + a^2*c*d)*e^3*f^4)*g - 2*(128*b^2*d^2*e^7 + 1287*a^2*c^2*e ^3*f^4 - 384*(b^2*c*d + a*b*d^2)*e^6*f + 312*(b^2*c^2 + 4*a*b*c*d + a^2*d^ 2)*e^5*f^2 - 1144*(a*b*c^2 + a^2*c*d)*e^4*f^3)*h - (2*(96*b^2*d^2*e^5*f...
Leaf count of result is larger than twice the leaf count of optimal. 1204 vs. \(2 (445) = 890\).
Time = 2.06 (sec) , antiderivative size = 1204, normalized size of antiderivative = 2.93 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx =\text {Too large to display} \] Input:
integrate((b*x+a)**2*(d*x+c)**2*(f*x+e)**(3/2)*(h*x+g),x)
Output:
Piecewise((2*(b**2*d**2*h*(e + f*x)**(15/2)/(15*f**5) + (e + f*x)**(13/2)* (2*a*b*d**2*f*h + 2*b**2*c*d*f*h - 5*b**2*d**2*e*h + b**2*d**2*f*g)/(13*f* *5) + (e + f*x)**(11/2)*(a**2*d**2*f**2*h + 4*a*b*c*d*f**2*h - 8*a*b*d**2* e*f*h + 2*a*b*d**2*f**2*g + b**2*c**2*f**2*h - 8*b**2*c*d*e*f*h + 2*b**2*c *d*f**2*g + 10*b**2*d**2*e**2*h - 4*b**2*d**2*e*f*g)/(11*f**5) + (e + f*x) **(9/2)*(2*a**2*c*d*f**3*h - 3*a**2*d**2*e*f**2*h + a**2*d**2*f**3*g + 2*a *b*c**2*f**3*h - 12*a*b*c*d*e*f**2*h + 4*a*b*c*d*f**3*g + 12*a*b*d**2*e**2 *f*h - 6*a*b*d**2*e*f**2*g - 3*b**2*c**2*e*f**2*h + b**2*c**2*f**3*g + 12* b**2*c*d*e**2*f*h - 6*b**2*c*d*e*f**2*g - 10*b**2*d**2*e**3*h + 6*b**2*d** 2*e**2*f*g)/(9*f**5) + (e + f*x)**(7/2)*(a**2*c**2*f**4*h - 4*a**2*c*d*e*f **3*h + 2*a**2*c*d*f**4*g + 3*a**2*d**2*e**2*f**2*h - 2*a**2*d**2*e*f**3*g - 4*a*b*c**2*e*f**3*h + 2*a*b*c**2*f**4*g + 12*a*b*c*d*e**2*f**2*h - 8*a* b*c*d*e*f**3*g - 8*a*b*d**2*e**3*f*h + 6*a*b*d**2*e**2*f**2*g + 3*b**2*c** 2*e**2*f**2*h - 2*b**2*c**2*e*f**3*g - 8*b**2*c*d*e**3*f*h + 6*b**2*c*d*e* *2*f**2*g + 5*b**2*d**2*e**4*h - 4*b**2*d**2*e**3*f*g)/(7*f**5) + (e + f*x )**(5/2)*(-a**2*c**2*e*f**4*h + a**2*c**2*f**5*g + 2*a**2*c*d*e**2*f**3*h - 2*a**2*c*d*e*f**4*g - a**2*d**2*e**3*f**2*h + a**2*d**2*e**2*f**3*g + 2* a*b*c**2*e**2*f**3*h - 2*a*b*c**2*e*f**4*g - 4*a*b*c*d*e**3*f**2*h + 4*a*b *c*d*e**2*f**3*g + 2*a*b*d**2*e**4*f*h - 2*a*b*d**2*e**3*f**2*g - b**2*c** 2*e**3*f**2*h + b**2*c**2*e**2*f**3*g + 2*b**2*c*d*e**4*f*h - 2*b**2*c*...
Time = 0.04 (sec) , antiderivative size = 695, normalized size of antiderivative = 1.69 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx =\text {Too large to display} \] Input:
integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^(3/2)*(h*x+g),x, algorithm="maxima")
Output:
2/45045*(3003*(f*x + e)^(15/2)*b^2*d^2*h + 3465*(b^2*d^2*f*g - (5*b^2*d^2* e - 2*(b^2*c*d + a*b*d^2)*f)*h)*(f*x + e)^(13/2) - 4095*(2*(2*b^2*d^2*e*f - (b^2*c*d + a*b*d^2)*f^2)*g - (10*b^2*d^2*e^2 - 8*(b^2*c*d + a*b*d^2)*e*f + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2)*h)*(f*x + e)^(11/2) + 5005*((6*b^2 *d^2*e^2*f - 6*(b^2*c*d + a*b*d^2)*e*f^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2) *f^3)*g - (10*b^2*d^2*e^3 - 12*(b^2*c*d + a*b*d^2)*e^2*f + 3*(b^2*c^2 + 4* a*b*c*d + a^2*d^2)*e*f^2 - 2*(a*b*c^2 + a^2*c*d)*f^3)*h)*(f*x + e)^(9/2) - 6435*(2*(2*b^2*d^2*e^3*f - 3*(b^2*c*d + a*b*d^2)*e^2*f^2 + (b^2*c^2 + 4*a *b*c*d + a^2*d^2)*e*f^3 - (a*b*c^2 + a^2*c*d)*f^4)*g - (5*b^2*d^2*e^4 + a^ 2*c^2*f^4 - 8*(b^2*c*d + a*b*d^2)*e^3*f + 3*(b^2*c^2 + 4*a*b*c*d + a^2*d^2 )*e^2*f^2 - 4*(a*b*c^2 + a^2*c*d)*e*f^3)*h)*(f*x + e)^(7/2) + 9009*((b^2*d ^2*e^4*f + a^2*c^2*f^5 - 2*(b^2*c*d + a*b*d^2)*e^3*f^2 + (b^2*c^2 + 4*a*b* c*d + a^2*d^2)*e^2*f^3 - 2*(a*b*c^2 + a^2*c*d)*e*f^4)*g - (b^2*d^2*e^5 + a ^2*c^2*e*f^4 - 2*(b^2*c*d + a*b*d^2)*e^4*f + (b^2*c^2 + 4*a*b*c*d + a^2*d^ 2)*e^3*f^2 - 2*(a*b*c^2 + a^2*c*d)*e^2*f^3)*h)*(f*x + e)^(5/2))/f^6
Leaf count of result is larger than twice the leaf count of optimal. 3372 vs. \(2 (387) = 774\).
Time = 0.16 (sec) , antiderivative size = 3372, normalized size of antiderivative = 8.20 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx=\text {Too large to display} \] Input:
integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^(3/2)*(h*x+g),x, algorithm="giac")
Output:
2/45045*(45045*sqrt(f*x + e)*a^2*c^2*e^2*g + 30030*((f*x + e)^(3/2) - 3*sq rt(f*x + e)*e)*a^2*c^2*e*g + 30030*((f*x + e)^(3/2) - 3*sqrt(f*x + e)*e)*a *b*c^2*e^2*g/f + 30030*((f*x + e)^(3/2) - 3*sqrt(f*x + e)*e)*a^2*c*d*e^2*g /f + 15015*((f*x + e)^(3/2) - 3*sqrt(f*x + e)*e)*a^2*c^2*e^2*h/f + 3003*(3 *(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a^2*c^2*g + 3003*(3*(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*b ^2*c^2*e^2*g/f^2 + 12012*(3*(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sq rt(f*x + e)*e^2)*a*b*c*d*e^2*g/f^2 + 3003*(3*(f*x + e)^(5/2) - 10*(f*x + e )^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a^2*d^2*e^2*g/f^2 + 12012*(3*(f*x + e)^( 5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a*b*c^2*e*g/f + 12012* (3*(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a^2*c*d* e*g/f + 6006*(3*(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)* e^2)*a*b*c^2*e^2*h/f^2 + 6006*(3*(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a^2*c*d*e^2*h/f^2 + 6006*(3*(f*x + e)^(5/2) - 10*(f* x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a^2*c^2*e*h/f + 2574*(5*(f*x + e)^( 7/2) - 21*(f*x + e)^(5/2)*e + 35*(f*x + e)^(3/2)*e^2 - 35*sqrt(f*x + e)*e^ 3)*b^2*c*d*e^2*g/f^3 + 2574*(5*(f*x + e)^(7/2) - 21*(f*x + e)^(5/2)*e + 35 *(f*x + e)^(3/2)*e^2 - 35*sqrt(f*x + e)*e^3)*a*b*d^2*e^2*g/f^3 + 2574*(5*( f*x + e)^(7/2) - 21*(f*x + e)^(5/2)*e + 35*(f*x + e)^(3/2)*e^2 - 35*sqrt(f *x + e)*e^3)*b^2*c^2*e*g/f^2 + 10296*(5*(f*x + e)^(7/2) - 21*(f*x + e)^...
Time = 0.12 (sec) , antiderivative size = 470, normalized size of antiderivative = 1.14 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx=\frac {{\left (e+f\,x\right )}^{9/2}\,\left (4\,h\,a^2\,c\,d\,f^3-6\,h\,a^2\,d^2\,e\,f^2+2\,g\,a^2\,d^2\,f^3+4\,h\,a\,b\,c^2\,f^3-24\,h\,a\,b\,c\,d\,e\,f^2+8\,g\,a\,b\,c\,d\,f^3+24\,h\,a\,b\,d^2\,e^2\,f-12\,g\,a\,b\,d^2\,e\,f^2-6\,h\,b^2\,c^2\,e\,f^2+2\,g\,b^2\,c^2\,f^3+24\,h\,b^2\,c\,d\,e^2\,f-12\,g\,b^2\,c\,d\,e\,f^2-20\,h\,b^2\,d^2\,e^3+12\,g\,b^2\,d^2\,e^2\,f\right )}{9\,f^6}+\frac {{\left (e+f\,x\right )}^{11/2}\,\left (2\,h\,a^2\,d^2\,f^2+8\,h\,a\,b\,c\,d\,f^2-16\,h\,a\,b\,d^2\,e\,f+4\,g\,a\,b\,d^2\,f^2+2\,h\,b^2\,c^2\,f^2-16\,h\,b^2\,c\,d\,e\,f+4\,g\,b^2\,c\,d\,f^2+20\,h\,b^2\,d^2\,e^2-8\,g\,b^2\,d^2\,e\,f\right )}{11\,f^6}-\frac {2\,{\left (e+f\,x\right )}^{5/2}\,{\left (a\,f-b\,e\right )}^2\,{\left (c\,f-d\,e\right )}^2\,\left (e\,h-f\,g\right )}{5\,f^6}+\frac {2\,b^2\,d^2\,h\,{\left (e+f\,x\right )}^{15/2}}{15\,f^6}+\frac {2\,b\,d\,{\left (e+f\,x\right )}^{13/2}\,\left (2\,a\,d\,f\,h+2\,b\,c\,f\,h-5\,b\,d\,e\,h+b\,d\,f\,g\right )}{13\,f^6}+\frac {2\,{\left (e+f\,x\right )}^{7/2}\,\left (a\,f-b\,e\right )\,\left (c\,f-d\,e\right )\,\left (a\,c\,f^2\,h+2\,a\,d\,f^2\,g+2\,b\,c\,f^2\,g+5\,b\,d\,e^2\,h-3\,a\,d\,e\,f\,h-3\,b\,c\,e\,f\,h-4\,b\,d\,e\,f\,g\right )}{7\,f^6} \] Input:
int((e + f*x)^(3/2)*(g + h*x)*(a + b*x)^2*(c + d*x)^2,x)
Output:
((e + f*x)^(9/2)*(2*a^2*d^2*f^3*g + 2*b^2*c^2*f^3*g - 20*b^2*d^2*e^3*h + 4 *a*b*c^2*f^3*h + 4*a^2*c*d*f^3*h - 6*a^2*d^2*e*f^2*h - 6*b^2*c^2*e*f^2*h + 12*b^2*d^2*e^2*f*g + 8*a*b*c*d*f^3*g - 12*a*b*d^2*e*f^2*g + 24*a*b*d^2*e^ 2*f*h - 12*b^2*c*d*e*f^2*g + 24*b^2*c*d*e^2*f*h - 24*a*b*c*d*e*f^2*h))/(9* f^6) + ((e + f*x)^(11/2)*(2*a^2*d^2*f^2*h + 2*b^2*c^2*f^2*h + 20*b^2*d^2*e ^2*h + 4*a*b*d^2*f^2*g + 4*b^2*c*d*f^2*g - 8*b^2*d^2*e*f*g + 8*a*b*c*d*f^2 *h - 16*a*b*d^2*e*f*h - 16*b^2*c*d*e*f*h))/(11*f^6) - (2*(e + f*x)^(5/2)*( a*f - b*e)^2*(c*f - d*e)^2*(e*h - f*g))/(5*f^6) + (2*b^2*d^2*h*(e + f*x)^( 15/2))/(15*f^6) + (2*b*d*(e + f*x)^(13/2)*(2*a*d*f*h + 2*b*c*f*h - 5*b*d*e *h + b*d*f*g))/(13*f^6) + (2*(e + f*x)^(7/2)*(a*f - b*e)*(c*f - d*e)*(a*c* f^2*h + 2*a*d*f^2*g + 2*b*c*f^2*g + 5*b*d*e^2*h - 3*a*d*e*f*h - 3*b*c*e*f* h - 4*b*d*e*f*g))/(7*f^6)
Time = 0.18 (sec) , antiderivative size = 1537, normalized size of antiderivative = 3.74 \[ \int (a+b x)^2 (c+d x)^2 (e+f x)^{3/2} (g+h x) \, dx =\text {Too large to display} \] Input:
int((b*x+a)^2*(d*x+c)^2*(f*x+e)^(3/2)*(h*x+g),x)
Output:
(2*sqrt(e + f*x)*( - 2574*a**2*c**2*e**3*f**4*h + 9009*a**2*c**2*e**2*f**5 *g + 1287*a**2*c**2*e**2*f**5*h*x + 18018*a**2*c**2*e*f**6*g*x + 10296*a** 2*c**2*e*f**6*h*x**2 + 9009*a**2*c**2*f**7*g*x**2 + 6435*a**2*c**2*f**7*h* x**3 + 2288*a**2*c*d*e**4*f**3*h - 5148*a**2*c*d*e**3*f**4*g - 1144*a**2*c *d*e**3*f**4*h*x + 2574*a**2*c*d*e**2*f**5*g*x + 858*a**2*c*d*e**2*f**5*h* x**2 + 20592*a**2*c*d*e*f**6*g*x**2 + 14300*a**2*c*d*e*f**6*h*x**3 + 12870 *a**2*c*d*f**7*g*x**3 + 10010*a**2*c*d*f**7*h*x**4 - 624*a**2*d**2*e**5*f* *2*h + 1144*a**2*d**2*e**4*f**3*g + 312*a**2*d**2*e**4*f**3*h*x - 572*a**2 *d**2*e**3*f**4*g*x - 234*a**2*d**2*e**3*f**4*h*x**2 + 429*a**2*d**2*e**2* f**5*g*x**2 + 195*a**2*d**2*e**2*f**5*h*x**3 + 7150*a**2*d**2*e*f**6*g*x** 3 + 5460*a**2*d**2*e*f**6*h*x**4 + 5005*a**2*d**2*f**7*g*x**4 + 4095*a**2* d**2*f**7*h*x**5 + 2288*a*b*c**2*e**4*f**3*h - 5148*a*b*c**2*e**3*f**4*g - 1144*a*b*c**2*e**3*f**4*h*x + 2574*a*b*c**2*e**2*f**5*g*x + 858*a*b*c**2* e**2*f**5*h*x**2 + 20592*a*b*c**2*e*f**6*g*x**2 + 14300*a*b*c**2*e*f**6*h* x**3 + 12870*a*b*c**2*f**7*g*x**3 + 10010*a*b*c**2*f**7*h*x**4 - 2496*a*b* c*d*e**5*f**2*h + 4576*a*b*c*d*e**4*f**3*g + 1248*a*b*c*d*e**4*f**3*h*x - 2288*a*b*c*d*e**3*f**4*g*x - 936*a*b*c*d*e**3*f**4*h*x**2 + 1716*a*b*c*d*e **2*f**5*g*x**2 + 780*a*b*c*d*e**2*f**5*h*x**3 + 28600*a*b*c*d*e*f**6*g*x* *3 + 21840*a*b*c*d*e*f**6*h*x**4 + 20020*a*b*c*d*f**7*g*x**4 + 16380*a*b*c *d*f**7*h*x**5 + 768*a*b*d**2*e**6*f*h - 1248*a*b*d**2*e**5*f**2*g - 38...