Integrand size = 29, antiderivative size = 411 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx=\frac {2 (b e-a f)^2 (d e-c f)^2 (f g-e h) (e+f x)^{3/2}}{3 f^6}-\frac {2 (b e-a f) (d e-c f) (b d e (4 f g-5 e h)-b c f (2 f g-3 e h)-a f (2 d f g-3 d e h+c f h)) (e+f x)^{5/2}}{5 f^6}+\frac {2 \left (a^2 d f^2 (d f g-3 d e h+2 c f h)+2 a b f \left (c^2 f^2 h+2 c d f (f g-3 e h)-3 d^2 e (f g-2 e h)\right )+b^2 \left (2 d^2 e^2 (3 f g-5 e h)+c^2 f^2 (f g-3 e h)-6 c d e f (f g-2 e h)\right )\right ) (e+f x)^{7/2}}{7 f^6}+\frac {2 \left (a^2 d^2 f^2 h+2 a b d f (d f g-4 d e h+2 c f h)+b^2 \left (c^2 f^2 h-2 d^2 e (2 f g-5 e h)+2 c d f (f g-4 e h)\right )\right ) (e+f x)^{9/2}}{9 f^6}+\frac {2 b d (2 a d f h+b (d f g-5 d e h+2 c f h)) (e+f x)^{11/2}}{11 f^6}+\frac {2 b^2 d^2 h (e+f x)^{13/2}}{13 f^6} \] Output:
2/3*(-a*f+b*e)^2*(-c*f+d*e)^2*(-e*h+f*g)*(f*x+e)^(3/2)/f^6-2/5*(-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)^(5/2)/f^6+2/7*(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)^(7/2)/f^6+ 2/9*(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)^(9/2)/f^6+2/11*b*d*(2*a*d* f*h+b*(2*c*f*h-5*d*e*h+d*f*g))*(f*x+e)^(11/2)/f^6+2/13*b^2*d^2*h*(f*x+e)^( 13/2)/f^6
Time = 0.47 (sec) , antiderivative size = 547, normalized size of antiderivative = 1.33 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx=\frac {2 (e+f x)^{3/2} \left (143 a^2 f^2 \left (21 c^2 f^2 (5 f g-2 e h+3 f h x)+6 c d f \left (8 e^2 h+3 f^2 x (7 g+5 h x)-2 e f (7 g+6 h x)\right )+d^2 \left (-16 e^3 h+24 e^2 f (g+h x)-6 e f^2 x (6 g+5 h x)+5 f^3 x^2 (9 g+7 h x)\right )\right )+26 a b f \left (33 c^2 f^2 \left (8 e^2 h+3 f^2 x (7 g+5 h x)-2 e f (7 g+6 h x)\right )+22 c d f \left (-16 e^3 h+24 e^2 f (g+h x)-6 e f^2 x (6 g+5 h x)+5 f^3 x^2 (9 g+7 h x)\right )+d^2 \left (128 e^4 h+35 f^4 x^3 (11 g+9 h x)+24 e^2 f^2 x (11 g+10 h x)-16 e^3 f (11 g+12 h x)-10 e f^3 x^2 (33 g+28 h x)\right )\right )+b^2 \left (143 c^2 f^2 \left (-16 e^3 h+24 e^2 f (g+h x)-6 e f^2 x (6 g+5 h x)+5 f^3 x^2 (9 g+7 h x)\right )+26 c d f \left (128 e^4 h+35 f^4 x^3 (11 g+9 h x)+24 e^2 f^2 x (11 g+10 h x)-16 e^3 f (11 g+12 h x)-10 e f^3 x^2 (33 g+28 h x)\right )+d^2 \left (-1280 e^5 h+315 f^5 x^4 (13 g+11 h x)+128 e^4 f (13 g+15 h x)-96 e^3 f^2 x (26 g+25 h x)+80 e^2 f^3 x^2 (39 g+35 h x)-70 e f^4 x^3 (52 g+45 h x)\right )\right )\right )}{45045 f^6} \] Input:
Integrate[(a + b*x)^2*(c + d*x)^2*Sqrt[e + f*x]*(g + h*x),x]
Output:
(2*(e + f*x)^(3/2)*(143*a^2*f^2*(21*c^2*f^2*(5*f*g - 2*e*h + 3*f*h*x) + 6* c*d*f*(8*e^2*h + 3*f^2*x*(7*g + 5*h*x) - 2*e*f*(7*g + 6*h*x)) + d^2*(-16*e ^3*h + 24*e^2*f*(g + h*x) - 6*e*f^2*x*(6*g + 5*h*x) + 5*f^3*x^2*(9*g + 7*h *x))) + 26*a*b*f*(33*c^2*f^2*(8*e^2*h + 3*f^2*x*(7*g + 5*h*x) - 2*e*f*(7*g + 6*h*x)) + 22*c*d*f*(-16*e^3*h + 24*e^2*f*(g + h*x) - 6*e*f^2*x*(6*g + 5 *h*x) + 5*f^3*x^2*(9*g + 7*h*x)) + d^2*(128*e^4*h + 35*f^4*x^3*(11*g + 9*h *x) + 24*e^2*f^2*x*(11*g + 10*h*x) - 16*e^3*f*(11*g + 12*h*x) - 10*e*f^3*x ^2*(33*g + 28*h*x))) + b^2*(143*c^2*f^2*(-16*e^3*h + 24*e^2*f*(g + h*x) - 6*e*f^2*x*(6*g + 5*h*x) + 5*f^3*x^2*(9*g + 7*h*x)) + 26*c*d*f*(128*e^4*h + 35*f^4*x^3*(11*g + 9*h*x) + 24*e^2*f^2*x*(11*g + 10*h*x) - 16*e^3*f*(11*g + 12*h*x) - 10*e*f^3*x^2*(33*g + 28*h*x)) + d^2*(-1280*e^5*h + 315*f^5*x^ 4*(13*g + 11*h*x) + 128*e^4*f*(13*g + 15*h*x) - 96*e^3*f^2*x*(26*g + 25*h* x) + 80*e^2*f^3*x^2*(39*g + 35*h*x) - 70*e*f^4*x^3*(52*g + 45*h*x)))))/(45 045*f^6)
Time = 0.70 (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.
| \(\displaystyle \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx\) |
| \(\Big \downarrow \) 165 |
| \(\displaystyle \int \left (\frac {(e+f x)^{5/2} \left (a^2 d f^2 (2 c f h-3 d e h+d f g)+2 a b f \left (c^2 f^2 h+2 c d f (f g-3 e h)-3 d^2 e (f g-2 e h)\right )+b^2 \left (c^2 f^2 (f g-3 e h)-6 c d e f (f g-2 e h)+2 d^2 e^2 (3 f g-5 e h)\right )\right )}{f^5}+\frac {(e+f x)^{7/2} \left (a^2 d^2 f^2 h+2 a b d f (2 c f h-4 d e h+d f g)+b^2 \left (c^2 f^2 h+2 c d f (f g-4 e h)-2 d^2 e (2 f g-5 e h)\right )\right )}{f^5}+\frac {b d (e+f x)^{9/2} (2 a d f h+b (2 c f h-5 d e h+d f g))}{f^5}+\frac {(e+f x)^{3/2} (b e-a f) (d e-c f) (a f (c f h-3 d e h+2 d f g)+b c f (2 f g-3 e h)-b d e (4 f g-5 e h))}{f^5}+\frac {\sqrt {e+f x} (a f-b e)^2 (c f-d e)^2 (f g-e h)}{f^5}+\frac {b^2 d^2 h (e+f x)^{11/2}}{f^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {2 (e+f x)^{7/2} \left (a^2 d f^2 (2 c f h-3 d e h+d f g)+2 a b f \left (c^2 f^2 h+2 c d f (f g-3 e h)-3 d^2 e (f g-2 e h)\right )+b^2 \left (c^2 f^2 (f g-3 e h)-6 c d e f (f g-2 e h)+2 d^2 e^2 (3 f g-5 e h)\right )\right )}{7 f^6}+\frac {2 (e+f x)^{9/2} \left (a^2 d^2 f^2 h+2 a b d f (2 c f h-4 d e h+d f g)+b^2 \left (c^2 f^2 h+2 c d f (f g-4 e h)-2 d^2 e (2 f g-5 e h)\right )\right )}{9 f^6}+\frac {2 b d (e+f x)^{11/2} (2 a d f h+b (2 c f h-5 d e h+d f g))}{11 f^6}-\frac {2 (e+f x)^{5/2} (b e-a f) (d e-c f) (-a f (c f h-3 d e h+2 d f g)-b c f (2 f g-3 e h)+b d e (4 f g-5 e h))}{5 f^6}+\frac {2 (e+f x)^{3/2} (b e-a f)^2 (d e-c f)^2 (f g-e h)}{3 f^6}+\frac {2 b^2 d^2 h (e+f x)^{13/2}}{13 f^6}\) |
Input:
Int[(a + b*x)^2*(c + d*x)^2*Sqrt[e + f*x]*(g + h*x),x]
Output:
(2*(b*e - a*f)^2*(d*e - c*f)^2*(f*g - e*h)*(e + f*x)^(3/2))/(3*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)^(5/2))/(5*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)^(7/2))/(7*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)^(9/2))/(9*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)^(11/2))/(11*f^6) + (2 *b^2*d^2*h*(e + f*x)^(13/2))/(13*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 = 1.01 (sec) , antiderivative size = 412, normalized size of antiderivative = 1.00
| method | result | size |
| derivativedivides | \(\frac {\frac {2 h \,b^{2} d^{2} \left (f x +e \right )^{\frac {13}{2}}}{13}+\frac {2 \left (\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) h +b^{2} d^{2} \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {11}{2}}}{11}+\frac {2 \left (\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) h +\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {9}{2}}}{9}+\frac {2 \left (\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) h +\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {7}{2}}}{7}+\frac {2 \left (\left (a f -b e \right )^{2} \left (c f -d e \right )^{2} h +\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) \left (-e h +f g \right )\right ) \left (f x +e \right )^{\frac {5}{2}}}{5}+\frac {2 \left (a f -b e \right )^{2} \left (c f -d e \right )^{2} \left (-e h +f g \right ) \left (f x +e \right )^{\frac {3}{2}}}{3}}{f^{6}}\) | \(412\) |
| default | \(\frac {\frac {2 h \,b^{2} d^{2} \left (f x +e \right )^{\frac {13}{2}}}{13}-\frac {2 \left (-\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) h +b^{2} d^{2} \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {11}{2}}}{11}-\frac {2 \left (-\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) h +\left (2 b \left (a f -b e \right ) d^{2}+2 b^{2} d \left (c f -d e \right )\right ) \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {9}{2}}}{9}-\frac {2 \left (-\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) h +\left (\left (a f -b e \right )^{2} d^{2}+4 b \left (a f -b e \right ) d \left (c f -d e \right )+b^{2} \left (c f -d e \right )^{2}\right ) \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {7}{2}}}{7}-\frac {2 \left (-\left (a f -b e \right )^{2} \left (c f -d e \right )^{2} h +\left (2 \left (a f -b e \right )^{2} d \left (c f -d e \right )+2 b \left (a f -b e \right ) \left (c f -d e \right )^{2}\right ) \left (e h -f g \right )\right ) \left (f x +e \right )^{\frac {5}{2}}}{5}-\frac {2 \left (a f -b e \right )^{2} \left (c f -d e \right )^{2} \left (e h -f g \right ) \left (f x +e \right )^{\frac {3}{2}}}{3}}{f^{6}}\) | \(416\) |
| pseudoelliptic | \(-\frac {4 \left (f x +e \right )^{\frac {3}{2}} \left (\left (-\frac {15 x^{2} \left (7 \left (\frac {1}{13} h \,x^{3}+\frac {1}{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^{2}}{14}-3 a x \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 ) b -\frac {5 a^{2} \left (\frac {3 x^{2} \left (\frac {7 h x}{9}+g \right ) d^{2}}{7}+\frac {6 x c \left (\frac {5 h x}{7}+g \right ) d}{5}+c^{2} \left (\frac {3 h x}{5}+g \right )\right )}{2}\right ) f^{5}+\left (\frac {6 x \left (\frac {70 x^{2} \left (\frac {45 h x}{52}+g \right ) d^{2}}{99}+\frac {5 x c \left (\frac {28 h x}{33}+g \right ) d}{3}+c^{2} \left (\frac {5 h x}{6}+g \right )\right ) b^{2}}{7}+2 a \left (\frac {5 x^{2} \left (\frac {28 h x}{33}+g \right ) d^{2}}{7}+\frac {12 x c \left (\frac {5 h x}{6}+g \right ) d}{7}+c^{2} \left (\frac {6 h x}{7}+g \right )\right ) b +a^{2} \left (\frac {6 x \left (\frac {5 h x}{6}+g \right ) d^{2}}{7}+2 c \left (\frac {6 h x}{7}+g \right ) d +h \,c^{2}\right )\right ) e \,f^{4}-\frac {8 \left (\left (\frac {5 x^{2} \left (\frac {35 h x}{39}+g \right ) d^{2}}{11}+x c \left (\frac {10 h x}{11}+g \right ) d +\frac {c^{2} \left (h x +g \right )}{2}\right ) b^{2}+a \left (x \left (\frac {10 h x}{11}+g \right ) d^{2}+2 c \left (h x +g \right ) d +h \,c^{2}\right ) b +a^{2} \left (\frac {\left (h x +g \right ) d}{2}+c h \right ) d \right ) e^{2} f^{3}}{7}+\frac {8 e^{3} \left (\left (\frac {12 \left (\frac {25 h x}{26}+g \right ) x \,d^{2}}{11}+2 c \left (\frac {12 h x}{11}+g \right ) d +h \,c^{2}\right ) b^{2}+4 a d \left (\left (\frac {6 h x}{11}+\frac {g}{2}\right ) d +c h \right ) b +a^{2} d^{2} h \right ) f^{2}}{21}-\frac {128 d \left (\left (\frac {\left (\frac {15 h x}{13}+g \right ) d}{2}+c h \right ) b +a d h \right ) b \,e^{4} f}{231}+\frac {640 b^{2} d^{2} e^{5} h}{3003}\right )}{15 f^{6}}\) | \(471\) |
| gosper | \(-\frac {2 \left (f x +e \right )^{\frac {3}{2}} \left (-3465 h \,b^{2} d^{2} x^{5} f^{5}-8190 a b \,d^{2} f^{5} h \,x^{4}-8190 b^{2} c d \,f^{5} h \,x^{4}+3150 b^{2} d^{2} e \,f^{4} h \,x^{4}-4095 b^{2} d^{2} f^{5} g \,x^{4}-5005 a^{2} d^{2} f^{5} h \,x^{3}-20020 a b c d \,f^{5} h \,x^{3}+7280 a b \,d^{2} e \,f^{4} h \,x^{3}-10010 a b \,d^{2} f^{5} g \,x^{3}-5005 b^{2} c^{2} f^{5} h \,x^{3}+7280 b^{2} c d e \,f^{4} h \,x^{3}-10010 b^{2} c d \,f^{5} g \,x^{3}-2800 b^{2} d^{2} e^{2} f^{3} h \,x^{3}+3640 b^{2} d^{2} e \,f^{4} g \,x^{3}-12870 a^{2} c d \,f^{5} h \,x^{2}+4290 a^{2} d^{2} e \,f^{4} h \,x^{2}-6435 a^{2} d^{2} f^{5} g \,x^{2}-12870 a b \,c^{2} f^{5} h \,x^{2}+17160 a b c d e \,f^{4} h \,x^{2}-25740 a b c d \,f^{5} g \,x^{2}-6240 a b \,d^{2} e^{2} f^{3} h \,x^{2}+8580 a b \,d^{2} e \,f^{4} g \,x^{2}+4290 b^{2} c^{2} e \,f^{4} h \,x^{2}-6435 b^{2} c^{2} f^{5} g \,x^{2}-6240 b^{2} c d \,e^{2} f^{3} h \,x^{2}+8580 b^{2} c d e \,f^{4} g \,x^{2}+2400 b^{2} d^{2} e^{3} f^{2} h \,x^{2}-3120 b^{2} d^{2} e^{2} f^{3} g \,x^{2}-9009 a^{2} c^{2} f^{5} h x +10296 a^{2} c d e \,f^{4} h x -18018 a^{2} c d \,f^{5} g x -3432 a^{2} d^{2} e^{2} f^{3} h x +5148 a^{2} d^{2} e \,f^{4} g x +10296 a b \,c^{2} e \,f^{4} h x -18018 a b \,c^{2} f^{5} g x -13728 a b c d \,e^{2} f^{3} h x +20592 a b c d e \,f^{4} g x +4992 a b \,d^{2} e^{3} f^{2} h x -6864 a b \,d^{2} e^{2} f^{3} g x -3432 b^{2} c^{2} e^{2} f^{3} h x +5148 b^{2} c^{2} e \,f^{4} g x +4992 b^{2} c d \,e^{3} f^{2} h x -6864 b^{2} c d \,e^{2} f^{3} g x -1920 b^{2} d^{2} e^{4} f h x +2496 b^{2} d^{2} e^{3} f^{2} g x +6006 a^{2} c^{2} e \,f^{4} h -15015 g \,a^{2} c^{2} f^{5}-6864 a^{2} c d \,e^{2} f^{3} h +12012 a^{2} c d e \,f^{4} g +2288 a^{2} d^{2} e^{3} f^{2} h -3432 a^{2} d^{2} e^{2} f^{3} g -6864 a b \,c^{2} e^{2} f^{3} h +12012 a b \,c^{2} e \,f^{4} g +9152 a b c d \,e^{3} f^{2} h -13728 a b c d \,e^{2} f^{3} g -3328 a b \,d^{2} e^{4} f h +4576 a b \,d^{2} e^{3} f^{2} g +2288 b^{2} c^{2} e^{3} f^{2} h -3432 b^{2} c^{2} e^{2} f^{3} g -3328 b^{2} c d \,e^{4} f h +4576 b^{2} c d \,e^{3} f^{2} g +1280 b^{2} d^{2} e^{5} h -1664 b^{2} d^{2} e^{4} f g \right )}{45045 f^{6}}\) | \(919\) |
| orering | \(-\frac {2 \left (f x +e \right )^{\frac {3}{2}} \left (-3465 h \,b^{2} d^{2} x^{5} f^{5}-8190 a b \,d^{2} f^{5} h \,x^{4}-8190 b^{2} c d \,f^{5} h \,x^{4}+3150 b^{2} d^{2} e \,f^{4} h \,x^{4}-4095 b^{2} d^{2} f^{5} g \,x^{4}-5005 a^{2} d^{2} f^{5} h \,x^{3}-20020 a b c d \,f^{5} h \,x^{3}+7280 a b \,d^{2} e \,f^{4} h \,x^{3}-10010 a b \,d^{2} f^{5} g \,x^{3}-5005 b^{2} c^{2} f^{5} h \,x^{3}+7280 b^{2} c d e \,f^{4} h \,x^{3}-10010 b^{2} c d \,f^{5} g \,x^{3}-2800 b^{2} d^{2} e^{2} f^{3} h \,x^{3}+3640 b^{2} d^{2} e \,f^{4} g \,x^{3}-12870 a^{2} c d \,f^{5} h \,x^{2}+4290 a^{2} d^{2} e \,f^{4} h \,x^{2}-6435 a^{2} d^{2} f^{5} g \,x^{2}-12870 a b \,c^{2} f^{5} h \,x^{2}+17160 a b c d e \,f^{4} h \,x^{2}-25740 a b c d \,f^{5} g \,x^{2}-6240 a b \,d^{2} e^{2} f^{3} h \,x^{2}+8580 a b \,d^{2} e \,f^{4} g \,x^{2}+4290 b^{2} c^{2} e \,f^{4} h \,x^{2}-6435 b^{2} c^{2} f^{5} g \,x^{2}-6240 b^{2} c d \,e^{2} f^{3} h \,x^{2}+8580 b^{2} c d e \,f^{4} g \,x^{2}+2400 b^{2} d^{2} e^{3} f^{2} h \,x^{2}-3120 b^{2} d^{2} e^{2} f^{3} g \,x^{2}-9009 a^{2} c^{2} f^{5} h x +10296 a^{2} c d e \,f^{4} h x -18018 a^{2} c d \,f^{5} g x -3432 a^{2} d^{2} e^{2} f^{3} h x +5148 a^{2} d^{2} e \,f^{4} g x +10296 a b \,c^{2} e \,f^{4} h x -18018 a b \,c^{2} f^{5} g x -13728 a b c d \,e^{2} f^{3} h x +20592 a b c d e \,f^{4} g x +4992 a b \,d^{2} e^{3} f^{2} h x -6864 a b \,d^{2} e^{2} f^{3} g x -3432 b^{2} c^{2} e^{2} f^{3} h x +5148 b^{2} c^{2} e \,f^{4} g x +4992 b^{2} c d \,e^{3} f^{2} h x -6864 b^{2} c d \,e^{2} f^{3} g x -1920 b^{2} d^{2} e^{4} f h x +2496 b^{2} d^{2} e^{3} f^{2} g x +6006 a^{2} c^{2} e \,f^{4} h -15015 g \,a^{2} c^{2} f^{5}-6864 a^{2} c d \,e^{2} f^{3} h +12012 a^{2} c d e \,f^{4} g +2288 a^{2} d^{2} e^{3} f^{2} h -3432 a^{2} d^{2} e^{2} f^{3} g -6864 a b \,c^{2} e^{2} f^{3} h +12012 a b \,c^{2} e \,f^{4} g +9152 a b c d \,e^{3} f^{2} h -13728 a b c d \,e^{2} f^{3} g -3328 a b \,d^{2} e^{4} f h +4576 a b \,d^{2} e^{3} f^{2} g +2288 b^{2} c^{2} e^{3} f^{2} h -3432 b^{2} c^{2} e^{2} f^{3} g -3328 b^{2} c d \,e^{4} f h +4576 b^{2} c d \,e^{3} f^{2} g +1280 b^{2} d^{2} e^{5} h -1664 b^{2} d^{2} e^{4} f g \right )}{45045 f^{6}}\) | \(919\) |
| trager | \(\text {Expression too large to display}\) | \(1227\) |
| risch | \(\text {Expression too large to display}\) | \(1227\) |
Input:
int((b*x+a)^2*(d*x+c)^2*(f*x+e)^(1/2)*(h*x+g),x,method=_RETURNVERBOSE)
Output:
2/f^6*(1/13*h*b^2*d^2*(f*x+e)^(13/2)+1/11*((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)^(11/2)+1/9*(((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)^(9/2)+1/7*((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)^(7/2)+1/5*((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)^(5/2)+1/3*(a*f-b* e)^2*(c*f-d*e)^2*(-e*h+f*g)*(f*x+e)^(3/2))
Leaf count of result is larger than twice the leaf count of optimal. 919 vs. \(2 (387) = 774\).
Time = 0.08 (sec) , antiderivative size = 919, normalized size of antiderivative = 2.24 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx =\text {Too large to display} \] Input:
integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^(1/2)*(h*x+g),x, algorithm="fricas")
Output:
2/45045*(3465*b^2*d^2*f^6*h*x^6 + 315*(13*b^2*d^2*f^6*g + (b^2*d^2*e*f^5 + 26*(b^2*c*d + a*b*d^2)*f^6)*h)*x^5 + 35*(13*(b^2*d^2*e*f^5 + 22*(b^2*c*d + a*b*d^2)*f^6)*g - (10*b^2*d^2*e^2*f^4 - 26*(b^2*c*d + a*b*d^2)*e*f^5 - 1 43*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^6)*h)*x^4 - 5*(13*(8*b^2*d^2*e^2*f^4 - 22*(b^2*c*d + a*b*d^2)*e*f^5 - 99*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^6)*g - (80*b^2*d^2*e^3*f^3 - 208*(b^2*c*d + a*b*d^2)*e^2*f^4 + 143*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e*f^5 + 2574*(a*b*c^2 + a^2*c*d)*f^6)*h)*x^3 + 3*(13* (16*b^2*d^2*e^3*f^3 - 44*(b^2*c*d + a*b*d^2)*e^2*f^4 + 33*(b^2*c^2 + 4*a*b *c*d + a^2*d^2)*e*f^5 + 462*(a*b*c^2 + a^2*c*d)*f^6)*g - (160*b^2*d^2*e^4* f^2 - 3003*a^2*c^2*f^6 - 416*(b^2*c*d + a*b*d^2)*e^3*f^3 + 286*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^2*f^4 - 858*(a*b*c^2 + a^2*c*d)*e*f^5)*h)*x^2 + 13* (128*b^2*d^2*e^5*f + 1155*a^2*c^2*e*f^5 - 352*(b^2*c*d + a*b*d^2)*e^4*f^2 + 264*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^3*f^3 - 924*(a*b*c^2 + a^2*c*d)*e^ 2*f^4)*g - 2*(640*b^2*d^2*e^6 + 3003*a^2*c^2*e^2*f^4 - 1664*(b^2*c*d + a*b *d^2)*e^5*f + 1144*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^4*f^2 - 3432*(a*b*c^2 + a^2*c*d)*e^3*f^3)*h - (13*(64*b^2*d^2*e^4*f^2 - 1155*a^2*c^2*f^6 - 176* (b^2*c*d + a*b*d^2)*e^3*f^3 + 132*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^2*f^4 - 462*(a*b*c^2 + a^2*c*d)*e*f^5)*g - (640*b^2*d^2*e^5*f + 3003*a^2*c^2*e*f ^5 - 1664*(b^2*c*d + a*b*d^2)*e^4*f^2 + 1144*(b^2*c^2 + 4*a*b*c*d + a^2*d^ 2)*e^3*f^3 - 3432*(a*b*c^2 + a^2*c*d)*e^2*f^4)*h)*x)*sqrt(f*x + e)/f^6
Leaf count of result is larger than twice the leaf count of optimal. 1204 vs. \(2 (445) = 890\).
Time = 2.02 (sec) , antiderivative size = 1204, normalized size of antiderivative = 2.93 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx =\text {Too large to display} \] Input:
integrate((b*x+a)**2*(d*x+c)**2*(f*x+e)**(1/2)*(h*x+g),x)
Output:
Piecewise((2*(b**2*d**2*h*(e + f*x)**(13/2)/(13*f**5) + (e + f*x)**(11/2)* (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)/(11*f* *5) + (e + f*x)**(9/2)*(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)/(9*f**5) + (e + f*x)** (7/2)*(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)/(7*f**5) + (e + f*x)**(5/2)*(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)/(5*f**5) + (e + f*x)* *(3/2)*(-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*d*...
Time = 0.04 (sec) , antiderivative size = 695, normalized size of antiderivative = 1.69 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx =\text {Too large to display} \] Input:
integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^(1/2)*(h*x+g),x, algorithm="maxima")
Output:
2/45045*(3465*(f*x + e)^(13/2)*b^2*d^2*h + 4095*(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)^(11/2) - 5005*(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)^(9/2) + 6435*((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)^(7/2) - 9009*(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)^(5/2) + 15015*((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)^(3/2))/f^6
Leaf count of result is larger than twice the leaf count of optimal. 2001 vs. \(2 (387) = 774\).
Time = 0.14 (sec) , antiderivative size = 2001, normalized size of antiderivative = 4.87 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx=\text {Too large to display} \] Input:
integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^(1/2)*(h*x+g),x, algorithm="giac")
Output:
2/45045*(45045*sqrt(f*x + e)*a^2*c^2*e*g + 15015*((f*x + e)^(3/2) - 3*sqrt (f*x + e)*e)*a^2*c^2*g + 30030*((f*x + e)^(3/2) - 3*sqrt(f*x + e)*e)*a*b*c ^2*e*g/f + 30030*((f*x + e)^(3/2) - 3*sqrt(f*x + e)*e)*a^2*c*d*e*g/f + 150 15*((f*x + e)^(3/2) - 3*sqrt(f*x + e)*e)*a^2*c^2*e*h/f + 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*g/f^2 + 12 012*(3*(f*x + e)^(5/2) - 10*(f*x + e)^(3/2)*e + 15*sqrt(f*x + e)*e^2)*a*b* c*d*e*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*g/f^2 + 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*g/f + 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*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*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*h /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*c^2*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*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*g/f^3 + 1287*(5*(f*x + e)^(7/2) - 21*(f*x + e)^(5/2)*e + 3 5*(f*x + e)^(3/2)*e^2 - 35*sqrt(f*x + e)*e^3)*b^2*c^2*g/f^2 + 5148*(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*c*d*g/f^2 + 1287*(5*(f*x + e)^(7/2) - 21*(f*x + e)^(5/2)*...
Time = 0.11 (sec) , antiderivative size = 470, normalized size of antiderivative = 1.14 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx=\frac {{\left (e+f\,x\right )}^{7/2}\,\left (4\,h\,a^2\,c\,d\,f^3-6\,h\,a^2\,d^2\,e\,f^2+2\,g\,a^2\,d^2\,f^3+4\,h\,a\,b\,c^2\,f^3-24\,h\,a\,b\,c\,d\,e\,f^2+8\,g\,a\,b\,c\,d\,f^3+24\,h\,a\,b\,d^2\,e^2\,f-12\,g\,a\,b\,d^2\,e\,f^2-6\,h\,b^2\,c^2\,e\,f^2+2\,g\,b^2\,c^2\,f^3+24\,h\,b^2\,c\,d\,e^2\,f-12\,g\,b^2\,c\,d\,e\,f^2-20\,h\,b^2\,d^2\,e^3+12\,g\,b^2\,d^2\,e^2\,f\right )}{7\,f^6}+\frac {{\left (e+f\,x\right )}^{9/2}\,\left (2\,h\,a^2\,d^2\,f^2+8\,h\,a\,b\,c\,d\,f^2-16\,h\,a\,b\,d^2\,e\,f+4\,g\,a\,b\,d^2\,f^2+2\,h\,b^2\,c^2\,f^2-16\,h\,b^2\,c\,d\,e\,f+4\,g\,b^2\,c\,d\,f^2+20\,h\,b^2\,d^2\,e^2-8\,g\,b^2\,d^2\,e\,f\right )}{9\,f^6}-\frac {2\,{\left (e+f\,x\right )}^{3/2}\,{\left (a\,f-b\,e\right )}^2\,{\left (c\,f-d\,e\right )}^2\,\left (e\,h-f\,g\right )}{3\,f^6}+\frac {2\,b^2\,d^2\,h\,{\left (e+f\,x\right )}^{13/2}}{13\,f^6}+\frac {2\,b\,d\,{\left (e+f\,x\right )}^{11/2}\,\left (2\,a\,d\,f\,h+2\,b\,c\,f\,h-5\,b\,d\,e\,h+b\,d\,f\,g\right )}{11\,f^6}+\frac {2\,{\left (e+f\,x\right )}^{5/2}\,\left (a\,f-b\,e\right )\,\left (c\,f-d\,e\right )\,\left (a\,c\,f^2\,h+2\,a\,d\,f^2\,g+2\,b\,c\,f^2\,g+5\,b\,d\,e^2\,h-3\,a\,d\,e\,f\,h-3\,b\,c\,e\,f\,h-4\,b\,d\,e\,f\,g\right )}{5\,f^6} \] Input:
int((e + f*x)^(1/2)*(g + h*x)*(a + b*x)^2*(c + d*x)^2,x)
Output:
((e + f*x)^(7/2)*(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))/(7* f^6) + ((e + f*x)^(9/2)*(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))/(9*f^6) - (2*(e + f*x)^(3/2)*(a* f - b*e)^2*(c*f - d*e)^2*(e*h - f*g))/(3*f^6) + (2*b^2*d^2*h*(e + f*x)^(13 /2))/(13*f^6) + (2*b*d*(e + f*x)^(11/2)*(2*a*d*f*h + 2*b*c*f*h - 5*b*d*e*h + b*d*f*g))/(11*f^6) + (2*(e + f*x)^(5/2)*(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))/(5*f^6)
Time = 0.17 (sec) , antiderivative size = 1225, normalized size of antiderivative = 2.98 \[ \int (a+b x)^2 (c+d x)^2 \sqrt {e+f x} (g+h x) \, dx =\text {Too large to display} \] Input:
int((b*x+a)^2*(d*x+c)^2*(f*x+e)^(1/2)*(h*x+g),x)
Output:
(2*sqrt(e + f*x)*( - 6006*a**2*c**2*e**2*f**4*h + 15015*a**2*c**2*e*f**5*g + 3003*a**2*c**2*e*f**5*h*x + 15015*a**2*c**2*f**6*g*x + 9009*a**2*c**2*f **6*h*x**2 + 6864*a**2*c*d*e**3*f**3*h - 12012*a**2*c*d*e**2*f**4*g - 3432 *a**2*c*d*e**2*f**4*h*x + 6006*a**2*c*d*e*f**5*g*x + 2574*a**2*c*d*e*f**5* h*x**2 + 18018*a**2*c*d*f**6*g*x**2 + 12870*a**2*c*d*f**6*h*x**3 - 2288*a* *2*d**2*e**4*f**2*h + 3432*a**2*d**2*e**3*f**3*g + 1144*a**2*d**2*e**3*f** 3*h*x - 1716*a**2*d**2*e**2*f**4*g*x - 858*a**2*d**2*e**2*f**4*h*x**2 + 12 87*a**2*d**2*e*f**5*g*x**2 + 715*a**2*d**2*e*f**5*h*x**3 + 6435*a**2*d**2* f**6*g*x**3 + 5005*a**2*d**2*f**6*h*x**4 + 6864*a*b*c**2*e**3*f**3*h - 120 12*a*b*c**2*e**2*f**4*g - 3432*a*b*c**2*e**2*f**4*h*x + 6006*a*b*c**2*e*f* *5*g*x + 2574*a*b*c**2*e*f**5*h*x**2 + 18018*a*b*c**2*f**6*g*x**2 + 12870* a*b*c**2*f**6*h*x**3 - 9152*a*b*c*d*e**4*f**2*h + 13728*a*b*c*d*e**3*f**3* g + 4576*a*b*c*d*e**3*f**3*h*x - 6864*a*b*c*d*e**2*f**4*g*x - 3432*a*b*c*d *e**2*f**4*h*x**2 + 5148*a*b*c*d*e*f**5*g*x**2 + 2860*a*b*c*d*e*f**5*h*x** 3 + 25740*a*b*c*d*f**6*g*x**3 + 20020*a*b*c*d*f**6*h*x**4 + 3328*a*b*d**2* e**5*f*h - 4576*a*b*d**2*e**4*f**2*g - 1664*a*b*d**2*e**4*f**2*h*x + 2288* a*b*d**2*e**3*f**3*g*x + 1248*a*b*d**2*e**3*f**3*h*x**2 - 1716*a*b*d**2*e* *2*f**4*g*x**2 - 1040*a*b*d**2*e**2*f**4*h*x**3 + 1430*a*b*d**2*e*f**5*g*x **3 + 910*a*b*d**2*e*f**5*h*x**4 + 10010*a*b*d**2*f**6*g*x**4 + 8190*a*b*d **2*f**6*h*x**5 - 2288*b**2*c**2*e**4*f**2*h + 3432*b**2*c**2*e**3*f**3...