Integrand size = 22, antiderivative size = 361 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=\frac {(b c-a d)^3 (b e-a f)^3 (a+b x)^4}{4 b^7}+\frac {3 (b c-a d)^2 (b e-a f)^2 (b d e+b c f-2 a d f) (a+b x)^5}{5 b^7}+\frac {(b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^6}{2 b^7}+\frac {(b d e+b c f-2 a d f) \left (10 a^2 d^2 f^2-10 a b d f (d e+c f)+b^2 \left (d^2 e^2+8 c d e f+c^2 f^2\right )\right ) (a+b x)^7}{7 b^7}+\frac {3 d f \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^8}{8 b^7}+\frac {d^2 f^2 (b d e+b c f-2 a d f) (a+b x)^9}{3 b^7}+\frac {d^3 f^3 (a+b x)^{10}}{10 b^7} \]
1/4*(-a*d+b*c)^3*(-a*f+b*e)^3*(b*x+a)^4/b^7+3/5*(-a*d+b*c)^2*(-a*f+b*e)^2* (-2*a*d*f+b*c*f+b*d*e)*(b*x+a)^5/b^7+1/2*(-a*d+b*c)*(-a*f+b*e)*(5*a^2*d^2* f^2-5*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*(b*x+a)^6/b^7+1/7 *(-2*a*d*f+b*c*f+b*d*e)*(10*a^2*d^2*f^2-10*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+ 8*c*d*e*f+d^2*e^2))*(b*x+a)^7/b^7+3/8*d*f*(5*a^2*d^2*f^2-5*a*b*d*f*(c*f+d* e)+b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*(b*x+a)^8/b^7+1/3*d^2*f^2*(-2*a*d*f+b* c*f+b*d*e)*(b*x+a)^9/b^7+1/10*d^3*f^3*(b*x+a)^10/b^7
Time = 0.18 (sec) , antiderivative size = 653, normalized size of antiderivative = 1.81 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=a^3 c^3 e^3 x+\frac {3}{2} a^2 c^2 e^2 (b c e+a d e+a c f) x^2+a c e \left (b^2 c^2 e^2+3 a b c e (d e+c f)+a^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^3+\frac {1}{4} \left (b^3 c^3 e^3+9 a b^2 c^2 e^2 (d e+c f)+9 a^2 b c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^4+\frac {3}{5} \left (b^3 c^2 e^2 (d e+c f)+3 a b^2 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^2 b \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^5+\frac {1}{2} \left (a^3 d^2 f^2 (d e+c f)+b^3 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+3 a^2 b d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a b^2 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^6+\frac {1}{7} \left (a^3 d^3 f^3+9 a^2 b d^2 f^2 (d e+c f)+9 a b^2 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+b^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^7+\frac {3}{8} b d f \left (a^2 d^2 f^2+3 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^8+\frac {1}{3} b^2 d^2 f^2 (b d e+b c f+a d f) x^9+\frac {1}{10} b^3 d^3 f^3 x^{10} \]
a^3*c^3*e^3*x + (3*a^2*c^2*e^2*(b*c*e + a*d*e + a*c*f)*x^2)/2 + a*c*e*(b^2 *c^2*e^2 + 3*a*b*c*e*(d*e + c*f) + a^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*x^ 3 + ((b^3*c^3*e^3 + 9*a*b^2*c^2*e^2*(d*e + c*f) + 9*a^2*b*c*e*(d^2*e^2 + 3 *c*d*e*f + c^2*f^2) + a^3*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f ^3))*x^4)/4 + (3*(b^3*c^2*e^2*(d*e + c*f) + 3*a*b^2*c*e*(d^2*e^2 + 3*c*d*e *f + c^2*f^2) + a^3*d*f*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + a^2*b*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f^3))*x^5)/5 + ((a^3*d^2*f^2*(d*e + c *f) + b^3*c*e*(d^2*e^2 + 3*c*d*e*f + c^2*f^2) + 3*a^2*b*d*f*(d^2*e^2 + 3*c *d*e*f + c^2*f^2) + a*b^2*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + c^3*f ^3))*x^6)/2 + ((a^3*d^3*f^3 + 9*a^2*b*d^2*f^2*(d*e + c*f) + 9*a*b^2*d*f*(d ^2*e^2 + 3*c*d*e*f + c^2*f^2) + b^3*(d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f ^2 + c^3*f^3))*x^7)/7 + (3*b*d*f*(a^2*d^2*f^2 + 3*a*b*d*f*(d*e + c*f) + b^ 2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*x^8)/8 + (b^2*d^2*f^2*(b*d*e + b*c*f + a*d*f)*x^9)/3 + (b^3*d^3*f^3*x^10)/10
Time = 0.85 (sec) , antiderivative size = 361, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {99, 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.
| \(\displaystyle \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx\) |
| \(\Big \downarrow \) 99 |
| \(\displaystyle \int \left (\frac {3 d f (a+b x)^7 \left (5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )}{b^6}+\frac {(a+b x)^6 (-2 a d f+b c f+b d e) \left (10 a^2 d^2 f^2-10 a b c d f^2-10 a b d^2 e f+b^2 c^2 f^2+8 b^2 c d e f+b^2 d^2 e^2\right )}{b^6}+\frac {3 (a+b x)^5 (b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )}{b^6}+\frac {3 d^2 f^2 (a+b x)^8 (-2 a d f+b c f+b d e)}{b^6}+\frac {3 (a+b x)^4 (b c-a d)^2 (b e-a f)^2 (-2 a d f+b c f+b d e)}{b^6}+\frac {(a+b x)^3 (b c-a d)^3 (b e-a f)^3}{b^6}+\frac {d^3 f^3 (a+b x)^9}{b^6}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {3 d f (a+b x)^8 \left (5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )}{8 b^7}+\frac {(a+b x)^7 (-2 a d f+b c f+b d e) \left (10 a^2 d^2 f^2-10 a b d f (c f+d e)+b^2 \left (c^2 f^2+8 c d e f+d^2 e^2\right )\right )}{7 b^7}+\frac {(a+b x)^6 (b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )}{2 b^7}+\frac {d^2 f^2 (a+b x)^9 (-2 a d f+b c f+b d e)}{3 b^7}+\frac {3 (a+b x)^5 (b c-a d)^2 (b e-a f)^2 (-2 a d f+b c f+b d e)}{5 b^7}+\frac {(a+b x)^4 (b c-a d)^3 (b e-a f)^3}{4 b^7}+\frac {d^3 f^3 (a+b x)^{10}}{10 b^7}\) |
((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^4)/(4*b^7) + (3*(b*c - a*d)^2*(b*e - a*f)^2*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^5)/(5*b^7) + ((b*c - a*d)*(b* e - a*f)*(5*a^2*d^2*f^2 - 5*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*(a + b*x)^6)/(2*b^7) + ((b*d*e + b*c*f - 2*a*d*f)*(10*a^2*d^2 *f^2 - 10*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 8*c*d*e*f + c^2*f^2))*(a + b*x)^7)/(7*b^7) + (3*d*f*(5*a^2*d^2*f^2 - 5*a*b*d*f*(d*e + c*f) + b^2*(d^2 *e^2 + 3*c*d*e*f + c^2*f^2))*(a + b*x)^8)/(8*b^7) + (d^2*f^2*(b*d*e + b*c* f - 2*a*d*f)*(a + b*x)^9)/(3*b^7) + (d^3*f^3*(a + b*x)^10)/(10*b^7)
3.18.11.3.1 Defintions of rubi rules used
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] && (IntegerQ[p] | | (GtQ[m, 0] && GeQ[n, -1]))
Leaf count of result is larger than twice the leaf count of optimal. \(766\) vs. \(2(347)=694\).
Time = 0.88 (sec) , antiderivative size = 767, normalized size of antiderivative = 2.12
| method | result | size |
| default | \(\frac {b^{3} d^{3} f^{3} x^{10}}{10}+\frac {\left (\left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) f^{3}+3 b^{3} d^{3} e \,f^{2}\right ) x^{9}}{9}+\frac {\left (\left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) f^{3}+3 \left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) e \,f^{2}+3 b^{3} d^{3} e^{2} f \right ) x^{8}}{8}+\frac {\left (\left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) f^{3}+3 \left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) e \,f^{2}+3 \left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) e^{2} f +b^{3} d^{3} e^{3}\right ) x^{7}}{7}+\frac {\left (\left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) f^{3}+3 \left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) e \,f^{2}+3 \left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) e^{2} f +\left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) e^{3}\right ) x^{6}}{6}+\frac {\left (\left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) f^{3}+3 \left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) e \,f^{2}+3 \left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) e^{2} f +\left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) e^{3}\right ) x^{5}}{5}+\frac {\left (c^{3} a^{3} f^{3}+3 \left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) e \,f^{2}+3 \left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) e^{2} f +\left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) e^{3}\right ) x^{4}}{4}+\frac {\left (3 c^{3} a^{3} e \,f^{2}+3 \left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) e^{2} f +\left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) e^{3}\right ) x^{3}}{3}+\frac {\left (3 c^{3} a^{3} e^{2} f +\left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) e^{3}\right ) x^{2}}{2}+c^{3} a^{3} e^{3} x\) | \(767\) |
| norman | \(\frac {b^{3} d^{3} f^{3} x^{10}}{10}+\left (\frac {1}{3} a \,b^{2} d^{3} f^{3}+\frac {1}{3} b^{3} c \,d^{2} f^{3}+\frac {1}{3} b^{3} d^{3} e \,f^{2}\right ) x^{9}+\left (\frac {3}{8} a^{2} b \,d^{3} f^{3}+\frac {9}{8} a \,b^{2} c \,d^{2} f^{3}+\frac {9}{8} a \,b^{2} d^{3} e \,f^{2}+\frac {3}{8} b^{3} c^{2} d \,f^{3}+\frac {9}{8} b^{3} c \,d^{2} e \,f^{2}+\frac {3}{8} b^{3} d^{3} e^{2} f \right ) x^{8}+\left (\frac {1}{7} a^{3} d^{3} f^{3}+\frac {9}{7} a^{2} b c \,d^{2} f^{3}+\frac {9}{7} a^{2} b \,d^{3} e \,f^{2}+\frac {9}{7} a \,b^{2} c^{2} d \,f^{3}+\frac {27}{7} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {9}{7} a \,b^{2} d^{3} e^{2} f +\frac {1}{7} b^{3} c^{3} f^{3}+\frac {9}{7} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} b^{3} c \,d^{2} e^{2} f +\frac {1}{7} b^{3} d^{3} e^{3}\right ) x^{7}+\left (\frac {1}{2} a^{3} c \,d^{2} f^{3}+\frac {1}{2} a^{3} d^{3} e \,f^{2}+\frac {3}{2} a^{2} b \,c^{2} d \,f^{3}+\frac {9}{2} a^{2} b c \,d^{2} e \,f^{2}+\frac {3}{2} a^{2} b \,d^{3} e^{2} f +\frac {1}{2} a \,b^{2} c^{3} f^{3}+\frac {9}{2} a \,b^{2} c^{2} d e \,f^{2}+\frac {9}{2} a \,b^{2} c \,d^{2} e^{2} f +\frac {1}{2} a \,b^{2} d^{3} e^{3}+\frac {1}{2} b^{3} c^{3} e \,f^{2}+\frac {3}{2} b^{3} c^{2} d \,e^{2} f +\frac {1}{2} b^{3} c \,d^{2} e^{3}\right ) x^{6}+\left (\frac {3}{5} a^{3} c^{2} d \,f^{3}+\frac {9}{5} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{5} a^{3} d^{3} e^{2} f +\frac {3}{5} a^{2} b \,c^{3} f^{3}+\frac {27}{5} a^{2} b \,c^{2} d e \,f^{2}+\frac {27}{5} a^{2} b c \,d^{2} e^{2} f +\frac {3}{5} a^{2} b \,d^{3} e^{3}+\frac {9}{5} a \,b^{2} c^{3} e \,f^{2}+\frac {27}{5} a \,b^{2} c^{2} d \,e^{2} f +\frac {9}{5} a \,b^{2} c \,d^{2} e^{3}+\frac {3}{5} b^{3} c^{3} e^{2} f +\frac {3}{5} b^{3} c^{2} d \,e^{3}\right ) x^{5}+\left (\frac {1}{4} c^{3} a^{3} f^{3}+\frac {9}{4} a^{3} c^{2} d e \,f^{2}+\frac {9}{4} a^{3} c \,d^{2} e^{2} f +\frac {1}{4} a^{3} d^{3} e^{3}+\frac {9}{4} a^{2} b \,c^{3} e \,f^{2}+\frac {27}{4} a^{2} b \,c^{2} d \,e^{2} f +\frac {9}{4} a^{2} b c \,d^{2} e^{3}+\frac {9}{4} a \,b^{2} c^{3} e^{2} f +\frac {9}{4} a \,b^{2} c^{2} d \,e^{3}+\frac {1}{4} b^{3} c^{3} e^{3}\right ) x^{4}+\left (c^{3} a^{3} e \,f^{2}+3 a^{3} c^{2} d \,e^{2} f +a^{3} c \,d^{2} e^{3}+3 a^{2} b \,c^{3} e^{2} f +3 a^{2} b \,c^{2} d \,e^{3}+a \,b^{2} c^{3} e^{3}\right ) x^{3}+\left (\frac {3}{2} c^{3} a^{3} e^{2} f +\frac {3}{2} a^{3} c^{2} d \,e^{3}+\frac {3}{2} a^{2} b \,c^{3} e^{3}\right ) x^{2}+c^{3} a^{3} e^{3} x\) | \(842\) |
| gosper | \(\frac {27}{5} x^{5} a \,b^{2} c^{2} d \,e^{2} f +\frac {27}{4} x^{4} a^{2} b \,c^{2} d \,e^{2} f +3 a^{2} b \,c^{2} d \,e^{3} x^{3}+3 a^{2} b \,c^{3} e^{2} f \,x^{3}+\frac {1}{7} x^{7} a^{3} d^{3} f^{3}+\frac {1}{7} x^{7} b^{3} c^{3} f^{3}+\frac {1}{7} x^{7} b^{3} d^{3} e^{3}+\frac {1}{4} x^{4} c^{3} a^{3} f^{3}+\frac {1}{4} x^{4} a^{3} d^{3} e^{3}+\frac {1}{4} x^{4} b^{3} c^{3} e^{3}+\frac {1}{10} b^{3} d^{3} f^{3} x^{10}+c^{3} a^{3} e^{3} x +\frac {9}{4} x^{4} a^{2} b \,c^{3} e \,f^{2}+\frac {9}{4} x^{4} a^{2} b c \,d^{2} e^{3}+\frac {9}{4} x^{4} a \,b^{2} c^{3} e^{2} f +\frac {9}{4} x^{4} a \,b^{2} c^{2} d \,e^{3}+3 a^{3} c^{2} d \,e^{2} f \,x^{3}+\frac {9}{4} x^{4} a^{3} c \,d^{2} e^{2} f +\frac {9}{4} x^{4} a^{3} c^{2} d e \,f^{2}+\frac {9}{5} x^{5} a \,b^{2} c \,d^{2} e^{3}+\frac {9}{5} x^{5} a \,b^{2} c^{3} e \,f^{2}+\frac {9}{5} x^{5} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{2} x^{6} b^{3} c^{2} d \,e^{2} f +\frac {3}{2} x^{6} a^{2} b \,c^{2} d \,f^{3}+\frac {3}{2} x^{6} a^{2} b \,d^{3} e^{2} f +\frac {9}{7} x^{7} b^{3} c \,d^{2} e^{2} f +\frac {9}{7} x^{7} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} x^{7} a \,b^{2} d^{3} e^{2} f +\frac {9}{7} x^{7} a \,b^{2} c^{2} d \,f^{3}+\frac {9}{7} x^{7} a^{2} b c \,d^{2} f^{3}+\frac {9}{7} x^{7} a^{2} b \,d^{3} e \,f^{2}+\frac {9}{8} x^{8} a \,b^{2} c \,d^{2} f^{3}+\frac {9}{8} x^{8} a \,b^{2} d^{3} e \,f^{2}+\frac {9}{8} x^{8} b^{3} c \,d^{2} e \,f^{2}+a \,b^{2} c^{3} e^{3} x^{3}+\frac {3}{2} x^{2} a^{3} c^{2} d \,e^{3}+\frac {3}{2} x^{2} a^{2} b \,c^{3} e^{3}+a^{3} c^{3} e \,f^{2} x^{3}+a^{3} c \,d^{2} e^{3} x^{3}+\frac {3}{5} x^{5} a^{2} b \,c^{3} f^{3}+\frac {3}{5} x^{5} a^{2} b \,d^{3} e^{3}+\frac {3}{5} x^{5} b^{3} c^{3} e^{2} f +\frac {3}{5} x^{5} b^{3} c^{2} d \,e^{3}+\frac {3}{2} x^{2} c^{3} a^{3} e^{2} f +\frac {3}{5} x^{5} a^{3} d^{3} e^{2} f +\frac {27}{7} x^{7} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {9}{2} x^{6} a^{2} b c \,d^{2} e \,f^{2}+\frac {9}{2} x^{6} a \,b^{2} c^{2} d e \,f^{2}+\frac {3}{8} x^{8} b^{3} d^{3} e^{2} f +\frac {1}{2} x^{6} a^{3} c \,d^{2} f^{3}+\frac {1}{2} x^{6} a^{3} d^{3} e \,f^{2}+\frac {1}{2} x^{6} a \,b^{2} c^{3} f^{3}+\frac {1}{3} x^{9} a \,b^{2} d^{3} f^{3}+\frac {1}{3} x^{9} b^{3} c \,d^{2} f^{3}+\frac {1}{3} x^{9} b^{3} d^{3} e \,f^{2}+\frac {3}{8} x^{8} a^{2} b \,d^{3} f^{3}+\frac {3}{8} x^{8} b^{3} c^{2} d \,f^{3}+\frac {1}{2} x^{6} a \,b^{2} d^{3} e^{3}+\frac {1}{2} x^{6} b^{3} c^{3} e \,f^{2}+\frac {1}{2} x^{6} b^{3} c \,d^{2} e^{3}+\frac {3}{5} x^{5} a^{3} c^{2} d \,f^{3}+\frac {27}{5} x^{5} a^{2} b c \,d^{2} e^{2} f +\frac {9}{2} x^{6} a \,b^{2} c \,d^{2} e^{2} f +\frac {27}{5} x^{5} a^{2} b \,c^{2} d e \,f^{2}\) | \(988\) |
| risch | \(\frac {27}{5} x^{5} a \,b^{2} c^{2} d \,e^{2} f +\frac {27}{4} x^{4} a^{2} b \,c^{2} d \,e^{2} f +3 a^{2} b \,c^{2} d \,e^{3} x^{3}+3 a^{2} b \,c^{3} e^{2} f \,x^{3}+\frac {1}{7} x^{7} a^{3} d^{3} f^{3}+\frac {1}{7} x^{7} b^{3} c^{3} f^{3}+\frac {1}{7} x^{7} b^{3} d^{3} e^{3}+\frac {1}{4} x^{4} c^{3} a^{3} f^{3}+\frac {1}{4} x^{4} a^{3} d^{3} e^{3}+\frac {1}{4} x^{4} b^{3} c^{3} e^{3}+\frac {1}{10} b^{3} d^{3} f^{3} x^{10}+c^{3} a^{3} e^{3} x +\frac {9}{4} x^{4} a^{2} b \,c^{3} e \,f^{2}+\frac {9}{4} x^{4} a^{2} b c \,d^{2} e^{3}+\frac {9}{4} x^{4} a \,b^{2} c^{3} e^{2} f +\frac {9}{4} x^{4} a \,b^{2} c^{2} d \,e^{3}+3 a^{3} c^{2} d \,e^{2} f \,x^{3}+\frac {9}{4} x^{4} a^{3} c \,d^{2} e^{2} f +\frac {9}{4} x^{4} a^{3} c^{2} d e \,f^{2}+\frac {9}{5} x^{5} a \,b^{2} c \,d^{2} e^{3}+\frac {9}{5} x^{5} a \,b^{2} c^{3} e \,f^{2}+\frac {9}{5} x^{5} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{2} x^{6} b^{3} c^{2} d \,e^{2} f +\frac {3}{2} x^{6} a^{2} b \,c^{2} d \,f^{3}+\frac {3}{2} x^{6} a^{2} b \,d^{3} e^{2} f +\frac {9}{7} x^{7} b^{3} c \,d^{2} e^{2} f +\frac {9}{7} x^{7} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} x^{7} a \,b^{2} d^{3} e^{2} f +\frac {9}{7} x^{7} a \,b^{2} c^{2} d \,f^{3}+\frac {9}{7} x^{7} a^{2} b c \,d^{2} f^{3}+\frac {9}{7} x^{7} a^{2} b \,d^{3} e \,f^{2}+\frac {9}{8} x^{8} a \,b^{2} c \,d^{2} f^{3}+\frac {9}{8} x^{8} a \,b^{2} d^{3} e \,f^{2}+\frac {9}{8} x^{8} b^{3} c \,d^{2} e \,f^{2}+a \,b^{2} c^{3} e^{3} x^{3}+\frac {3}{2} x^{2} a^{3} c^{2} d \,e^{3}+\frac {3}{2} x^{2} a^{2} b \,c^{3} e^{3}+a^{3} c^{3} e \,f^{2} x^{3}+a^{3} c \,d^{2} e^{3} x^{3}+\frac {3}{5} x^{5} a^{2} b \,c^{3} f^{3}+\frac {3}{5} x^{5} a^{2} b \,d^{3} e^{3}+\frac {3}{5} x^{5} b^{3} c^{3} e^{2} f +\frac {3}{5} x^{5} b^{3} c^{2} d \,e^{3}+\frac {3}{2} x^{2} c^{3} a^{3} e^{2} f +\frac {3}{5} x^{5} a^{3} d^{3} e^{2} f +\frac {27}{7} x^{7} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {9}{2} x^{6} a^{2} b c \,d^{2} e \,f^{2}+\frac {9}{2} x^{6} a \,b^{2} c^{2} d e \,f^{2}+\frac {3}{8} x^{8} b^{3} d^{3} e^{2} f +\frac {1}{2} x^{6} a^{3} c \,d^{2} f^{3}+\frac {1}{2} x^{6} a^{3} d^{3} e \,f^{2}+\frac {1}{2} x^{6} a \,b^{2} c^{3} f^{3}+\frac {1}{3} x^{9} a \,b^{2} d^{3} f^{3}+\frac {1}{3} x^{9} b^{3} c \,d^{2} f^{3}+\frac {1}{3} x^{9} b^{3} d^{3} e \,f^{2}+\frac {3}{8} x^{8} a^{2} b \,d^{3} f^{3}+\frac {3}{8} x^{8} b^{3} c^{2} d \,f^{3}+\frac {1}{2} x^{6} a \,b^{2} d^{3} e^{3}+\frac {1}{2} x^{6} b^{3} c^{3} e \,f^{2}+\frac {1}{2} x^{6} b^{3} c \,d^{2} e^{3}+\frac {3}{5} x^{5} a^{3} c^{2} d \,f^{3}+\frac {27}{5} x^{5} a^{2} b c \,d^{2} e^{2} f +\frac {9}{2} x^{6} a \,b^{2} c \,d^{2} e^{2} f +\frac {27}{5} x^{5} a^{2} b \,c^{2} d e \,f^{2}\) | \(988\) |
| parallelrisch | \(\frac {27}{5} x^{5} a \,b^{2} c^{2} d \,e^{2} f +\frac {27}{4} x^{4} a^{2} b \,c^{2} d \,e^{2} f +3 a^{2} b \,c^{2} d \,e^{3} x^{3}+3 a^{2} b \,c^{3} e^{2} f \,x^{3}+\frac {1}{7} x^{7} a^{3} d^{3} f^{3}+\frac {1}{7} x^{7} b^{3} c^{3} f^{3}+\frac {1}{7} x^{7} b^{3} d^{3} e^{3}+\frac {1}{4} x^{4} c^{3} a^{3} f^{3}+\frac {1}{4} x^{4} a^{3} d^{3} e^{3}+\frac {1}{4} x^{4} b^{3} c^{3} e^{3}+\frac {1}{10} b^{3} d^{3} f^{3} x^{10}+c^{3} a^{3} e^{3} x +\frac {9}{4} x^{4} a^{2} b \,c^{3} e \,f^{2}+\frac {9}{4} x^{4} a^{2} b c \,d^{2} e^{3}+\frac {9}{4} x^{4} a \,b^{2} c^{3} e^{2} f +\frac {9}{4} x^{4} a \,b^{2} c^{2} d \,e^{3}+3 a^{3} c^{2} d \,e^{2} f \,x^{3}+\frac {9}{4} x^{4} a^{3} c \,d^{2} e^{2} f +\frac {9}{4} x^{4} a^{3} c^{2} d e \,f^{2}+\frac {9}{5} x^{5} a \,b^{2} c \,d^{2} e^{3}+\frac {9}{5} x^{5} a \,b^{2} c^{3} e \,f^{2}+\frac {9}{5} x^{5} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{2} x^{6} b^{3} c^{2} d \,e^{2} f +\frac {3}{2} x^{6} a^{2} b \,c^{2} d \,f^{3}+\frac {3}{2} x^{6} a^{2} b \,d^{3} e^{2} f +\frac {9}{7} x^{7} b^{3} c \,d^{2} e^{2} f +\frac {9}{7} x^{7} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} x^{7} a \,b^{2} d^{3} e^{2} f +\frac {9}{7} x^{7} a \,b^{2} c^{2} d \,f^{3}+\frac {9}{7} x^{7} a^{2} b c \,d^{2} f^{3}+\frac {9}{7} x^{7} a^{2} b \,d^{3} e \,f^{2}+\frac {9}{8} x^{8} a \,b^{2} c \,d^{2} f^{3}+\frac {9}{8} x^{8} a \,b^{2} d^{3} e \,f^{2}+\frac {9}{8} x^{8} b^{3} c \,d^{2} e \,f^{2}+a \,b^{2} c^{3} e^{3} x^{3}+\frac {3}{2} x^{2} a^{3} c^{2} d \,e^{3}+\frac {3}{2} x^{2} a^{2} b \,c^{3} e^{3}+a^{3} c^{3} e \,f^{2} x^{3}+a^{3} c \,d^{2} e^{3} x^{3}+\frac {3}{5} x^{5} a^{2} b \,c^{3} f^{3}+\frac {3}{5} x^{5} a^{2} b \,d^{3} e^{3}+\frac {3}{5} x^{5} b^{3} c^{3} e^{2} f +\frac {3}{5} x^{5} b^{3} c^{2} d \,e^{3}+\frac {3}{2} x^{2} c^{3} a^{3} e^{2} f +\frac {3}{5} x^{5} a^{3} d^{3} e^{2} f +\frac {27}{7} x^{7} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {9}{2} x^{6} a^{2} b c \,d^{2} e \,f^{2}+\frac {9}{2} x^{6} a \,b^{2} c^{2} d e \,f^{2}+\frac {3}{8} x^{8} b^{3} d^{3} e^{2} f +\frac {1}{2} x^{6} a^{3} c \,d^{2} f^{3}+\frac {1}{2} x^{6} a^{3} d^{3} e \,f^{2}+\frac {1}{2} x^{6} a \,b^{2} c^{3} f^{3}+\frac {1}{3} x^{9} a \,b^{2} d^{3} f^{3}+\frac {1}{3} x^{9} b^{3} c \,d^{2} f^{3}+\frac {1}{3} x^{9} b^{3} d^{3} e \,f^{2}+\frac {3}{8} x^{8} a^{2} b \,d^{3} f^{3}+\frac {3}{8} x^{8} b^{3} c^{2} d \,f^{3}+\frac {1}{2} x^{6} a \,b^{2} d^{3} e^{3}+\frac {1}{2} x^{6} b^{3} c^{3} e \,f^{2}+\frac {1}{2} x^{6} b^{3} c \,d^{2} e^{3}+\frac {3}{5} x^{5} a^{3} c^{2} d \,f^{3}+\frac {27}{5} x^{5} a^{2} b c \,d^{2} e^{2} f +\frac {9}{2} x^{6} a \,b^{2} c \,d^{2} e^{2} f +\frac {27}{5} x^{5} a^{2} b \,c^{2} d e \,f^{2}\) | \(988\) |
1/10*b^3*d^3*f^3*x^10+1/9*((3*a*b^2*d^3+3*b^3*c*d^2)*f^3+3*b^3*d^3*e*f^2)* x^9+1/8*((3*a^2*b*d^3+9*a*b^2*c*d^2+3*b^3*c^2*d)*f^3+3*(3*a*b^2*d^3+3*b^3* c*d^2)*e*f^2+3*b^3*d^3*e^2*f)*x^8+1/7*((a^3*d^3+9*a^2*b*c*d^2+9*a*b^2*c^2* d+b^3*c^3)*f^3+3*(3*a^2*b*d^3+9*a*b^2*c*d^2+3*b^3*c^2*d)*e*f^2+3*(3*a*b^2* d^3+3*b^3*c*d^2)*e^2*f+b^3*d^3*e^3)*x^7+1/6*((3*a^3*c*d^2+9*a^2*b*c^2*d+3* a*b^2*c^3)*f^3+3*(a^3*d^3+9*a^2*b*c*d^2+9*a*b^2*c^2*d+b^3*c^3)*e*f^2+3*(3* a^2*b*d^3+9*a*b^2*c*d^2+3*b^3*c^2*d)*e^2*f+(3*a*b^2*d^3+3*b^3*c*d^2)*e^3)* x^6+1/5*((3*a^3*c^2*d+3*a^2*b*c^3)*f^3+3*(3*a^3*c*d^2+9*a^2*b*c^2*d+3*a*b^ 2*c^3)*e*f^2+3*(a^3*d^3+9*a^2*b*c*d^2+9*a*b^2*c^2*d+b^3*c^3)*e^2*f+(3*a^2* b*d^3+9*a*b^2*c*d^2+3*b^3*c^2*d)*e^3)*x^5+1/4*(c^3*a^3*f^3+3*(3*a^3*c^2*d+ 3*a^2*b*c^3)*e*f^2+3*(3*a^3*c*d^2+9*a^2*b*c^2*d+3*a*b^2*c^3)*e^2*f+(a^3*d^ 3+9*a^2*b*c*d^2+9*a*b^2*c^2*d+b^3*c^3)*e^3)*x^4+1/3*(3*c^3*a^3*e*f^2+3*(3* a^3*c^2*d+3*a^2*b*c^3)*e^2*f+(3*a^3*c*d^2+9*a^2*b*c^2*d+3*a*b^2*c^3)*e^3)* x^3+1/2*(3*c^3*a^3*e^2*f+(3*a^3*c^2*d+3*a^2*b*c^3)*e^3)*x^2+c^3*a^3*e^3*x
Leaf count of result is larger than twice the leaf count of optimal. 727 vs. \(2 (347) = 694\).
Time = 0.23 (sec) , antiderivative size = 727, normalized size of antiderivative = 2.01 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=\frac {1}{10} \, b^{3} d^{3} f^{3} x^{10} + a^{3} c^{3} e^{3} x + \frac {1}{3} \, {\left (b^{3} d^{3} e f^{2} + {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{3}\right )} x^{9} + \frac {3}{8} \, {\left (b^{3} d^{3} e^{2} f + 3 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} e f^{2} + {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} f^{3}\right )} x^{8} + \frac {1}{7} \, {\left (b^{3} d^{3} e^{3} + 9 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} e^{2} f + 9 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} e f^{2} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} f^{3}\right )} x^{7} + \frac {1}{2} \, {\left ({\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} e^{3} + 3 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} e^{2} f + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} e f^{2} + {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} f^{3}\right )} x^{6} + \frac {3}{5} \, {\left ({\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} e^{3} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} e^{2} f + 3 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} e f^{2} + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} f^{3}\right )} x^{5} + \frac {1}{4} \, {\left (a^{3} c^{3} f^{3} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} e^{3} + 9 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} e^{2} f + 9 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e f^{2}\right )} x^{4} + {\left (a^{3} c^{3} e f^{2} + {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} e^{3} + 3 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e^{2} f\right )} x^{3} + \frac {3}{2} \, {\left (a^{3} c^{3} e^{2} f + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e^{3}\right )} x^{2} \]
1/10*b^3*d^3*f^3*x^10 + a^3*c^3*e^3*x + 1/3*(b^3*d^3*e*f^2 + (b^3*c*d^2 + a*b^2*d^3)*f^3)*x^9 + 3/8*(b^3*d^3*e^2*f + 3*(b^3*c*d^2 + a*b^2*d^3)*e*f^2 + (b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^3)*x^8 + 1/7*(b^3*d^3*e^3 + 9 *(b^3*c*d^2 + a*b^2*d^3)*e^2*f + 9*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3) *e*f^2 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3)*x^7 + 1/ 2*((b^3*c*d^2 + a*b^2*d^3)*e^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3) *e^2*f + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e*f^2 + (a*b^ 2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3)*x^6 + 3/5*((b^3*c^2*d + 3*a*b^2*c* d^2 + a^2*b*d^3)*e^3 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3) *e^2*f + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e*f^2 + (a^2*b*c^3 + a^ 3*c^2*d)*f^3)*x^5 + 1/4*(a^3*c^3*f^3 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b* c*d^2 + a^3*d^3)*e^3 + 9*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^2*f + 9 *(a^2*b*c^3 + a^3*c^2*d)*e*f^2)*x^4 + (a^3*c^3*e*f^2 + (a*b^2*c^3 + 3*a^2* b*c^2*d + a^3*c*d^2)*e^3 + 3*(a^2*b*c^3 + a^3*c^2*d)*e^2*f)*x^3 + 3/2*(a^3 *c^3*e^2*f + (a^2*b*c^3 + a^3*c^2*d)*e^3)*x^2
Leaf count of result is larger than twice the leaf count of optimal. 1018 vs. \(2 (364) = 728\).
Time = 0.07 (sec) , antiderivative size = 1018, normalized size of antiderivative = 2.82 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=a^{3} c^{3} e^{3} x + \frac {b^{3} d^{3} f^{3} x^{10}}{10} + x^{9} \left (\frac {a b^{2} d^{3} f^{3}}{3} + \frac {b^{3} c d^{2} f^{3}}{3} + \frac {b^{3} d^{3} e f^{2}}{3}\right ) + x^{8} \cdot \left (\frac {3 a^{2} b d^{3} f^{3}}{8} + \frac {9 a b^{2} c d^{2} f^{3}}{8} + \frac {9 a b^{2} d^{3} e f^{2}}{8} + \frac {3 b^{3} c^{2} d f^{3}}{8} + \frac {9 b^{3} c d^{2} e f^{2}}{8} + \frac {3 b^{3} d^{3} e^{2} f}{8}\right ) + x^{7} \left (\frac {a^{3} d^{3} f^{3}}{7} + \frac {9 a^{2} b c d^{2} f^{3}}{7} + \frac {9 a^{2} b d^{3} e f^{2}}{7} + \frac {9 a b^{2} c^{2} d f^{3}}{7} + \frac {27 a b^{2} c d^{2} e f^{2}}{7} + \frac {9 a b^{2} d^{3} e^{2} f}{7} + \frac {b^{3} c^{3} f^{3}}{7} + \frac {9 b^{3} c^{2} d e f^{2}}{7} + \frac {9 b^{3} c d^{2} e^{2} f}{7} + \frac {b^{3} d^{3} e^{3}}{7}\right ) + x^{6} \left (\frac {a^{3} c d^{2} f^{3}}{2} + \frac {a^{3} d^{3} e f^{2}}{2} + \frac {3 a^{2} b c^{2} d f^{3}}{2} + \frac {9 a^{2} b c d^{2} e f^{2}}{2} + \frac {3 a^{2} b d^{3} e^{2} f}{2} + \frac {a b^{2} c^{3} f^{3}}{2} + \frac {9 a b^{2} c^{2} d e f^{2}}{2} + \frac {9 a b^{2} c d^{2} e^{2} f}{2} + \frac {a b^{2} d^{3} e^{3}}{2} + \frac {b^{3} c^{3} e f^{2}}{2} + \frac {3 b^{3} c^{2} d e^{2} f}{2} + \frac {b^{3} c d^{2} e^{3}}{2}\right ) + x^{5} \cdot \left (\frac {3 a^{3} c^{2} d f^{3}}{5} + \frac {9 a^{3} c d^{2} e f^{2}}{5} + \frac {3 a^{3} d^{3} e^{2} f}{5} + \frac {3 a^{2} b c^{3} f^{3}}{5} + \frac {27 a^{2} b c^{2} d e f^{2}}{5} + \frac {27 a^{2} b c d^{2} e^{2} f}{5} + \frac {3 a^{2} b d^{3} e^{3}}{5} + \frac {9 a b^{2} c^{3} e f^{2}}{5} + \frac {27 a b^{2} c^{2} d e^{2} f}{5} + \frac {9 a b^{2} c d^{2} e^{3}}{5} + \frac {3 b^{3} c^{3} e^{2} f}{5} + \frac {3 b^{3} c^{2} d e^{3}}{5}\right ) + x^{4} \left (\frac {a^{3} c^{3} f^{3}}{4} + \frac {9 a^{3} c^{2} d e f^{2}}{4} + \frac {9 a^{3} c d^{2} e^{2} f}{4} + \frac {a^{3} d^{3} e^{3}}{4} + \frac {9 a^{2} b c^{3} e f^{2}}{4} + \frac {27 a^{2} b c^{2} d e^{2} f}{4} + \frac {9 a^{2} b c d^{2} e^{3}}{4} + \frac {9 a b^{2} c^{3} e^{2} f}{4} + \frac {9 a b^{2} c^{2} d e^{3}}{4} + \frac {b^{3} c^{3} e^{3}}{4}\right ) + x^{3} \left (a^{3} c^{3} e f^{2} + 3 a^{3} c^{2} d e^{2} f + a^{3} c d^{2} e^{3} + 3 a^{2} b c^{3} e^{2} f + 3 a^{2} b c^{2} d e^{3} + a b^{2} c^{3} e^{3}\right ) + x^{2} \cdot \left (\frac {3 a^{3} c^{3} e^{2} f}{2} + \frac {3 a^{3} c^{2} d e^{3}}{2} + \frac {3 a^{2} b c^{3} e^{3}}{2}\right ) \]
a**3*c**3*e**3*x + b**3*d**3*f**3*x**10/10 + x**9*(a*b**2*d**3*f**3/3 + b* *3*c*d**2*f**3/3 + b**3*d**3*e*f**2/3) + x**8*(3*a**2*b*d**3*f**3/8 + 9*a* b**2*c*d**2*f**3/8 + 9*a*b**2*d**3*e*f**2/8 + 3*b**3*c**2*d*f**3/8 + 9*b** 3*c*d**2*e*f**2/8 + 3*b**3*d**3*e**2*f/8) + x**7*(a**3*d**3*f**3/7 + 9*a** 2*b*c*d**2*f**3/7 + 9*a**2*b*d**3*e*f**2/7 + 9*a*b**2*c**2*d*f**3/7 + 27*a *b**2*c*d**2*e*f**2/7 + 9*a*b**2*d**3*e**2*f/7 + b**3*c**3*f**3/7 + 9*b**3 *c**2*d*e*f**2/7 + 9*b**3*c*d**2*e**2*f/7 + b**3*d**3*e**3/7) + x**6*(a**3 *c*d**2*f**3/2 + a**3*d**3*e*f**2/2 + 3*a**2*b*c**2*d*f**3/2 + 9*a**2*b*c* d**2*e*f**2/2 + 3*a**2*b*d**3*e**2*f/2 + a*b**2*c**3*f**3/2 + 9*a*b**2*c** 2*d*e*f**2/2 + 9*a*b**2*c*d**2*e**2*f/2 + a*b**2*d**3*e**3/2 + b**3*c**3*e *f**2/2 + 3*b**3*c**2*d*e**2*f/2 + b**3*c*d**2*e**3/2) + x**5*(3*a**3*c**2 *d*f**3/5 + 9*a**3*c*d**2*e*f**2/5 + 3*a**3*d**3*e**2*f/5 + 3*a**2*b*c**3* f**3/5 + 27*a**2*b*c**2*d*e*f**2/5 + 27*a**2*b*c*d**2*e**2*f/5 + 3*a**2*b* d**3*e**3/5 + 9*a*b**2*c**3*e*f**2/5 + 27*a*b**2*c**2*d*e**2*f/5 + 9*a*b** 2*c*d**2*e**3/5 + 3*b**3*c**3*e**2*f/5 + 3*b**3*c**2*d*e**3/5) + x**4*(a** 3*c**3*f**3/4 + 9*a**3*c**2*d*e*f**2/4 + 9*a**3*c*d**2*e**2*f/4 + a**3*d** 3*e**3/4 + 9*a**2*b*c**3*e*f**2/4 + 27*a**2*b*c**2*d*e**2*f/4 + 9*a**2*b*c *d**2*e**3/4 + 9*a*b**2*c**3*e**2*f/4 + 9*a*b**2*c**2*d*e**3/4 + b**3*c**3 *e**3/4) + x**3*(a**3*c**3*e*f**2 + 3*a**3*c**2*d*e**2*f + a**3*c*d**2*e** 3 + 3*a**2*b*c**3*e**2*f + 3*a**2*b*c**2*d*e**3 + a*b**2*c**3*e**3) + x...
Leaf count of result is larger than twice the leaf count of optimal. 727 vs. \(2 (347) = 694\).
Time = 0.21 (sec) , antiderivative size = 727, normalized size of antiderivative = 2.01 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=\frac {1}{10} \, b^{3} d^{3} f^{3} x^{10} + a^{3} c^{3} e^{3} x + \frac {1}{3} \, {\left (b^{3} d^{3} e f^{2} + {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{3}\right )} x^{9} + \frac {3}{8} \, {\left (b^{3} d^{3} e^{2} f + 3 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} e f^{2} + {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} f^{3}\right )} x^{8} + \frac {1}{7} \, {\left (b^{3} d^{3} e^{3} + 9 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} e^{2} f + 9 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} e f^{2} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} f^{3}\right )} x^{7} + \frac {1}{2} \, {\left ({\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} e^{3} + 3 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} e^{2} f + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} e f^{2} + {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} f^{3}\right )} x^{6} + \frac {3}{5} \, {\left ({\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} e^{3} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} e^{2} f + 3 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} e f^{2} + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} f^{3}\right )} x^{5} + \frac {1}{4} \, {\left (a^{3} c^{3} f^{3} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} e^{3} + 9 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} e^{2} f + 9 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e f^{2}\right )} x^{4} + {\left (a^{3} c^{3} e f^{2} + {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} e^{3} + 3 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e^{2} f\right )} x^{3} + \frac {3}{2} \, {\left (a^{3} c^{3} e^{2} f + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e^{3}\right )} x^{2} \]
1/10*b^3*d^3*f^3*x^10 + a^3*c^3*e^3*x + 1/3*(b^3*d^3*e*f^2 + (b^3*c*d^2 + a*b^2*d^3)*f^3)*x^9 + 3/8*(b^3*d^3*e^2*f + 3*(b^3*c*d^2 + a*b^2*d^3)*e*f^2 + (b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^3)*x^8 + 1/7*(b^3*d^3*e^3 + 9 *(b^3*c*d^2 + a*b^2*d^3)*e^2*f + 9*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3) *e*f^2 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3)*x^7 + 1/ 2*((b^3*c*d^2 + a*b^2*d^3)*e^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3) *e^2*f + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e*f^2 + (a*b^ 2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3)*x^6 + 3/5*((b^3*c^2*d + 3*a*b^2*c* d^2 + a^2*b*d^3)*e^3 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3) *e^2*f + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e*f^2 + (a^2*b*c^3 + a^ 3*c^2*d)*f^3)*x^5 + 1/4*(a^3*c^3*f^3 + (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b* c*d^2 + a^3*d^3)*e^3 + 9*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^2*f + 9 *(a^2*b*c^3 + a^3*c^2*d)*e*f^2)*x^4 + (a^3*c^3*e*f^2 + (a*b^2*c^3 + 3*a^2* b*c^2*d + a^3*c*d^2)*e^3 + 3*(a^2*b*c^3 + a^3*c^2*d)*e^2*f)*x^3 + 3/2*(a^3 *c^3*e^2*f + (a^2*b*c^3 + a^3*c^2*d)*e^3)*x^2
Leaf count of result is larger than twice the leaf count of optimal. 987 vs. \(2 (347) = 694\).
Time = 0.28 (sec) , antiderivative size = 987, normalized size of antiderivative = 2.73 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=\frac {1}{10} \, b^{3} d^{3} f^{3} x^{10} + \frac {1}{3} \, b^{3} d^{3} e f^{2} x^{9} + \frac {1}{3} \, b^{3} c d^{2} f^{3} x^{9} + \frac {1}{3} \, a b^{2} d^{3} f^{3} x^{9} + \frac {3}{8} \, b^{3} d^{3} e^{2} f x^{8} + \frac {9}{8} \, b^{3} c d^{2} e f^{2} x^{8} + \frac {9}{8} \, a b^{2} d^{3} e f^{2} x^{8} + \frac {3}{8} \, b^{3} c^{2} d f^{3} x^{8} + \frac {9}{8} \, a b^{2} c d^{2} f^{3} x^{8} + \frac {3}{8} \, a^{2} b d^{3} f^{3} x^{8} + \frac {1}{7} \, b^{3} d^{3} e^{3} x^{7} + \frac {9}{7} \, b^{3} c d^{2} e^{2} f x^{7} + \frac {9}{7} \, a b^{2} d^{3} e^{2} f x^{7} + \frac {9}{7} \, b^{3} c^{2} d e f^{2} x^{7} + \frac {27}{7} \, a b^{2} c d^{2} e f^{2} x^{7} + \frac {9}{7} \, a^{2} b d^{3} e f^{2} x^{7} + \frac {1}{7} \, b^{3} c^{3} f^{3} x^{7} + \frac {9}{7} \, a b^{2} c^{2} d f^{3} x^{7} + \frac {9}{7} \, a^{2} b c d^{2} f^{3} x^{7} + \frac {1}{7} \, a^{3} d^{3} f^{3} x^{7} + \frac {1}{2} \, b^{3} c d^{2} e^{3} x^{6} + \frac {1}{2} \, a b^{2} d^{3} e^{3} x^{6} + \frac {3}{2} \, b^{3} c^{2} d e^{2} f x^{6} + \frac {9}{2} \, a b^{2} c d^{2} e^{2} f x^{6} + \frac {3}{2} \, a^{2} b d^{3} e^{2} f x^{6} + \frac {1}{2} \, b^{3} c^{3} e f^{2} x^{6} + \frac {9}{2} \, a b^{2} c^{2} d e f^{2} x^{6} + \frac {9}{2} \, a^{2} b c d^{2} e f^{2} x^{6} + \frac {1}{2} \, a^{3} d^{3} e f^{2} x^{6} + \frac {1}{2} \, a b^{2} c^{3} f^{3} x^{6} + \frac {3}{2} \, a^{2} b c^{2} d f^{3} x^{6} + \frac {1}{2} \, a^{3} c d^{2} f^{3} x^{6} + \frac {3}{5} \, b^{3} c^{2} d e^{3} x^{5} + \frac {9}{5} \, a b^{2} c d^{2} e^{3} x^{5} + \frac {3}{5} \, a^{2} b d^{3} e^{3} x^{5} + \frac {3}{5} \, b^{3} c^{3} e^{2} f x^{5} + \frac {27}{5} \, a b^{2} c^{2} d e^{2} f x^{5} + \frac {27}{5} \, a^{2} b c d^{2} e^{2} f x^{5} + \frac {3}{5} \, a^{3} d^{3} e^{2} f x^{5} + \frac {9}{5} \, a b^{2} c^{3} e f^{2} x^{5} + \frac {27}{5} \, a^{2} b c^{2} d e f^{2} x^{5} + \frac {9}{5} \, a^{3} c d^{2} e f^{2} x^{5} + \frac {3}{5} \, a^{2} b c^{3} f^{3} x^{5} + \frac {3}{5} \, a^{3} c^{2} d f^{3} x^{5} + \frac {1}{4} \, b^{3} c^{3} e^{3} x^{4} + \frac {9}{4} \, a b^{2} c^{2} d e^{3} x^{4} + \frac {9}{4} \, a^{2} b c d^{2} e^{3} x^{4} + \frac {1}{4} \, a^{3} d^{3} e^{3} x^{4} + \frac {9}{4} \, a b^{2} c^{3} e^{2} f x^{4} + \frac {27}{4} \, a^{2} b c^{2} d e^{2} f x^{4} + \frac {9}{4} \, a^{3} c d^{2} e^{2} f x^{4} + \frac {9}{4} \, a^{2} b c^{3} e f^{2} x^{4} + \frac {9}{4} \, a^{3} c^{2} d e f^{2} x^{4} + \frac {1}{4} \, a^{3} c^{3} f^{3} x^{4} + a b^{2} c^{3} e^{3} x^{3} + 3 \, a^{2} b c^{2} d e^{3} x^{3} + a^{3} c d^{2} e^{3} x^{3} + 3 \, a^{2} b c^{3} e^{2} f x^{3} + 3 \, a^{3} c^{2} d e^{2} f x^{3} + a^{3} c^{3} e f^{2} x^{3} + \frac {3}{2} \, a^{2} b c^{3} e^{3} x^{2} + \frac {3}{2} \, a^{3} c^{2} d e^{3} x^{2} + \frac {3}{2} \, a^{3} c^{3} e^{2} f x^{2} + a^{3} c^{3} e^{3} x \]
1/10*b^3*d^3*f^3*x^10 + 1/3*b^3*d^3*e*f^2*x^9 + 1/3*b^3*c*d^2*f^3*x^9 + 1/ 3*a*b^2*d^3*f^3*x^9 + 3/8*b^3*d^3*e^2*f*x^8 + 9/8*b^3*c*d^2*e*f^2*x^8 + 9/ 8*a*b^2*d^3*e*f^2*x^8 + 3/8*b^3*c^2*d*f^3*x^8 + 9/8*a*b^2*c*d^2*f^3*x^8 + 3/8*a^2*b*d^3*f^3*x^8 + 1/7*b^3*d^3*e^3*x^7 + 9/7*b^3*c*d^2*e^2*f*x^7 + 9/ 7*a*b^2*d^3*e^2*f*x^7 + 9/7*b^3*c^2*d*e*f^2*x^7 + 27/7*a*b^2*c*d^2*e*f^2*x ^7 + 9/7*a^2*b*d^3*e*f^2*x^7 + 1/7*b^3*c^3*f^3*x^7 + 9/7*a*b^2*c^2*d*f^3*x ^7 + 9/7*a^2*b*c*d^2*f^3*x^7 + 1/7*a^3*d^3*f^3*x^7 + 1/2*b^3*c*d^2*e^3*x^6 + 1/2*a*b^2*d^3*e^3*x^6 + 3/2*b^3*c^2*d*e^2*f*x^6 + 9/2*a*b^2*c*d^2*e^2*f *x^6 + 3/2*a^2*b*d^3*e^2*f*x^6 + 1/2*b^3*c^3*e*f^2*x^6 + 9/2*a*b^2*c^2*d*e *f^2*x^6 + 9/2*a^2*b*c*d^2*e*f^2*x^6 + 1/2*a^3*d^3*e*f^2*x^6 + 1/2*a*b^2*c ^3*f^3*x^6 + 3/2*a^2*b*c^2*d*f^3*x^6 + 1/2*a^3*c*d^2*f^3*x^6 + 3/5*b^3*c^2 *d*e^3*x^5 + 9/5*a*b^2*c*d^2*e^3*x^5 + 3/5*a^2*b*d^3*e^3*x^5 + 3/5*b^3*c^3 *e^2*f*x^5 + 27/5*a*b^2*c^2*d*e^2*f*x^5 + 27/5*a^2*b*c*d^2*e^2*f*x^5 + 3/5 *a^3*d^3*e^2*f*x^5 + 9/5*a*b^2*c^3*e*f^2*x^5 + 27/5*a^2*b*c^2*d*e*f^2*x^5 + 9/5*a^3*c*d^2*e*f^2*x^5 + 3/5*a^2*b*c^3*f^3*x^5 + 3/5*a^3*c^2*d*f^3*x^5 + 1/4*b^3*c^3*e^3*x^4 + 9/4*a*b^2*c^2*d*e^3*x^4 + 9/4*a^2*b*c*d^2*e^3*x^4 + 1/4*a^3*d^3*e^3*x^4 + 9/4*a*b^2*c^3*e^2*f*x^4 + 27/4*a^2*b*c^2*d*e^2*f*x ^4 + 9/4*a^3*c*d^2*e^2*f*x^4 + 9/4*a^2*b*c^3*e*f^2*x^4 + 9/4*a^3*c^2*d*e*f ^2*x^4 + 1/4*a^3*c^3*f^3*x^4 + a*b^2*c^3*e^3*x^3 + 3*a^2*b*c^2*d*e^3*x^3 + a^3*c*d^2*e^3*x^3 + 3*a^2*b*c^3*e^2*f*x^3 + 3*a^3*c^2*d*e^2*f*x^3 + a^...
Time = 1.33 (sec) , antiderivative size = 787, normalized size of antiderivative = 2.18 \[ \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx=x^7\,\left (\frac {a^3\,d^3\,f^3}{7}+\frac {9\,a^2\,b\,c\,d^2\,f^3}{7}+\frac {9\,a^2\,b\,d^3\,e\,f^2}{7}+\frac {9\,a\,b^2\,c^2\,d\,f^3}{7}+\frac {27\,a\,b^2\,c\,d^2\,e\,f^2}{7}+\frac {9\,a\,b^2\,d^3\,e^2\,f}{7}+\frac {b^3\,c^3\,f^3}{7}+\frac {9\,b^3\,c^2\,d\,e\,f^2}{7}+\frac {9\,b^3\,c\,d^2\,e^2\,f}{7}+\frac {b^3\,d^3\,e^3}{7}\right )+x^5\,\left (\frac {3\,a^3\,c^2\,d\,f^3}{5}+\frac {9\,a^3\,c\,d^2\,e\,f^2}{5}+\frac {3\,a^3\,d^3\,e^2\,f}{5}+\frac {3\,a^2\,b\,c^3\,f^3}{5}+\frac {27\,a^2\,b\,c^2\,d\,e\,f^2}{5}+\frac {27\,a^2\,b\,c\,d^2\,e^2\,f}{5}+\frac {3\,a^2\,b\,d^3\,e^3}{5}+\frac {9\,a\,b^2\,c^3\,e\,f^2}{5}+\frac {27\,a\,b^2\,c^2\,d\,e^2\,f}{5}+\frac {9\,a\,b^2\,c\,d^2\,e^3}{5}+\frac {3\,b^3\,c^3\,e^2\,f}{5}+\frac {3\,b^3\,c^2\,d\,e^3}{5}\right )+x^6\,\left (\frac {a^3\,c\,d^2\,f^3}{2}+\frac {a^3\,d^3\,e\,f^2}{2}+\frac {3\,a^2\,b\,c^2\,d\,f^3}{2}+\frac {9\,a^2\,b\,c\,d^2\,e\,f^2}{2}+\frac {3\,a^2\,b\,d^3\,e^2\,f}{2}+\frac {a\,b^2\,c^3\,f^3}{2}+\frac {9\,a\,b^2\,c^2\,d\,e\,f^2}{2}+\frac {9\,a\,b^2\,c\,d^2\,e^2\,f}{2}+\frac {a\,b^2\,d^3\,e^3}{2}+\frac {b^3\,c^3\,e\,f^2}{2}+\frac {3\,b^3\,c^2\,d\,e^2\,f}{2}+\frac {b^3\,c\,d^2\,e^3}{2}\right )+x^4\,\left (\frac {a^3\,c^3\,f^3}{4}+\frac {9\,a^3\,c^2\,d\,e\,f^2}{4}+\frac {9\,a^3\,c\,d^2\,e^2\,f}{4}+\frac {a^3\,d^3\,e^3}{4}+\frac {9\,a^2\,b\,c^3\,e\,f^2}{4}+\frac {27\,a^2\,b\,c^2\,d\,e^2\,f}{4}+\frac {9\,a^2\,b\,c\,d^2\,e^3}{4}+\frac {9\,a\,b^2\,c^3\,e^2\,f}{4}+\frac {9\,a\,b^2\,c^2\,d\,e^3}{4}+\frac {b^3\,c^3\,e^3}{4}\right )+a^3\,c^3\,e^3\,x+\frac {b^3\,d^3\,f^3\,x^{10}}{10}+\frac {3\,a^2\,c^2\,e^2\,x^2\,\left (a\,c\,f+a\,d\,e+b\,c\,e\right )}{2}+\frac {b^2\,d^2\,f^2\,x^9\,\left (a\,d\,f+b\,c\,f+b\,d\,e\right )}{3}+a\,c\,e\,x^3\,\left (a^2\,c^2\,f^2+3\,a^2\,c\,d\,e\,f+a^2\,d^2\,e^2+3\,a\,b\,c^2\,e\,f+3\,a\,b\,c\,d\,e^2+b^2\,c^2\,e^2\right )+\frac {3\,b\,d\,f\,x^8\,\left (a^2\,d^2\,f^2+3\,a\,b\,c\,d\,f^2+3\,a\,b\,d^2\,e\,f+b^2\,c^2\,f^2+3\,b^2\,c\,d\,e\,f+b^2\,d^2\,e^2\right )}{8} \]
x^7*((a^3*d^3*f^3)/7 + (b^3*c^3*f^3)/7 + (b^3*d^3*e^3)/7 + (9*a*b^2*c^2*d* f^3)/7 + (9*a^2*b*c*d^2*f^3)/7 + (9*a*b^2*d^3*e^2*f)/7 + (9*a^2*b*d^3*e*f^ 2)/7 + (9*b^3*c*d^2*e^2*f)/7 + (9*b^3*c^2*d*e*f^2)/7 + (27*a*b^2*c*d^2*e*f ^2)/7) + x^5*((3*a^2*b*c^3*f^3)/5 + (3*a^2*b*d^3*e^3)/5 + (3*a^3*c^2*d*f^3 )/5 + (3*b^3*c^2*d*e^3)/5 + (3*a^3*d^3*e^2*f)/5 + (3*b^3*c^3*e^2*f)/5 + (9 *a*b^2*c*d^2*e^3)/5 + (9*a*b^2*c^3*e*f^2)/5 + (9*a^3*c*d^2*e*f^2)/5 + (27* a*b^2*c^2*d*e^2*f)/5 + (27*a^2*b*c*d^2*e^2*f)/5 + (27*a^2*b*c^2*d*e*f^2)/5 ) + x^6*((a*b^2*c^3*f^3)/2 + (a*b^2*d^3*e^3)/2 + (a^3*c*d^2*f^3)/2 + (b^3* c*d^2*e^3)/2 + (a^3*d^3*e*f^2)/2 + (b^3*c^3*e*f^2)/2 + (3*a^2*b*c^2*d*f^3) /2 + (3*a^2*b*d^3*e^2*f)/2 + (3*b^3*c^2*d*e^2*f)/2 + (9*a*b^2*c*d^2*e^2*f) /2 + (9*a*b^2*c^2*d*e*f^2)/2 + (9*a^2*b*c*d^2*e*f^2)/2) + x^4*((a^3*c^3*f^ 3)/4 + (a^3*d^3*e^3)/4 + (b^3*c^3*e^3)/4 + (9*a*b^2*c^2*d*e^3)/4 + (9*a^2* b*c*d^2*e^3)/4 + (9*a*b^2*c^3*e^2*f)/4 + (9*a^2*b*c^3*e*f^2)/4 + (9*a^3*c* d^2*e^2*f)/4 + (9*a^3*c^2*d*e*f^2)/4 + (27*a^2*b*c^2*d*e^2*f)/4) + a^3*c^3 *e^3*x + (b^3*d^3*f^3*x^10)/10 + (3*a^2*c^2*e^2*x^2*(a*c*f + a*d*e + b*c*e ))/2 + (b^2*d^2*f^2*x^9*(a*d*f + b*c*f + b*d*e))/3 + a*c*e*x^3*(a^2*c^2*f^ 2 + a^2*d^2*e^2 + b^2*c^2*e^2 + 3*a*b*c*d*e^2 + 3*a*b*c^2*e*f + 3*a^2*c*d* e*f) + (3*b*d*f*x^8*(a^2*d^2*f^2 + b^2*c^2*f^2 + b^2*d^2*e^2 + 3*a*b*c*d*f ^2 + 3*a*b*d^2*e*f + 3*b^2*c*d*e*f))/8