Integrand size = 28, antiderivative size = 653 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx=a^3 c^3 e^3 x+a^2 c^2 e^2 (b c e+a d e+a c f) x^3+\frac {3}{5} a c e \left (b^2 c^2 e^2+3 a b c e (d e+c f)+a^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^5+\frac {1}{7} \left (b^3 c^3 e^3+9 a b^2 c^2 e^2 (d e+c f)+9 a^2 b c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^7+\frac {1}{3} \left (b^3 c^2 e^2 (d e+c f)+3 a b^2 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^2 b \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^9+\frac {3}{11} \left (a^3 d^2 f^2 (d e+c f)+b^3 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+3 a^2 b d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a b^2 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^{11}+\frac {1}{13} \left (a^3 d^3 f^3+9 a^2 b d^2 f^2 (d e+c f)+9 a b^2 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+b^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^{13}+\frac {1}{5} b d f \left (a^2 d^2 f^2+3 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^{15}+\frac {3}{17} b^2 d^2 f^2 (b d e+b c f+a d f) x^{17}+\frac {1}{19} b^3 d^3 f^3 x^{19} \] Output:
a^3*c^3*e^3*x+a^2*c^2*e^2*(a*c*f+a*d*e+b*c*e)*x^3+3/5*a*c*e*(b^2*c^2*e^2+3 *a*b*c*e*(c*f+d*e)+a^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^5+1/7*(b^3*c^3*e^3+9 *a*b^2*c^2*e^2*(c*f+d*e)+9*a^2*b*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a^3*(c^3* f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^7+1/3*(b^3*c^2*e^2*(c*f+d*e)+3 *a*b^2*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a^3*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2) +a^2*b*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^9+3/11*(a^3*d^2*f^ 2*(c*f+d*e)+b^3*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+3*a^2*b*d*f*(c^2*f^2+3*c*d *e*f+d^2*e^2)+a*b^2*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^11+1/ 13*(a^3*d^3*f^3+9*a^2*b*d^2*f^2*(c*f+d*e)+9*a*b^2*d*f*(c^2*f^2+3*c*d*e*f+d ^2*e^2)+b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^13+1/5*b*d*f* (a^2*d^2*f^2+3*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^15+3/1 7*b^2*d^2*f^2*(a*d*f+b*c*f+b*d*e)*x^17+1/19*b^3*d^3*f^3*x^19
Time = 0.24 (sec) , antiderivative size = 653, normalized size of antiderivative = 1.00 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx=a^3 c^3 e^3 x+a^2 c^2 e^2 (b c e+a d e+a c f) x^3+\frac {3}{5} a c e \left (b^2 c^2 e^2+3 a b c e (d e+c f)+a^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^5+\frac {1}{7} \left (b^3 c^3 e^3+9 a b^2 c^2 e^2 (d e+c f)+9 a^2 b c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^7+\frac {1}{3} \left (b^3 c^2 e^2 (d e+c f)+3 a b^2 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^2 b \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^9+\frac {3}{11} \left (a^3 d^2 f^2 (d e+c f)+b^3 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+3 a^2 b d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a b^2 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^{11}+\frac {1}{13} \left (a^3 d^3 f^3+9 a^2 b d^2 f^2 (d e+c f)+9 a b^2 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+b^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^{13}+\frac {1}{5} b d f \left (a^2 d^2 f^2+3 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^{15}+\frac {3}{17} b^2 d^2 f^2 (b d e+b c f+a d f) x^{17}+\frac {1}{19} b^3 d^3 f^3 x^{19} \] Input:
Integrate[(a + b*x^2)^3*(c + d*x^2)^3*(e + f*x^2)^3,x]
Output:
a^3*c^3*e^3*x + a^2*c^2*e^2*(b*c*e + a*d*e + a*c*f)*x^3 + (3*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^5)/ 5 + ((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^7)/7 + ((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^9)/3 + (3*(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^11)/11 + ((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^13)/13 + (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^15)/5 + (3*b^2*d^2*f^2*(b*d*e + b*c *f + a*d*f)*x^17)/17 + (b^3*d^3*f^3*x^19)/19
Time = 1.01 (sec) , antiderivative size = 653, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {396, 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.
| \(\displaystyle \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx\) |
| \(\Big \downarrow \) 396 |
| \(\displaystyle \int \left (a^3 c^3 e^3+3 b d f x^{14} \left (a^2 d^2 f^2+3 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )+3 a c e x^4 \left (a^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )+3 a b c e (c f+d e)+b^2 c^2 e^2\right )+3 a^2 c^2 e^2 x^2 (a c f+a d e+b c e)+x^{12} \left (a^3 d^3 f^3+9 a^2 b d^2 f^2 (c f+d e)+9 a b^2 d f \left (c^2 f^2+3 c d e f+d^2 e^2\right )+b^3 \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )\right )+3 x^{10} \left (a^3 d^2 f^2 (c f+d e)+3 a^2 b d f \left (c^2 f^2+3 c d e f+d^2 e^2\right )+a b^2 \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )+b^3 c e \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )+3 x^8 \left (a^3 d f \left (c^2 f^2+3 c d e f+d^2 e^2\right )+a^2 b \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )+3 a b^2 c e \left (c^2 f^2+3 c d e f+d^2 e^2\right )+b^3 c^2 e^2 (c f+d e)\right )+x^6 \left (a^3 \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )+9 a^2 b c e \left (c^2 f^2+3 c d e f+d^2 e^2\right )+9 a b^2 c^2 e^2 (c f+d e)+b^3 c^3 e^3\right )+3 b^2 d^2 f^2 x^{16} (a d f+b c f+b d e)+b^3 d^3 f^3 x^{18}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle a^3 c^3 e^3 x+\frac {1}{5} b d f x^{15} \left (a^2 d^2 f^2+3 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )+\frac {3}{5} a c e x^5 \left (a^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )+3 a b c e (c f+d e)+b^2 c^2 e^2\right )+a^2 c^2 e^2 x^3 (a c f+a d e+b c e)+\frac {1}{13} x^{13} \left (a^3 d^3 f^3+9 a^2 b d^2 f^2 (c f+d e)+9 a b^2 d f \left (c^2 f^2+3 c d e f+d^2 e^2\right )+b^3 \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )\right )+\frac {3}{11} x^{11} \left (a^3 d^2 f^2 (c f+d e)+3 a^2 b d f \left (c^2 f^2+3 c d e f+d^2 e^2\right )+a b^2 \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )+b^3 c e \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )+\frac {1}{3} x^9 \left (a^3 d f \left (c^2 f^2+3 c d e f+d^2 e^2\right )+a^2 b \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )+3 a b^2 c e \left (c^2 f^2+3 c d e f+d^2 e^2\right )+b^3 c^2 e^2 (c f+d e)\right )+\frac {1}{7} x^7 \left (a^3 \left (c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+d^3 e^3\right )+9 a^2 b c e \left (c^2 f^2+3 c d e f+d^2 e^2\right )+9 a b^2 c^2 e^2 (c f+d e)+b^3 c^3 e^3\right )+\frac {3}{17} b^2 d^2 f^2 x^{17} (a d f+b c f+b d e)+\frac {1}{19} b^3 d^3 f^3 x^{19}\) |
Input:
Int[(a + b*x^2)^3*(c + d*x^2)^3*(e + f*x^2)^3,x]
Output:
a^3*c^3*e^3*x + a^2*c^2*e^2*(b*c*e + a*d*e + a*c*f)*x^3 + (3*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^5)/ 5 + ((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^7)/7 + ((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^9)/3 + (3*(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^11)/11 + ((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^13)/13 + (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^15)/5 + (3*b^2*d^2*f^2*(b*d*e + b*c *f + a*d*f)*x^17)/17 + (b^3*d^3*f^3*x^19)/19
Int[((a_) + (b_.)*(x_)^2)^(p_.)*((c_) + (d_.)*(x_)^2)^(q_.)*((e_) + (f_.)*( x_)^2)^(r_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x^2)^p*(c + d*x^2)^q* (e + f*x^2)^r, x], x] /; FreeQ[{a, b, c, d, e, f}, x] && IGtQ[p, 0] && IGtQ [q, 0] && IGtQ[r, 0]
Time = 0.54 (sec) , antiderivative size = 767, normalized size of antiderivative = 1.17
| method | result | size |
| default | \(\frac {b^{3} d^{3} f^{3} x^{19}}{19}+\frac {\left (\left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) f^{3}+3 b^{3} d^{3} e \,f^{2}\right ) x^{17}}{17}+\frac {\left (\left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) f^{3}+3 \left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) e \,f^{2}+3 b^{3} d^{3} e^{2} f \right ) x^{15}}{15}+\frac {\left (\left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) f^{3}+3 \left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) e \,f^{2}+3 \left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) e^{2} f +b^{3} d^{3} e^{3}\right ) x^{13}}{13}+\frac {\left (\left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) f^{3}+3 \left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) e \,f^{2}+3 \left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) e^{2} f +\left (3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right ) e^{3}\right ) x^{11}}{11}+\frac {\left (\left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) f^{3}+3 \left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) e \,f^{2}+3 \left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) e^{2} f +\left (3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right ) e^{3}\right ) x^{9}}{9}+\frac {\left (c^{3} a^{3} f^{3}+3 \left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) e \,f^{2}+3 \left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) e^{2} f +\left (a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right ) e^{3}\right ) x^{7}}{7}+\frac {\left (3 c^{3} a^{3} e \,f^{2}+3 \left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) e^{2} f +\left (3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 b^{2} c^{3} a \right ) e^{3}\right ) x^{5}}{5}+\frac {\left (3 c^{3} a^{3} e^{2} f +\left (3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right ) e^{3}\right ) x^{3}}{3}+c^{3} a^{3} e^{3} x\) | \(767\) |
| norman | \(c^{3} a^{3} e^{3} x +\left (c^{3} a^{3} e^{2} f +a^{3} c^{2} d \,e^{3}+a^{2} b \,c^{3} e^{3}\right ) x^{3}+\left (\frac {3}{5} c^{3} a^{3} e \,f^{2}+\frac {9}{5} a^{3} c^{2} d \,e^{2} f +\frac {3}{5} a^{3} c \,d^{2} e^{3}+\frac {9}{5} a^{2} b \,c^{3} e^{2} f +\frac {9}{5} a^{2} b \,c^{2} d \,e^{3}+\frac {3}{5} a \,b^{2} c^{3} e^{3}\right ) x^{5}+\left (\frac {1}{7} c^{3} a^{3} f^{3}+\frac {9}{7} a^{3} c^{2} d e \,f^{2}+\frac {9}{7} a^{3} c \,d^{2} e^{2} f +\frac {1}{7} a^{3} d^{3} e^{3}+\frac {9}{7} a^{2} b \,c^{3} e \,f^{2}+\frac {27}{7} a^{2} b \,c^{2} d \,e^{2} f +\frac {9}{7} a^{2} b c \,d^{2} e^{3}+\frac {9}{7} a \,b^{2} c^{3} e^{2} f +\frac {9}{7} a \,b^{2} c^{2} d \,e^{3}+\frac {1}{7} b^{3} c^{3} e^{3}\right ) x^{7}+\left (\frac {1}{3} a^{3} c^{2} d \,f^{3}+a^{3} c \,d^{2} e \,f^{2}+\frac {1}{3} a^{3} d^{3} e^{2} f +\frac {1}{3} a^{2} b \,c^{3} f^{3}+3 a^{2} b \,c^{2} d e \,f^{2}+3 a^{2} b c \,d^{2} e^{2} f +\frac {1}{3} a^{2} b \,d^{3} e^{3}+a \,b^{2} c^{3} e \,f^{2}+3 a \,b^{2} c^{2} d \,e^{2} f +a \,b^{2} c \,d^{2} e^{3}+\frac {1}{3} b^{3} c^{3} e^{2} f +\frac {1}{3} b^{3} c^{2} d \,e^{3}\right ) x^{9}+\left (\frac {3}{11} a^{3} c \,d^{2} f^{3}+\frac {3}{11} a^{3} d^{3} e \,f^{2}+\frac {9}{11} a^{2} b \,c^{2} d \,f^{3}+\frac {27}{11} a^{2} b c \,d^{2} e \,f^{2}+\frac {9}{11} a^{2} b \,d^{3} e^{2} f +\frac {3}{11} a \,b^{2} c^{3} f^{3}+\frac {27}{11} a \,b^{2} c^{2} d e \,f^{2}+\frac {27}{11} a \,b^{2} c \,d^{2} e^{2} f +\frac {3}{11} a \,b^{2} d^{3} e^{3}+\frac {3}{11} b^{3} c^{3} e \,f^{2}+\frac {9}{11} b^{3} c^{2} d \,e^{2} f +\frac {3}{11} b^{3} c \,d^{2} e^{3}\right ) x^{11}+\left (\frac {1}{13} a^{3} d^{3} f^{3}+\frac {9}{13} a^{2} b c \,d^{2} f^{3}+\frac {9}{13} a^{2} b \,d^{3} e \,f^{2}+\frac {9}{13} a \,b^{2} c^{2} d \,f^{3}+\frac {27}{13} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {9}{13} a \,b^{2} d^{3} e^{2} f +\frac {1}{13} b^{3} c^{3} f^{3}+\frac {9}{13} b^{3} c^{2} d e \,f^{2}+\frac {9}{13} b^{3} c \,d^{2} e^{2} f +\frac {1}{13} b^{3} d^{3} e^{3}\right ) x^{13}+\left (\frac {1}{5} a^{2} b \,d^{3} f^{3}+\frac {3}{5} a \,b^{2} c \,d^{2} f^{3}+\frac {3}{5} a \,b^{2} d^{3} e \,f^{2}+\frac {1}{5} b^{3} c^{2} d \,f^{3}+\frac {3}{5} b^{3} c \,d^{2} e \,f^{2}+\frac {1}{5} b^{3} d^{3} e^{2} f \right ) x^{15}+\left (\frac {3}{17} a \,b^{2} d^{3} f^{3}+\frac {3}{17} b^{3} c \,d^{2} f^{3}+\frac {3}{17} b^{3} d^{3} e \,f^{2}\right ) x^{17}+\frac {b^{3} d^{3} f^{3} x^{19}}{19}\) | \(839\) |
| gosper | \(\frac {9}{11} x^{11} a^{2} b \,d^{3} e^{2} f +\frac {3}{17} x^{17} a \,b^{2} d^{3} f^{3}+\frac {3}{17} x^{17} b^{3} c \,d^{2} f^{3}+\frac {3}{17} x^{17} b^{3} d^{3} e \,f^{2}+a^{3} c^{3} e^{2} f \,x^{3}+a^{3} c^{2} d \,e^{3} x^{3}+\frac {9}{13} x^{13} a^{2} b \,d^{3} e \,f^{2}+\frac {3}{5} x^{15} b^{3} c \,d^{2} e \,f^{2}+\frac {27}{11} x^{11} a \,b^{2} c \,d^{2} e^{2} f +\frac {27}{13} x^{13} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {3}{11} x^{11} b^{3} c^{3} e \,f^{2}+\frac {9}{13} x^{13} a^{2} b c \,d^{2} f^{3}+\frac {9}{11} x^{11} b^{3} c^{2} d \,e^{2} f +\frac {9}{5} x^{5} a^{3} c^{2} d \,e^{2} f +c^{3} a^{3} e^{3} x +\frac {1}{7} x^{7} a^{3} d^{3} e^{3}+\frac {9}{13} x^{13} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} x^{7} a \,b^{2} c^{3} e^{2} f +\frac {3}{11} x^{11} b^{3} c \,d^{2} e^{3}+\frac {1}{5} x^{15} a^{2} b \,d^{3} f^{3}+\frac {1}{5} x^{15} b^{3} c^{2} d \,f^{3}+a^{2} b \,c^{3} e^{3} x^{3}+\frac {9}{7} x^{7} a \,b^{2} c^{2} d \,e^{3}+\frac {9}{13} x^{13} a \,b^{2} c^{2} d \,f^{3}+x^{9} a \,b^{2} c^{3} e \,f^{2}+\frac {1}{5} x^{15} b^{3} d^{3} e^{2} f +\frac {9}{13} x^{13} b^{3} c \,d^{2} e^{2} f +\frac {3}{5} x^{15} a \,b^{2} c \,d^{2} f^{3}+\frac {3}{5} x^{15} a \,b^{2} d^{3} e \,f^{2}+\frac {1}{13} x^{13} b^{3} c^{3} f^{3}+\frac {1}{13} x^{13} b^{3} d^{3} e^{3}+\frac {1}{7} x^{7} b^{3} c^{3} e^{3}+\frac {1}{13} x^{13} a^{3} d^{3} f^{3}+\frac {9}{13} x^{13} a \,b^{2} d^{3} e^{2} f +x^{9} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{11} x^{11} a \,b^{2} d^{3} e^{3}+\frac {1}{3} x^{9} a^{3} c^{2} d \,f^{3}+\frac {9}{5} x^{5} a^{2} b \,c^{3} e^{2} f +\frac {9}{5} x^{5} a^{2} b \,c^{2} d \,e^{3}+\frac {27}{7} x^{7} a^{2} b \,c^{2} d \,e^{2} f +3 x^{9} a^{2} b \,c^{2} d e \,f^{2}+3 x^{9} a^{2} b c \,d^{2} e^{2} f +3 x^{9} a \,b^{2} c^{2} d \,e^{2} f +\frac {27}{11} x^{11} a^{2} b c \,d^{2} e \,f^{2}+\frac {27}{11} x^{11} a \,b^{2} c^{2} d e \,f^{2}+\frac {1}{7} x^{7} c^{3} a^{3} f^{3}+\frac {1}{3} x^{9} a^{2} b \,d^{3} e^{3}+\frac {1}{3} x^{9} b^{3} c^{3} e^{2} f +\frac {9}{7} x^{7} a^{2} b c \,d^{2} e^{3}+x^{9} a \,b^{2} c \,d^{2} e^{3}+\frac {9}{11} x^{11} a^{2} b \,c^{2} d \,f^{3}+\frac {1}{3} x^{9} a^{3} d^{3} e^{2} f +\frac {1}{3} x^{9} a^{2} b \,c^{3} f^{3}+\frac {1}{3} x^{9} b^{3} c^{2} d \,e^{3}+\frac {3}{11} x^{11} a^{3} c \,d^{2} f^{3}+\frac {3}{5} x^{5} c^{3} a^{3} e \,f^{2}+\frac {3}{5} x^{5} a^{3} c \,d^{2} e^{3}+\frac {3}{5} x^{5} a \,b^{2} c^{3} e^{3}+\frac {9}{7} x^{7} a^{3} c \,d^{2} e^{2} f +\frac {9}{7} x^{7} a^{2} b \,c^{3} e \,f^{2}+\frac {9}{7} x^{7} a^{3} c^{2} d e \,f^{2}+\frac {3}{11} x^{11} a^{3} d^{3} e \,f^{2}+\frac {3}{11} x^{11} a \,b^{2} c^{3} f^{3}+\frac {1}{19} b^{3} d^{3} f^{3} x^{19}\) | \(985\) |
| risch | \(\frac {9}{11} x^{11} a^{2} b \,d^{3} e^{2} f +\frac {3}{17} x^{17} a \,b^{2} d^{3} f^{3}+\frac {3}{17} x^{17} b^{3} c \,d^{2} f^{3}+\frac {3}{17} x^{17} b^{3} d^{3} e \,f^{2}+a^{3} c^{3} e^{2} f \,x^{3}+a^{3} c^{2} d \,e^{3} x^{3}+\frac {9}{13} x^{13} a^{2} b \,d^{3} e \,f^{2}+\frac {3}{5} x^{15} b^{3} c \,d^{2} e \,f^{2}+\frac {27}{11} x^{11} a \,b^{2} c \,d^{2} e^{2} f +\frac {27}{13} x^{13} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {3}{11} x^{11} b^{3} c^{3} e \,f^{2}+\frac {9}{13} x^{13} a^{2} b c \,d^{2} f^{3}+\frac {9}{11} x^{11} b^{3} c^{2} d \,e^{2} f +\frac {9}{5} x^{5} a^{3} c^{2} d \,e^{2} f +c^{3} a^{3} e^{3} x +\frac {1}{7} x^{7} a^{3} d^{3} e^{3}+\frac {9}{13} x^{13} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} x^{7} a \,b^{2} c^{3} e^{2} f +\frac {3}{11} x^{11} b^{3} c \,d^{2} e^{3}+\frac {1}{5} x^{15} a^{2} b \,d^{3} f^{3}+\frac {1}{5} x^{15} b^{3} c^{2} d \,f^{3}+a^{2} b \,c^{3} e^{3} x^{3}+\frac {9}{7} x^{7} a \,b^{2} c^{2} d \,e^{3}+\frac {9}{13} x^{13} a \,b^{2} c^{2} d \,f^{3}+x^{9} a \,b^{2} c^{3} e \,f^{2}+\frac {1}{5} x^{15} b^{3} d^{3} e^{2} f +\frac {9}{13} x^{13} b^{3} c \,d^{2} e^{2} f +\frac {3}{5} x^{15} a \,b^{2} c \,d^{2} f^{3}+\frac {3}{5} x^{15} a \,b^{2} d^{3} e \,f^{2}+\frac {1}{13} x^{13} b^{3} c^{3} f^{3}+\frac {1}{13} x^{13} b^{3} d^{3} e^{3}+\frac {1}{7} x^{7} b^{3} c^{3} e^{3}+\frac {1}{13} x^{13} a^{3} d^{3} f^{3}+\frac {9}{13} x^{13} a \,b^{2} d^{3} e^{2} f +x^{9} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{11} x^{11} a \,b^{2} d^{3} e^{3}+\frac {1}{3} x^{9} a^{3} c^{2} d \,f^{3}+\frac {9}{5} x^{5} a^{2} b \,c^{3} e^{2} f +\frac {9}{5} x^{5} a^{2} b \,c^{2} d \,e^{3}+\frac {27}{7} x^{7} a^{2} b \,c^{2} d \,e^{2} f +3 x^{9} a^{2} b \,c^{2} d e \,f^{2}+3 x^{9} a^{2} b c \,d^{2} e^{2} f +3 x^{9} a \,b^{2} c^{2} d \,e^{2} f +\frac {27}{11} x^{11} a^{2} b c \,d^{2} e \,f^{2}+\frac {27}{11} x^{11} a \,b^{2} c^{2} d e \,f^{2}+\frac {1}{7} x^{7} c^{3} a^{3} f^{3}+\frac {1}{3} x^{9} a^{2} b \,d^{3} e^{3}+\frac {1}{3} x^{9} b^{3} c^{3} e^{2} f +\frac {9}{7} x^{7} a^{2} b c \,d^{2} e^{3}+x^{9} a \,b^{2} c \,d^{2} e^{3}+\frac {9}{11} x^{11} a^{2} b \,c^{2} d \,f^{3}+\frac {1}{3} x^{9} a^{3} d^{3} e^{2} f +\frac {1}{3} x^{9} a^{2} b \,c^{3} f^{3}+\frac {1}{3} x^{9} b^{3} c^{2} d \,e^{3}+\frac {3}{11} x^{11} a^{3} c \,d^{2} f^{3}+\frac {3}{5} x^{5} c^{3} a^{3} e \,f^{2}+\frac {3}{5} x^{5} a^{3} c \,d^{2} e^{3}+\frac {3}{5} x^{5} a \,b^{2} c^{3} e^{3}+\frac {9}{7} x^{7} a^{3} c \,d^{2} e^{2} f +\frac {9}{7} x^{7} a^{2} b \,c^{3} e \,f^{2}+\frac {9}{7} x^{7} a^{3} c^{2} d e \,f^{2}+\frac {3}{11} x^{11} a^{3} d^{3} e \,f^{2}+\frac {3}{11} x^{11} a \,b^{2} c^{3} f^{3}+\frac {1}{19} b^{3} d^{3} f^{3} x^{19}\) | \(985\) |
| parallelrisch | \(\frac {9}{11} x^{11} a^{2} b \,d^{3} e^{2} f +\frac {3}{17} x^{17} a \,b^{2} d^{3} f^{3}+\frac {3}{17} x^{17} b^{3} c \,d^{2} f^{3}+\frac {3}{17} x^{17} b^{3} d^{3} e \,f^{2}+a^{3} c^{3} e^{2} f \,x^{3}+a^{3} c^{2} d \,e^{3} x^{3}+\frac {9}{13} x^{13} a^{2} b \,d^{3} e \,f^{2}+\frac {3}{5} x^{15} b^{3} c \,d^{2} e \,f^{2}+\frac {27}{11} x^{11} a \,b^{2} c \,d^{2} e^{2} f +\frac {27}{13} x^{13} a \,b^{2} c \,d^{2} e \,f^{2}+\frac {3}{11} x^{11} b^{3} c^{3} e \,f^{2}+\frac {9}{13} x^{13} a^{2} b c \,d^{2} f^{3}+\frac {9}{11} x^{11} b^{3} c^{2} d \,e^{2} f +\frac {9}{5} x^{5} a^{3} c^{2} d \,e^{2} f +c^{3} a^{3} e^{3} x +\frac {1}{7} x^{7} a^{3} d^{3} e^{3}+\frac {9}{13} x^{13} b^{3} c^{2} d e \,f^{2}+\frac {9}{7} x^{7} a \,b^{2} c^{3} e^{2} f +\frac {3}{11} x^{11} b^{3} c \,d^{2} e^{3}+\frac {1}{5} x^{15} a^{2} b \,d^{3} f^{3}+\frac {1}{5} x^{15} b^{3} c^{2} d \,f^{3}+a^{2} b \,c^{3} e^{3} x^{3}+\frac {9}{7} x^{7} a \,b^{2} c^{2} d \,e^{3}+\frac {9}{13} x^{13} a \,b^{2} c^{2} d \,f^{3}+x^{9} a \,b^{2} c^{3} e \,f^{2}+\frac {1}{5} x^{15} b^{3} d^{3} e^{2} f +\frac {9}{13} x^{13} b^{3} c \,d^{2} e^{2} f +\frac {3}{5} x^{15} a \,b^{2} c \,d^{2} f^{3}+\frac {3}{5} x^{15} a \,b^{2} d^{3} e \,f^{2}+\frac {1}{13} x^{13} b^{3} c^{3} f^{3}+\frac {1}{13} x^{13} b^{3} d^{3} e^{3}+\frac {1}{7} x^{7} b^{3} c^{3} e^{3}+\frac {1}{13} x^{13} a^{3} d^{3} f^{3}+\frac {9}{13} x^{13} a \,b^{2} d^{3} e^{2} f +x^{9} a^{3} c \,d^{2} e \,f^{2}+\frac {3}{11} x^{11} a \,b^{2} d^{3} e^{3}+\frac {1}{3} x^{9} a^{3} c^{2} d \,f^{3}+\frac {9}{5} x^{5} a^{2} b \,c^{3} e^{2} f +\frac {9}{5} x^{5} a^{2} b \,c^{2} d \,e^{3}+\frac {27}{7} x^{7} a^{2} b \,c^{2} d \,e^{2} f +3 x^{9} a^{2} b \,c^{2} d e \,f^{2}+3 x^{9} a^{2} b c \,d^{2} e^{2} f +3 x^{9} a \,b^{2} c^{2} d \,e^{2} f +\frac {27}{11} x^{11} a^{2} b c \,d^{2} e \,f^{2}+\frac {27}{11} x^{11} a \,b^{2} c^{2} d e \,f^{2}+\frac {1}{7} x^{7} c^{3} a^{3} f^{3}+\frac {1}{3} x^{9} a^{2} b \,d^{3} e^{3}+\frac {1}{3} x^{9} b^{3} c^{3} e^{2} f +\frac {9}{7} x^{7} a^{2} b c \,d^{2} e^{3}+x^{9} a \,b^{2} c \,d^{2} e^{3}+\frac {9}{11} x^{11} a^{2} b \,c^{2} d \,f^{3}+\frac {1}{3} x^{9} a^{3} d^{3} e^{2} f +\frac {1}{3} x^{9} a^{2} b \,c^{3} f^{3}+\frac {1}{3} x^{9} b^{3} c^{2} d \,e^{3}+\frac {3}{11} x^{11} a^{3} c \,d^{2} f^{3}+\frac {3}{5} x^{5} c^{3} a^{3} e \,f^{2}+\frac {3}{5} x^{5} a^{3} c \,d^{2} e^{3}+\frac {3}{5} x^{5} a \,b^{2} c^{3} e^{3}+\frac {9}{7} x^{7} a^{3} c \,d^{2} e^{2} f +\frac {9}{7} x^{7} a^{2} b \,c^{3} e \,f^{2}+\frac {9}{7} x^{7} a^{3} c^{2} d e \,f^{2}+\frac {3}{11} x^{11} a^{3} d^{3} e \,f^{2}+\frac {3}{11} x^{11} a \,b^{2} c^{3} f^{3}+\frac {1}{19} b^{3} d^{3} f^{3} x^{19}\) | \(985\) |
| orering | \(\frac {x \left (255255 b^{3} d^{3} f^{3} x^{18}+855855 a \,b^{2} d^{3} f^{3} x^{16}+855855 b^{3} c \,d^{2} f^{3} x^{16}+855855 b^{3} d^{3} e \,f^{2} x^{16}+969969 a^{2} b \,d^{3} f^{3} x^{14}+2909907 a \,b^{2} c \,d^{2} f^{3} x^{14}+2909907 a \,b^{2} d^{3} e \,f^{2} x^{14}+969969 b^{3} c^{2} d \,f^{3} x^{14}+2909907 b^{3} c \,d^{2} e \,f^{2} x^{14}+969969 b^{3} d^{3} e^{2} f \,x^{14}+373065 a^{3} d^{3} f^{3} x^{12}+3357585 a^{2} b c \,d^{2} f^{3} x^{12}+3357585 a^{2} b \,d^{3} e \,f^{2} x^{12}+3357585 a \,b^{2} c^{2} d \,f^{3} x^{12}+10072755 a \,b^{2} c \,d^{2} e \,f^{2} x^{12}+3357585 a \,b^{2} d^{3} e^{2} f \,x^{12}+373065 b^{3} c^{3} f^{3} x^{12}+3357585 b^{3} c^{2} d e \,f^{2} x^{12}+3357585 b^{3} c \,d^{2} e^{2} f \,x^{12}+373065 b^{3} d^{3} e^{3} x^{12}+1322685 a^{3} c \,d^{2} f^{3} x^{10}+1322685 a^{3} d^{3} e \,f^{2} x^{10}+3968055 a^{2} b \,c^{2} d \,f^{3} x^{10}+11904165 a^{2} b c \,d^{2} e \,f^{2} x^{10}+3968055 a^{2} b \,d^{3} e^{2} f \,x^{10}+1322685 a \,b^{2} c^{3} f^{3} x^{10}+11904165 a \,b^{2} c^{2} d e \,f^{2} x^{10}+11904165 a \,b^{2} c \,d^{2} e^{2} f \,x^{10}+1322685 a \,b^{2} d^{3} e^{3} x^{10}+1322685 b^{3} c^{3} e \,f^{2} x^{10}+3968055 b^{3} c^{2} d \,e^{2} f \,x^{10}+1322685 b^{3} c \,d^{2} e^{3} x^{10}+1616615 a^{3} c^{2} d \,f^{3} x^{8}+4849845 a^{3} c \,d^{2} e \,f^{2} x^{8}+1616615 a^{3} d^{3} e^{2} f \,x^{8}+1616615 a^{2} b \,c^{3} f^{3} x^{8}+14549535 a^{2} b \,c^{2} d e \,f^{2} x^{8}+14549535 a^{2} b c \,d^{2} e^{2} f \,x^{8}+1616615 a^{2} b \,d^{3} e^{3} x^{8}+4849845 a \,b^{2} c^{3} e \,f^{2} x^{8}+14549535 a \,b^{2} c^{2} d \,e^{2} f \,x^{8}+4849845 a \,b^{2} c \,d^{2} e^{3} x^{8}+1616615 b^{3} c^{3} e^{2} f \,x^{8}+1616615 b^{3} c^{2} d \,e^{3} x^{8}+692835 a^{3} c^{3} f^{3} x^{6}+6235515 a^{3} c^{2} d e \,f^{2} x^{6}+6235515 a^{3} c \,d^{2} e^{2} f \,x^{6}+692835 a^{3} d^{3} e^{3} x^{6}+6235515 a^{2} b \,c^{3} e \,f^{2} x^{6}+18706545 a^{2} b \,c^{2} d \,e^{2} f \,x^{6}+6235515 a^{2} b c \,d^{2} e^{3} x^{6}+6235515 a \,b^{2} c^{3} e^{2} f \,x^{6}+6235515 a \,b^{2} c^{2} d \,e^{3} x^{6}+692835 b^{3} c^{3} e^{3} x^{6}+2909907 a^{3} c^{3} e \,f^{2} x^{4}+8729721 a^{3} c^{2} d \,e^{2} f \,x^{4}+2909907 a^{3} c \,d^{2} e^{3} x^{4}+8729721 a^{2} b \,c^{3} e^{2} f \,x^{4}+8729721 a^{2} b \,c^{2} d \,e^{3} x^{4}+2909907 a \,b^{2} c^{3} e^{3} x^{4}+4849845 a^{3} c^{3} e^{2} f \,x^{2}+4849845 a^{3} c^{2} d \,e^{3} x^{2}+4849845 a^{2} b \,c^{3} e^{3} x^{2}+4849845 c^{3} a^{3} e^{3}\right )}{4849845}\) | \(994\) |
Input:
int((b*x^2+a)^3*(d*x^2+c)^3*(f*x^2+e)^3,x,method=_RETURNVERBOSE)
Output:
1/19*b^3*d^3*f^3*x^19+1/17*((3*a*b^2*d^3+3*b^3*c*d^2)*f^3+3*b^3*d^3*e*f^2) *x^17+1/15*((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^15+1/13*((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^13+1/11*((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^11+1/9*((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^9+1/7*(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^7+1/5*(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^5+1/3*(3*c^3*a^3*e^2*f+(3*a^3*c^2*d+3*a^2*b*c^3)*e^3)*x^3+c^3*a^ 3*e^3*x
Time = 0.08 (sec) , antiderivative size = 727, normalized size of antiderivative = 1.11 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx=\frac {1}{19} \, b^{3} d^{3} f^{3} x^{19} + \frac {3}{17} \, {\left (b^{3} d^{3} e f^{2} + {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{3}\right )} x^{17} + \frac {1}{5} \, {\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^{15} + \frac {1}{13} \, {\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^{13} + \frac {3}{11} \, {\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^{11} + a^{3} c^{3} e^{3} x + \frac {1}{3} \, {\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^{9} + \frac {1}{7} \, {\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^{7} + \frac {3}{5} \, {\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^{5} + {\left (a^{3} c^{3} e^{2} f + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e^{3}\right )} x^{3} \] Input:
integrate((b*x^2+a)^3*(d*x^2+c)^3*(f*x^2+e)^3,x, algorithm="fricas")
Output:
1/19*b^3*d^3*f^3*x^19 + 3/17*(b^3*d^3*e*f^2 + (b^3*c*d^2 + a*b^2*d^3)*f^3) *x^17 + 1/5*(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^15 + 1/13*(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^13 + 3/11*((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^11 + a^3*c^3*e^3*x + 1/3*((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^9 + 1/7*(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^7 + 3/5*(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^5 + (a^3*c^3*e^2*f + (a^2*b*c^3 + a^3*c^2*d)*e^3)*x^3
Time = 0.08 (sec) , antiderivative size = 1008, normalized size of antiderivative = 1.54 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx =\text {Too large to display} \] Input:
integrate((b*x**2+a)**3*(d*x**2+c)**3*(f*x**2+e)**3,x)
Output:
a**3*c**3*e**3*x + b**3*d**3*f**3*x**19/19 + x**17*(3*a*b**2*d**3*f**3/17 + 3*b**3*c*d**2*f**3/17 + 3*b**3*d**3*e*f**2/17) + x**15*(a**2*b*d**3*f**3 /5 + 3*a*b**2*c*d**2*f**3/5 + 3*a*b**2*d**3*e*f**2/5 + b**3*c**2*d*f**3/5 + 3*b**3*c*d**2*e*f**2/5 + b**3*d**3*e**2*f/5) + x**13*(a**3*d**3*f**3/13 + 9*a**2*b*c*d**2*f**3/13 + 9*a**2*b*d**3*e*f**2/13 + 9*a*b**2*c**2*d*f**3 /13 + 27*a*b**2*c*d**2*e*f**2/13 + 9*a*b**2*d**3*e**2*f/13 + b**3*c**3*f** 3/13 + 9*b**3*c**2*d*e*f**2/13 + 9*b**3*c*d**2*e**2*f/13 + b**3*d**3*e**3/ 13) + x**11*(3*a**3*c*d**2*f**3/11 + 3*a**3*d**3*e*f**2/11 + 9*a**2*b*c**2 *d*f**3/11 + 27*a**2*b*c*d**2*e*f**2/11 + 9*a**2*b*d**3*e**2*f/11 + 3*a*b* *2*c**3*f**3/11 + 27*a*b**2*c**2*d*e*f**2/11 + 27*a*b**2*c*d**2*e**2*f/11 + 3*a*b**2*d**3*e**3/11 + 3*b**3*c**3*e*f**2/11 + 9*b**3*c**2*d*e**2*f/11 + 3*b**3*c*d**2*e**3/11) + x**9*(a**3*c**2*d*f**3/3 + a**3*c*d**2*e*f**2 + a**3*d**3*e**2*f/3 + a**2*b*c**3*f**3/3 + 3*a**2*b*c**2*d*e*f**2 + 3*a**2 *b*c*d**2*e**2*f + a**2*b*d**3*e**3/3 + a*b**2*c**3*e*f**2 + 3*a*b**2*c**2 *d*e**2*f + a*b**2*c*d**2*e**3 + b**3*c**3*e**2*f/3 + b**3*c**2*d*e**3/3) + x**7*(a**3*c**3*f**3/7 + 9*a**3*c**2*d*e*f**2/7 + 9*a**3*c*d**2*e**2*f/7 + a**3*d**3*e**3/7 + 9*a**2*b*c**3*e*f**2/7 + 27*a**2*b*c**2*d*e**2*f/7 + 9*a**2*b*c*d**2*e**3/7 + 9*a*b**2*c**3*e**2*f/7 + 9*a*b**2*c**2*d*e**3/7 + b**3*c**3*e**3/7) + x**5*(3*a**3*c**3*e*f**2/5 + 9*a**3*c**2*d*e**2*f/5 + 3*a**3*c*d**2*e**3/5 + 9*a**2*b*c**3*e**2*f/5 + 9*a**2*b*c**2*d*e**3/...
Time = 0.04 (sec) , antiderivative size = 727, normalized size of antiderivative = 1.11 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx=\frac {1}{19} \, b^{3} d^{3} f^{3} x^{19} + \frac {3}{17} \, {\left (b^{3} d^{3} e f^{2} + {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{3}\right )} x^{17} + \frac {1}{5} \, {\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^{15} + \frac {1}{13} \, {\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^{13} + \frac {3}{11} \, {\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^{11} + a^{3} c^{3} e^{3} x + \frac {1}{3} \, {\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^{9} + \frac {1}{7} \, {\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^{7} + \frac {3}{5} \, {\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^{5} + {\left (a^{3} c^{3} e^{2} f + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} e^{3}\right )} x^{3} \] Input:
integrate((b*x^2+a)^3*(d*x^2+c)^3*(f*x^2+e)^3,x, algorithm="maxima")
Output:
1/19*b^3*d^3*f^3*x^19 + 3/17*(b^3*d^3*e*f^2 + (b^3*c*d^2 + a*b^2*d^3)*f^3) *x^17 + 1/5*(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^15 + 1/13*(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^13 + 3/11*((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^11 + a^3*c^3*e^3*x + 1/3*((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^9 + 1/7*(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^7 + 3/5*(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^5 + (a^3*c^3*e^2*f + (a^2*b*c^3 + a^3*c^2*d)*e^3)*x^3
Time = 0.12 (sec) , antiderivative size = 984, normalized size of antiderivative = 1.51 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx =\text {Too large to display} \] Input:
integrate((b*x^2+a)^3*(d*x^2+c)^3*(f*x^2+e)^3,x, algorithm="giac")
Output:
1/19*b^3*d^3*f^3*x^19 + 3/17*b^3*d^3*e*f^2*x^17 + 3/17*b^3*c*d^2*f^3*x^17 + 3/17*a*b^2*d^3*f^3*x^17 + 1/5*b^3*d^3*e^2*f*x^15 + 3/5*b^3*c*d^2*e*f^2*x ^15 + 3/5*a*b^2*d^3*e*f^2*x^15 + 1/5*b^3*c^2*d*f^3*x^15 + 3/5*a*b^2*c*d^2* f^3*x^15 + 1/5*a^2*b*d^3*f^3*x^15 + 1/13*b^3*d^3*e^3*x^13 + 9/13*b^3*c*d^2 *e^2*f*x^13 + 9/13*a*b^2*d^3*e^2*f*x^13 + 9/13*b^3*c^2*d*e*f^2*x^13 + 27/1 3*a*b^2*c*d^2*e*f^2*x^13 + 9/13*a^2*b*d^3*e*f^2*x^13 + 1/13*b^3*c^3*f^3*x^ 13 + 9/13*a*b^2*c^2*d*f^3*x^13 + 9/13*a^2*b*c*d^2*f^3*x^13 + 1/13*a^3*d^3* f^3*x^13 + 3/11*b^3*c*d^2*e^3*x^11 + 3/11*a*b^2*d^3*e^3*x^11 + 9/11*b^3*c^ 2*d*e^2*f*x^11 + 27/11*a*b^2*c*d^2*e^2*f*x^11 + 9/11*a^2*b*d^3*e^2*f*x^11 + 3/11*b^3*c^3*e*f^2*x^11 + 27/11*a*b^2*c^2*d*e*f^2*x^11 + 27/11*a^2*b*c*d ^2*e*f^2*x^11 + 3/11*a^3*d^3*e*f^2*x^11 + 3/11*a*b^2*c^3*f^3*x^11 + 9/11*a ^2*b*c^2*d*f^3*x^11 + 3/11*a^3*c*d^2*f^3*x^11 + 1/3*b^3*c^2*d*e^3*x^9 + a* b^2*c*d^2*e^3*x^9 + 1/3*a^2*b*d^3*e^3*x^9 + 1/3*b^3*c^3*e^2*f*x^9 + 3*a*b^ 2*c^2*d*e^2*f*x^9 + 3*a^2*b*c*d^2*e^2*f*x^9 + 1/3*a^3*d^3*e^2*f*x^9 + a*b^ 2*c^3*e*f^2*x^9 + 3*a^2*b*c^2*d*e*f^2*x^9 + a^3*c*d^2*e*f^2*x^9 + 1/3*a^2* b*c^3*f^3*x^9 + 1/3*a^3*c^2*d*f^3*x^9 + 1/7*b^3*c^3*e^3*x^7 + 9/7*a*b^2*c^ 2*d*e^3*x^7 + 9/7*a^2*b*c*d^2*e^3*x^7 + 1/7*a^3*d^3*e^3*x^7 + 9/7*a*b^2*c^ 3*e^2*f*x^7 + 27/7*a^2*b*c^2*d*e^2*f*x^7 + 9/7*a^3*c*d^2*e^2*f*x^7 + 9/7*a ^2*b*c^3*e*f^2*x^7 + 9/7*a^3*c^2*d*e*f^2*x^7 + 1/7*a^3*c^3*f^3*x^7 + 3/5*a *b^2*c^3*e^3*x^5 + 9/5*a^2*b*c^2*d*e^3*x^5 + 3/5*a^3*c*d^2*e^3*x^5 + 9/...
Time = 0.22 (sec) , antiderivative size = 784, normalized size of antiderivative = 1.20 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx=x^{13}\,\left (\frac {a^3\,d^3\,f^3}{13}+\frac {9\,a^2\,b\,c\,d^2\,f^3}{13}+\frac {9\,a^2\,b\,d^3\,e\,f^2}{13}+\frac {9\,a\,b^2\,c^2\,d\,f^3}{13}+\frac {27\,a\,b^2\,c\,d^2\,e\,f^2}{13}+\frac {9\,a\,b^2\,d^3\,e^2\,f}{13}+\frac {b^3\,c^3\,f^3}{13}+\frac {9\,b^3\,c^2\,d\,e\,f^2}{13}+\frac {9\,b^3\,c\,d^2\,e^2\,f}{13}+\frac {b^3\,d^3\,e^3}{13}\right )+x^9\,\left (\frac {a^3\,c^2\,d\,f^3}{3}+a^3\,c\,d^2\,e\,f^2+\frac {a^3\,d^3\,e^2\,f}{3}+\frac {a^2\,b\,c^3\,f^3}{3}+3\,a^2\,b\,c^2\,d\,e\,f^2+3\,a^2\,b\,c\,d^2\,e^2\,f+\frac {a^2\,b\,d^3\,e^3}{3}+a\,b^2\,c^3\,e\,f^2+3\,a\,b^2\,c^2\,d\,e^2\,f+a\,b^2\,c\,d^2\,e^3+\frac {b^3\,c^3\,e^2\,f}{3}+\frac {b^3\,c^2\,d\,e^3}{3}\right )+x^{11}\,\left (\frac {3\,a^3\,c\,d^2\,f^3}{11}+\frac {3\,a^3\,d^3\,e\,f^2}{11}+\frac {9\,a^2\,b\,c^2\,d\,f^3}{11}+\frac {27\,a^2\,b\,c\,d^2\,e\,f^2}{11}+\frac {9\,a^2\,b\,d^3\,e^2\,f}{11}+\frac {3\,a\,b^2\,c^3\,f^3}{11}+\frac {27\,a\,b^2\,c^2\,d\,e\,f^2}{11}+\frac {27\,a\,b^2\,c\,d^2\,e^2\,f}{11}+\frac {3\,a\,b^2\,d^3\,e^3}{11}+\frac {3\,b^3\,c^3\,e\,f^2}{11}+\frac {9\,b^3\,c^2\,d\,e^2\,f}{11}+\frac {3\,b^3\,c\,d^2\,e^3}{11}\right )+x^7\,\left (\frac {a^3\,c^3\,f^3}{7}+\frac {9\,a^3\,c^2\,d\,e\,f^2}{7}+\frac {9\,a^3\,c\,d^2\,e^2\,f}{7}+\frac {a^3\,d^3\,e^3}{7}+\frac {9\,a^2\,b\,c^3\,e\,f^2}{7}+\frac {27\,a^2\,b\,c^2\,d\,e^2\,f}{7}+\frac {9\,a^2\,b\,c\,d^2\,e^3}{7}+\frac {9\,a\,b^2\,c^3\,e^2\,f}{7}+\frac {9\,a\,b^2\,c^2\,d\,e^3}{7}+\frac {b^3\,c^3\,e^3}{7}\right )+a^3\,c^3\,e^3\,x+\frac {b^3\,d^3\,f^3\,x^{19}}{19}+a^2\,c^2\,e^2\,x^3\,\left (a\,c\,f+a\,d\,e+b\,c\,e\right )+\frac {3\,b^2\,d^2\,f^2\,x^{17}\,\left (a\,d\,f+b\,c\,f+b\,d\,e\right )}{17}+\frac {3\,a\,c\,e\,x^5\,\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 )}{5}+\frac {b\,d\,f\,x^{15}\,\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 )}{5} \] Input:
int((a + b*x^2)^3*(c + d*x^2)^3*(e + f*x^2)^3,x)
Output:
x^13*((a^3*d^3*f^3)/13 + (b^3*c^3*f^3)/13 + (b^3*d^3*e^3)/13 + (9*a*b^2*c^ 2*d*f^3)/13 + (9*a^2*b*c*d^2*f^3)/13 + (9*a*b^2*d^3*e^2*f)/13 + (9*a^2*b*d ^3*e*f^2)/13 + (9*b^3*c*d^2*e^2*f)/13 + (9*b^3*c^2*d*e*f^2)/13 + (27*a*b^2 *c*d^2*e*f^2)/13) + x^9*((a^2*b*c^3*f^3)/3 + (a^2*b*d^3*e^3)/3 + (a^3*c^2* d*f^3)/3 + (b^3*c^2*d*e^3)/3 + (a^3*d^3*e^2*f)/3 + (b^3*c^3*e^2*f)/3 + a*b ^2*c*d^2*e^3 + a*b^2*c^3*e*f^2 + a^3*c*d^2*e*f^2 + 3*a*b^2*c^2*d*e^2*f + 3 *a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2) + x^11*((3*a*b^2*c^3*f^3)/11 + ( 3*a*b^2*d^3*e^3)/11 + (3*a^3*c*d^2*f^3)/11 + (3*b^3*c*d^2*e^3)/11 + (3*a^3 *d^3*e*f^2)/11 + (3*b^3*c^3*e*f^2)/11 + (9*a^2*b*c^2*d*f^3)/11 + (9*a^2*b* d^3*e^2*f)/11 + (9*b^3*c^2*d*e^2*f)/11 + (27*a*b^2*c*d^2*e^2*f)/11 + (27*a *b^2*c^2*d*e*f^2)/11 + (27*a^2*b*c*d^2*e*f^2)/11) + x^7*((a^3*c^3*f^3)/7 + (a^3*d^3*e^3)/7 + (b^3*c^3*e^3)/7 + (9*a*b^2*c^2*d*e^3)/7 + (9*a^2*b*c*d^ 2*e^3)/7 + (9*a*b^2*c^3*e^2*f)/7 + (9*a^2*b*c^3*e*f^2)/7 + (9*a^3*c*d^2*e^ 2*f)/7 + (9*a^3*c^2*d*e*f^2)/7 + (27*a^2*b*c^2*d*e^2*f)/7) + a^3*c^3*e^3*x + (b^3*d^3*f^3*x^19)/19 + a^2*c^2*e^2*x^3*(a*c*f + a*d*e + b*c*e) + (3*b^ 2*d^2*f^2*x^17*(a*d*f + b*c*f + b*d*e))/17 + (3*a*c*e*x^5*(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)) /5 + (b*d*f*x^15*(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))/5
Time = 0.15 (sec) , antiderivative size = 993, normalized size of antiderivative = 1.52 \[ \int \left (a+b x^2\right )^3 \left (c+d x^2\right )^3 \left (e+f x^2\right )^3 \, dx =\text {Too large to display} \] Input:
int((b*x^2+a)^3*(d*x^2+c)^3*(f*x^2+e)^3,x)
Output:
(x*(4849845*a**3*c**3*e**3 + 4849845*a**3*c**3*e**2*f*x**2 + 2909907*a**3* c**3*e*f**2*x**4 + 692835*a**3*c**3*f**3*x**6 + 4849845*a**3*c**2*d*e**3*x **2 + 8729721*a**3*c**2*d*e**2*f*x**4 + 6235515*a**3*c**2*d*e*f**2*x**6 + 1616615*a**3*c**2*d*f**3*x**8 + 2909907*a**3*c*d**2*e**3*x**4 + 6235515*a* *3*c*d**2*e**2*f*x**6 + 4849845*a**3*c*d**2*e*f**2*x**8 + 1322685*a**3*c*d **2*f**3*x**10 + 692835*a**3*d**3*e**3*x**6 + 1616615*a**3*d**3*e**2*f*x** 8 + 1322685*a**3*d**3*e*f**2*x**10 + 373065*a**3*d**3*f**3*x**12 + 4849845 *a**2*b*c**3*e**3*x**2 + 8729721*a**2*b*c**3*e**2*f*x**4 + 6235515*a**2*b* c**3*e*f**2*x**6 + 1616615*a**2*b*c**3*f**3*x**8 + 8729721*a**2*b*c**2*d*e **3*x**4 + 18706545*a**2*b*c**2*d*e**2*f*x**6 + 14549535*a**2*b*c**2*d*e*f **2*x**8 + 3968055*a**2*b*c**2*d*f**3*x**10 + 6235515*a**2*b*c*d**2*e**3*x **6 + 14549535*a**2*b*c*d**2*e**2*f*x**8 + 11904165*a**2*b*c*d**2*e*f**2*x **10 + 3357585*a**2*b*c*d**2*f**3*x**12 + 1616615*a**2*b*d**3*e**3*x**8 + 3968055*a**2*b*d**3*e**2*f*x**10 + 3357585*a**2*b*d**3*e*f**2*x**12 + 9699 69*a**2*b*d**3*f**3*x**14 + 2909907*a*b**2*c**3*e**3*x**4 + 6235515*a*b**2 *c**3*e**2*f*x**6 + 4849845*a*b**2*c**3*e*f**2*x**8 + 1322685*a*b**2*c**3* f**3*x**10 + 6235515*a*b**2*c**2*d*e**3*x**6 + 14549535*a*b**2*c**2*d*e**2 *f*x**8 + 11904165*a*b**2*c**2*d*e*f**2*x**10 + 3357585*a*b**2*c**2*d*f**3 *x**12 + 4849845*a*b**2*c*d**2*e**3*x**8 + 11904165*a*b**2*c*d**2*e**2*f*x **10 + 10072755*a*b**2*c*d**2*e*f**2*x**12 + 2909907*a*b**2*c*d**2*f**3...