Integrand size = 25, antiderivative size = 80 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=144 x+384 x^2+\frac {3016 x^3}{3}+1838 x^4+\frac {14801 x^5}{5}+\frac {10771 x^6}{3}+\frac {27763 x^7}{7}+3315 x^8+\frac {24859 x^9}{9}+1571 x^{10}+\frac {11525 x^{11}}{11}+\frac {875 x^{12}}{3}+\frac {2500 x^{13}}{13} \] Output:
144*x+384*x^2+3016/3*x^3+1838*x^4+14801/5*x^5+10771/3*x^6+27763/7*x^7+3315 *x^8+24859/9*x^9+1571*x^10+11525/11*x^11+875/3*x^12+2500/13*x^13
Time = 0.01 (sec) , antiderivative size = 80, normalized size of antiderivative = 1.00 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=144 x+384 x^2+\frac {3016 x^3}{3}+1838 x^4+\frac {14801 x^5}{5}+\frac {10771 x^6}{3}+\frac {27763 x^7}{7}+3315 x^8+\frac {24859 x^9}{9}+1571 x^{10}+\frac {11525 x^{11}}{11}+\frac {875 x^{12}}{3}+\frac {2500 x^{13}}{13} \] Input:
Integrate[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^4,x]
Output:
144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (27763*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/3 + (2500*x^13)/13
Time = 0.27 (sec) , antiderivative size = 80, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {2188, 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.
\(\displaystyle \int \left (2 x^2-x+3\right )^2 \left (5 x^2+3 x+2\right )^4 \, dx\) |
\(\Big \downarrow \) 2188 |
\(\displaystyle \int \left (2500 x^{12}+3500 x^{11}+11525 x^{10}+15710 x^9+24859 x^8+26520 x^7+27763 x^6+21542 x^5+14801 x^4+7352 x^3+3016 x^2+768 x+144\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {2500 x^{13}}{13}+\frac {875 x^{12}}{3}+\frac {11525 x^{11}}{11}+1571 x^{10}+\frac {24859 x^9}{9}+3315 x^8+\frac {27763 x^7}{7}+\frac {10771 x^6}{3}+\frac {14801 x^5}{5}+1838 x^4+\frac {3016 x^3}{3}+384 x^2+144 x\) |
Input:
Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^4,x]
Output:
144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (27763*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/3 + (2500*x^13)/13
Int[(Pq_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[Expand Integrand[Pq*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c}, x] && PolyQ[Pq , x] && IGtQ[p, -2]
Time = 1.69 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.80
method | result | size |
orering | \(\frac {x \left (8662500 x^{12}+13138125 x^{11}+47194875 x^{10}+70765695 x^{9}+124419295 x^{8}+149324175 x^{7}+178654905 x^{6}+161726565 x^{5}+133342209 x^{4}+82792710 x^{3}+45285240 x^{2}+17297280 x +6486480\right )}{45045}\) | \(64\) |
gosper | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
default | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
norman | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
risch | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
parallelrisch | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
Input:
int((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x,method=_RETURNVERBOSE)
Output:
1/45045*x*(8662500*x^12+13138125*x^11+47194875*x^10+70765695*x^9+124419295 *x^8+149324175*x^7+178654905*x^6+161726565*x^5+133342209*x^4+82792710*x^3+ 45285240*x^2+17297280*x+6486480)
Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.80 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=\frac {2500}{13} \, x^{13} + \frac {875}{3} \, x^{12} + \frac {11525}{11} \, x^{11} + 1571 \, x^{10} + \frac {24859}{9} \, x^{9} + 3315 \, x^{8} + \frac {27763}{7} \, x^{7} + \frac {10771}{3} \, x^{6} + \frac {14801}{5} \, x^{5} + 1838 \, x^{4} + \frac {3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \] Input:
integrate((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x, algorithm="fricas")
Output:
2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315 *x^8 + 27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 3 84*x^2 + 144*x
Time = 0.07 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.95 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=\frac {2500 x^{13}}{13} + \frac {875 x^{12}}{3} + \frac {11525 x^{11}}{11} + 1571 x^{10} + \frac {24859 x^{9}}{9} + 3315 x^{8} + \frac {27763 x^{7}}{7} + \frac {10771 x^{6}}{3} + \frac {14801 x^{5}}{5} + 1838 x^{4} + \frac {3016 x^{3}}{3} + 384 x^{2} + 144 x \] Input:
integrate((2*x**2-x+3)**2*(5*x**2+3*x+2)**4,x)
Output:
2500*x**13/13 + 875*x**12/3 + 11525*x**11/11 + 1571*x**10 + 24859*x**9/9 + 3315*x**8 + 27763*x**7/7 + 10771*x**6/3 + 14801*x**5/5 + 1838*x**4 + 3016 *x**3/3 + 384*x**2 + 144*x
Time = 0.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.80 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=\frac {2500}{13} \, x^{13} + \frac {875}{3} \, x^{12} + \frac {11525}{11} \, x^{11} + 1571 \, x^{10} + \frac {24859}{9} \, x^{9} + 3315 \, x^{8} + \frac {27763}{7} \, x^{7} + \frac {10771}{3} \, x^{6} + \frac {14801}{5} \, x^{5} + 1838 \, x^{4} + \frac {3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \] Input:
integrate((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x, algorithm="maxima")
Output:
2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315 *x^8 + 27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 3 84*x^2 + 144*x
Time = 0.13 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.80 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=\frac {2500}{13} \, x^{13} + \frac {875}{3} \, x^{12} + \frac {11525}{11} \, x^{11} + 1571 \, x^{10} + \frac {24859}{9} \, x^{9} + 3315 \, x^{8} + \frac {27763}{7} \, x^{7} + \frac {10771}{3} \, x^{6} + \frac {14801}{5} \, x^{5} + 1838 \, x^{4} + \frac {3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \] Input:
integrate((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x, algorithm="giac")
Output:
2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315 *x^8 + 27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 3 84*x^2 + 144*x
Time = 0.11 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.80 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=\frac {2500\,x^{13}}{13}+\frac {875\,x^{12}}{3}+\frac {11525\,x^{11}}{11}+1571\,x^{10}+\frac {24859\,x^9}{9}+3315\,x^8+\frac {27763\,x^7}{7}+\frac {10771\,x^6}{3}+\frac {14801\,x^5}{5}+1838\,x^4+\frac {3016\,x^3}{3}+384\,x^2+144\,x \] Input:
int((2*x^2 - x + 3)^2*(3*x + 5*x^2 + 2)^4,x)
Output:
144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (27763*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/3 + (2500*x^13)/13
Time = 0.19 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.79 \[ \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx=\frac {x \left (8662500 x^{12}+13138125 x^{11}+47194875 x^{10}+70765695 x^{9}+124419295 x^{8}+149324175 x^{7}+178654905 x^{6}+161726565 x^{5}+133342209 x^{4}+82792710 x^{3}+45285240 x^{2}+17297280 x +6486480\right )}{45045} \] Input:
int((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x)
Output:
(x*(8662500*x**12 + 13138125*x**11 + 47194875*x**10 + 70765695*x**9 + 1244 19295*x**8 + 149324175*x**7 + 178654905*x**6 + 161726565*x**5 + 133342209* x**4 + 82792710*x**3 + 45285240*x**2 + 17297280*x + 6486480))/45045