Integrand size = 25, antiderivative size = 82 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=216 x+378 x^2+870 x^3+\frac {4483 x^4}{4}+\frac {8292 x^5}{5}+\frac {2873 x^6}{2}+\frac {12016 x^7}{7}+\frac {7869 x^8}{8}+\frac {3316 x^9}{3}+\frac {3061 x^{10}}{10}+\frac {4830 x^{11}}{11}+25 x^{12}+\frac {1000 x^{13}}{13} \] Output:
216*x+378*x^2+870*x^3+4483/4*x^4+8292/5*x^5+2873/2*x^6+12016/7*x^7+7869/8* x^8+3316/3*x^9+3061/10*x^10+4830/11*x^11+25*x^12+1000/13*x^13
Time = 0.00 (sec) , antiderivative size = 82, normalized size of antiderivative = 1.00 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=216 x+378 x^2+870 x^3+\frac {4483 x^4}{4}+\frac {8292 x^5}{5}+\frac {2873 x^6}{2}+\frac {12016 x^7}{7}+\frac {7869 x^8}{8}+\frac {3316 x^9}{3}+\frac {3061 x^{10}}{10}+\frac {4830 x^{11}}{11}+25 x^{12}+\frac {1000 x^{13}}{13} \] Input:
Integrate[(3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^3,x]
Output:
216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + ( 12016*x^7)/7 + (7869*x^8)/8 + (3316*x^9)/3 + (3061*x^10)/10 + (4830*x^11)/ 11 + 25*x^12 + (1000*x^13)/13
Time = 0.26 (sec) , antiderivative size = 82, 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.
\(\displaystyle \int \left (2 x^2-x+3\right )^3 \left (5 x^2+3 x+2\right )^3 \, dx\) |
\(\Big \downarrow \) 2188 |
\(\displaystyle \int \left (1000 x^{12}+300 x^{11}+4830 x^{10}+3061 x^9+9948 x^8+7869 x^7+12016 x^6+8619 x^5+8292 x^4+4483 x^3+2610 x^2+756 x+216\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {1000 x^{13}}{13}+25 x^{12}+\frac {4830 x^{11}}{11}+\frac {3061 x^{10}}{10}+\frac {3316 x^9}{3}+\frac {7869 x^8}{8}+\frac {12016 x^7}{7}+\frac {2873 x^6}{2}+\frac {8292 x^5}{5}+\frac {4483 x^4}{4}+870 x^3+378 x^2+216 x\) |
Input:
Int[(3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^3,x]
Output:
216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + ( 12016*x^7)/7 + (7869*x^8)/8 + (3316*x^9)/3 + (3061*x^10)/10 + (4830*x^11)/ 11 + 25*x^12 + (1000*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 = 1.72 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.78
method | result | size |
orering | \(\frac {x \left (9240000 x^{12}+3003000 x^{11}+52743600 x^{10}+36768732 x^{9}+132772640 x^{8}+118153035 x^{7}+206194560 x^{6}+172552380 x^{5}+199207008 x^{4}+134624490 x^{3}+104504400 x^{2}+45405360 x +25945920\right )}{120120}\) | \(64\) |
gosper | \(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\) | \(65\) |
default | \(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\) | \(65\) |
norman | \(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\) | \(65\) |
risch | \(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\) | \(65\) |
parallelrisch | \(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\) | \(65\) |
Input:
int((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x,method=_RETURNVERBOSE)
Output:
1/120120*x*(9240000*x^12+3003000*x^11+52743600*x^10+36768732*x^9+132772640 *x^8+118153035*x^7+206194560*x^6+172552380*x^5+199207008*x^4+134624490*x^3 +104504400*x^2+45405360*x+25945920)
Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.78 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=\frac {1000}{13} \, x^{13} + 25 \, x^{12} + \frac {4830}{11} \, x^{11} + \frac {3061}{10} \, x^{10} + \frac {3316}{3} \, x^{9} + \frac {7869}{8} \, x^{8} + \frac {12016}{7} \, x^{7} + \frac {2873}{2} \, x^{6} + \frac {8292}{5} \, x^{5} + \frac {4483}{4} \, x^{4} + 870 \, x^{3} + 378 \, x^{2} + 216 \, x \] Input:
integrate((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x, algorithm="fricas")
Output:
1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8 *x^8 + 12016/7*x^7 + 2873/2*x^6 + 8292/5*x^5 + 4483/4*x^4 + 870*x^3 + 378* x^2 + 216*x
Time = 0.03 (sec) , antiderivative size = 78, normalized size of antiderivative = 0.95 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=\frac {1000 x^{13}}{13} + 25 x^{12} + \frac {4830 x^{11}}{11} + \frac {3061 x^{10}}{10} + \frac {3316 x^{9}}{3} + \frac {7869 x^{8}}{8} + \frac {12016 x^{7}}{7} + \frac {2873 x^{6}}{2} + \frac {8292 x^{5}}{5} + \frac {4483 x^{4}}{4} + 870 x^{3} + 378 x^{2} + 216 x \] Input:
integrate((2*x**2-x+3)**3*(5*x**2+3*x+2)**3,x)
Output:
1000*x**13/13 + 25*x**12 + 4830*x**11/11 + 3061*x**10/10 + 3316*x**9/3 + 7 869*x**8/8 + 12016*x**7/7 + 2873*x**6/2 + 8292*x**5/5 + 4483*x**4/4 + 870* x**3 + 378*x**2 + 216*x
Time = 0.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.78 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=\frac {1000}{13} \, x^{13} + 25 \, x^{12} + \frac {4830}{11} \, x^{11} + \frac {3061}{10} \, x^{10} + \frac {3316}{3} \, x^{9} + \frac {7869}{8} \, x^{8} + \frac {12016}{7} \, x^{7} + \frac {2873}{2} \, x^{6} + \frac {8292}{5} \, x^{5} + \frac {4483}{4} \, x^{4} + 870 \, x^{3} + 378 \, x^{2} + 216 \, x \] Input:
integrate((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x, algorithm="maxima")
Output:
1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8 *x^8 + 12016/7*x^7 + 2873/2*x^6 + 8292/5*x^5 + 4483/4*x^4 + 870*x^3 + 378* x^2 + 216*x
Time = 0.11 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.78 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=\frac {1000}{13} \, x^{13} + 25 \, x^{12} + \frac {4830}{11} \, x^{11} + \frac {3061}{10} \, x^{10} + \frac {3316}{3} \, x^{9} + \frac {7869}{8} \, x^{8} + \frac {12016}{7} \, x^{7} + \frac {2873}{2} \, x^{6} + \frac {8292}{5} \, x^{5} + \frac {4483}{4} \, x^{4} + 870 \, x^{3} + 378 \, x^{2} + 216 \, x \] Input:
integrate((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x, algorithm="giac")
Output:
1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8 *x^8 + 12016/7*x^7 + 2873/2*x^6 + 8292/5*x^5 + 4483/4*x^4 + 870*x^3 + 378* x^2 + 216*x
Time = 0.11 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.78 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=\frac {1000\,x^{13}}{13}+25\,x^{12}+\frac {4830\,x^{11}}{11}+\frac {3061\,x^{10}}{10}+\frac {3316\,x^9}{3}+\frac {7869\,x^8}{8}+\frac {12016\,x^7}{7}+\frac {2873\,x^6}{2}+\frac {8292\,x^5}{5}+\frac {4483\,x^4}{4}+870\,x^3+378\,x^2+216\,x \] Input:
int((2*x^2 - x + 3)^3*(3*x + 5*x^2 + 2)^3,x)
Output:
216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + ( 12016*x^7)/7 + (7869*x^8)/8 + (3316*x^9)/3 + (3061*x^10)/10 + (4830*x^11)/ 11 + 25*x^12 + (1000*x^13)/13
Time = 0.19 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.77 \[ \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx=\frac {x \left (9240000 x^{12}+3003000 x^{11}+52743600 x^{10}+36768732 x^{9}+132772640 x^{8}+118153035 x^{7}+206194560 x^{6}+172552380 x^{5}+199207008 x^{4}+134624490 x^{3}+104504400 x^{2}+45405360 x +25945920\right )}{120120} \] Input:
int((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x)
Output:
(x*(9240000*x**12 + 3003000*x**11 + 52743600*x**10 + 36768732*x**9 + 13277 2640*x**8 + 118153035*x**7 + 206194560*x**6 + 172552380*x**5 + 199207008*x **4 + 134624490*x**3 + 104504400*x**2 + 45405360*x + 25945920))/120120