Integrand size = 22, antiderivative size = 78 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^7}{2187}+\frac {1813 (2+3 x)^8}{5832}-\frac {10073 (2+3 x)^9}{6561}+\frac {66193 (2+3 x)^{10}}{21870}-\frac {14390 (2+3 x)^{11}}{8019}+\frac {925 (2+3 x)^{12}}{2187}-\frac {1000 (2+3 x)^{13}}{28431} \] Output:
-49/2187*(2+3*x)^7+1813/5832*(2+3*x)^8-10073/6561*(2+3*x)^9+66193/21870*(2 +3*x)^10-14390/8019*(2+3*x)^11+925/2187*(2+3*x)^12-1000/28431*(2+3*x)^13
Time = 0.00 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.95 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=1728 x+6912 x^2+8688 x^3-20140 x^4-\frac {390396 x^5}{5}-51908 x^6+155453 x^7+\frac {2623581 x^8}{8}+122655 x^9-\frac {3110589 x^{10}}{10}-\frac {5100570 x^{11}}{11}-261225 x^{12}-\frac {729000 x^{13}}{13} \] Input:
Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]
Output:
1728*x + 6912*x^2 + 8688*x^3 - 20140*x^4 - (390396*x^5)/5 - 51908*x^6 + 15 5453*x^7 + (2623581*x^8)/8 + 122655*x^9 - (3110589*x^10)/10 - (5100570*x^1 1)/11 - 261225*x^12 - (729000*x^13)/13
Time = 0.27 (sec) , antiderivative size = 78, 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.
\(\displaystyle \int (1-2 x)^3 (3 x+2)^6 (5 x+3)^3 \, dx\) |
\(\Big \downarrow \) 99 |
\(\displaystyle \int \left (-\frac {1000}{729} (3 x+2)^{12}+\frac {3700}{243} (3 x+2)^{11}-\frac {14390}{243} (3 x+2)^{10}+\frac {66193}{729} (3 x+2)^9-\frac {10073}{243} (3 x+2)^8+\frac {1813}{243} (3 x+2)^7-\frac {343}{729} (3 x+2)^6\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -\frac {1000 (3 x+2)^{13}}{28431}+\frac {925 (3 x+2)^{12}}{2187}-\frac {14390 (3 x+2)^{11}}{8019}+\frac {66193 (3 x+2)^{10}}{21870}-\frac {10073 (3 x+2)^9}{6561}+\frac {1813 (3 x+2)^8}{5832}-\frac {49 (3 x+2)^7}{2187}\) |
Input:
Int[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3,x]
Output:
(-49*(2 + 3*x)^7)/2187 + (1813*(2 + 3*x)^8)/5832 - (10073*(2 + 3*x)^9)/656 1 + (66193*(2 + 3*x)^10)/21870 - (14390*(2 + 3*x)^11)/8019 + (925*(2 + 3*x )^12)/2187 - (1000*(2 + 3*x)^13)/28431
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]))
Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82
method | result | size |
gosper | \(-\frac {x \left (320760000 x^{12}+1494207000 x^{11}+2652296400 x^{10}+1779256908 x^{9}-701586600 x^{8}-1875860415 x^{7}-889191160 x^{6}+296913760 x^{5}+446613024 x^{4}+115200800 x^{3}-49695360 x^{2}-39536640 x -9884160\right )}{5720}\) | \(64\) |
default | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
norman | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
risch | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
parallelrisch | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
orering | \(\frac {x \left (320760000 x^{12}+1494207000 x^{11}+2652296400 x^{10}+1779256908 x^{9}-701586600 x^{8}-1875860415 x^{7}-889191160 x^{6}+296913760 x^{5}+446613024 x^{4}+115200800 x^{3}-49695360 x^{2}-39536640 x -9884160\right ) \left (1-2 x \right )^{3}}{5720 \left (-1+2 x \right )^{3}}\) | \(78\) |
Input:
int((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x,method=_RETURNVERBOSE)
Output:
-1/5720*x*(320760000*x^12+1494207000*x^11+2652296400*x^10+1779256908*x^9-7 01586600*x^8-1875860415*x^7-889191160*x^6+296913760*x^5+446613024*x^4+1152 00800*x^3-49695360*x^2-39536640*x-9884160)
Time = 0.08 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \] Input:
integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm="fricas")
Output:
-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655 *x^9 + 2623581/8*x^8 + 155453*x^7 - 51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x
Time = 0.03 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.91 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=- \frac {729000 x^{13}}{13} - 261225 x^{12} - \frac {5100570 x^{11}}{11} - \frac {3110589 x^{10}}{10} + 122655 x^{9} + \frac {2623581 x^{8}}{8} + 155453 x^{7} - 51908 x^{6} - \frac {390396 x^{5}}{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x \] Input:
integrate((1-2*x)**3*(2+3*x)**6*(3+5*x)**3,x)
Output:
-729000*x**13/13 - 261225*x**12 - 5100570*x**11/11 - 3110589*x**10/10 + 12 2655*x**9 + 2623581*x**8/8 + 155453*x**7 - 51908*x**6 - 390396*x**5/5 - 20 140*x**4 + 8688*x**3 + 6912*x**2 + 1728*x
Time = 0.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \] Input:
integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm="maxima")
Output:
-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655 *x^9 + 2623581/8*x^8 + 155453*x^7 - 51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x
Time = 0.13 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \] Input:
integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm="giac")
Output:
-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655 *x^9 + 2623581/8*x^8 + 155453*x^7 - 51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x
Time = 0.05 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000\,x^{13}}{13}-261225\,x^{12}-\frac {5100570\,x^{11}}{11}-\frac {3110589\,x^{10}}{10}+122655\,x^9+\frac {2623581\,x^8}{8}+155453\,x^7-51908\,x^6-\frac {390396\,x^5}{5}-20140\,x^4+8688\,x^3+6912\,x^2+1728\,x \] Input:
int(-(2*x - 1)^3*(3*x + 2)^6*(5*x + 3)^3,x)
Output:
1728*x + 6912*x^2 + 8688*x^3 - 20140*x^4 - (390396*x^5)/5 - 51908*x^6 + 15 5453*x^7 + (2623581*x^8)/8 + 122655*x^9 - (3110589*x^10)/10 - (5100570*x^1 1)/11 - 261225*x^12 - (729000*x^13)/13
Time = 0.16 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=\frac {x \left (-320760000 x^{12}-1494207000 x^{11}-2652296400 x^{10}-1779256908 x^{9}+701586600 x^{8}+1875860415 x^{7}+889191160 x^{6}-296913760 x^{5}-446613024 x^{4}-115200800 x^{3}+49695360 x^{2}+39536640 x +9884160\right )}{5720} \] Input:
int((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x)
Output:
(x*( - 320760000*x**12 - 1494207000*x**11 - 2652296400*x**10 - 1779256908* x**9 + 701586600*x**8 + 1875860415*x**7 + 889191160*x**6 - 296913760*x**5 - 446613024*x**4 - 115200800*x**3 + 49695360*x**2 + 39536640*x + 9884160)) /5720