Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^8}{5832}+\frac {763 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{7290}+\frac {8285 (2+3 x)^{11}}{8019}-\frac {950 (2+3 x)^{12}}{2187}+\frac {500 (2+3 x)^{13}}{9477} \] Output:
-49/5832*(2+3*x)^8+763/6561*(2+3*x)^9-4099/7290*(2+3*x)^10+8285/8019*(2+3* x)^11-950/2187*(2+3*x)^12+500/9477*(2+3*x)^13
Time = 0.00 (sec) , antiderivative size = 76, normalized size of antiderivative = 1.13 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=3456 x+19872 x^2+57696 x^3+65812 x^4-\frac {495976 x^5}{5}-\frac {1393018 x^6}{3}-618582 x^7-\frac {148473 x^8}{8}+1086843 x^9+\frac {16653681 x^{10}}{10}+\frac {13774455 x^{11}}{11}+498150 x^{12}+\frac {1093500 x^{13}}{13} \] Input:
Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]
Output:
3456*x + 19872*x^2 + 57696*x^3 + 65812*x^4 - (495976*x^5)/5 - (1393018*x^6 )/3 - 618582*x^7 - (148473*x^8)/8 + 1086843*x^9 + (16653681*x^10)/10 + (13 774455*x^11)/11 + 498150*x^12 + (1093500*x^13)/13
Time = 0.25 (sec) , antiderivative size = 67, 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.
\(\displaystyle \int (1-2 x)^2 (3 x+2)^7 (5 x+3)^3 \, dx\) |
\(\Big \downarrow \) 99 |
\(\displaystyle \int \left (\frac {500}{243} (3 x+2)^{12}-\frac {3800}{243} (3 x+2)^{11}+\frac {8285}{243} (3 x+2)^{10}-\frac {4099}{243} (3 x+2)^9+\frac {763}{243} (3 x+2)^8-\frac {49}{243} (3 x+2)^7\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {500 (3 x+2)^{13}}{9477}-\frac {950 (3 x+2)^{12}}{2187}+\frac {8285 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{7290}+\frac {763 (3 x+2)^9}{6561}-\frac {49 (3 x+2)^8}{5832}\) |
Input:
Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]
Output:
(-49*(2 + 3*x)^8)/5832 + (763*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/7290 + (8285*(2 + 3*x)^11)/8019 - (950*(2 + 3*x)^12)/2187 + (500*(2 + 3*x)^13) /9477
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 = 0.96
method | result | size |
gosper | \(\frac {x \left (1443420000 x^{12}+8548254000 x^{11}+21488149800 x^{10}+28577716596 x^{9}+18650225880 x^{8}-318474585 x^{7}-10614867120 x^{6}-7968062960 x^{5}-1702189632 x^{4}+1129333920 x^{3}+990063360 x^{2}+341003520 x +59304960\right )}{17160}\) | \(64\) |
default | \(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\) | \(65\) |
norman | \(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\) | \(65\) |
risch | \(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\) | \(65\) |
parallelrisch | \(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\) | \(65\) |
orering | \(\frac {x \left (1443420000 x^{12}+8548254000 x^{11}+21488149800 x^{10}+28577716596 x^{9}+18650225880 x^{8}-318474585 x^{7}-10614867120 x^{6}-7968062960 x^{5}-1702189632 x^{4}+1129333920 x^{3}+990063360 x^{2}+341003520 x +59304960\right ) \left (1-2 x \right )^{2}}{17160 \left (-1+2 x \right )^{2}}\) | \(78\) |
Input:
int((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x,method=_RETURNVERBOSE)
Output:
1/17160*x*(1443420000*x^12+8548254000*x^11+21488149800*x^10+28577716596*x^ 9+18650225880*x^8-318474585*x^7-10614867120*x^6-7968062960*x^5-1702189632* x^4+1129333920*x^3+990063360*x^2+341003520*x+59304960)
Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=\frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \] Input:
integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="fricas")
Output:
1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086 843*x^9 - 148473/8*x^8 - 618582*x^7 - 1393018/3*x^6 - 495976/5*x^5 + 65812 *x^4 + 57696*x^3 + 19872*x^2 + 3456*x
Time = 0.03 (sec) , antiderivative size = 73, normalized size of antiderivative = 1.09 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=\frac {1093500 x^{13}}{13} + 498150 x^{12} + \frac {13774455 x^{11}}{11} + \frac {16653681 x^{10}}{10} + 1086843 x^{9} - \frac {148473 x^{8}}{8} - 618582 x^{7} - \frac {1393018 x^{6}}{3} - \frac {495976 x^{5}}{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \] Input:
integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**3,x)
Output:
1093500*x**13/13 + 498150*x**12 + 13774455*x**11/11 + 16653681*x**10/10 + 1086843*x**9 - 148473*x**8/8 - 618582*x**7 - 1393018*x**6/3 - 495976*x**5/ 5 + 65812*x**4 + 57696*x**3 + 19872*x**2 + 3456*x
Time = 0.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=\frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \] Input:
integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="maxima")
Output:
1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086 843*x^9 - 148473/8*x^8 - 618582*x^7 - 1393018/3*x^6 - 495976/5*x^5 + 65812 *x^4 + 57696*x^3 + 19872*x^2 + 3456*x
Time = 0.12 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=\frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \] Input:
integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="giac")
Output:
1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086 843*x^9 - 148473/8*x^8 - 618582*x^7 - 1393018/3*x^6 - 495976/5*x^5 + 65812 *x^4 + 57696*x^3 + 19872*x^2 + 3456*x
Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=\frac {1093500\,x^{13}}{13}+498150\,x^{12}+\frac {13774455\,x^{11}}{11}+\frac {16653681\,x^{10}}{10}+1086843\,x^9-\frac {148473\,x^8}{8}-618582\,x^7-\frac {1393018\,x^6}{3}-\frac {495976\,x^5}{5}+65812\,x^4+57696\,x^3+19872\,x^2+3456\,x \] Input:
int((2*x - 1)^2*(3*x + 2)^7*(5*x + 3)^3,x)
Output:
3456*x + 19872*x^2 + 57696*x^3 + 65812*x^4 - (495976*x^5)/5 - (1393018*x^6 )/3 - 618582*x^7 - (148473*x^8)/8 + 1086843*x^9 + (16653681*x^10)/10 + (13 774455*x^11)/11 + 498150*x^12 + (1093500*x^13)/13
Time = 0.15 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx=\frac {x \left (1443420000 x^{12}+8548254000 x^{11}+21488149800 x^{10}+28577716596 x^{9}+18650225880 x^{8}-318474585 x^{7}-10614867120 x^{6}-7968062960 x^{5}-1702189632 x^{4}+1129333920 x^{3}+990063360 x^{2}+341003520 x +59304960\right )}{17160} \] Input:
int((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x)
Output:
(x*(1443420000*x**12 + 8548254000*x**11 + 21488149800*x**10 + 28577716596* x**9 + 18650225880*x**8 - 318474585*x**7 - 10614867120*x**6 - 7968062960*x **5 - 1702189632*x**4 + 1129333920*x**3 + 990063360*x**2 + 341003520*x + 5 9304960))/17160