Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=\frac {343 (2+3 x)^8}{5832}-\frac {3724 (2+3 x)^9}{6561}+\frac {11599 (2+3 x)^{10}}{7290}-\frac {8198 (2+3 x)^{11}}{8019}+\frac {545 (2+3 x)^{12}}{2187}-\frac {200 (2+3 x)^{13}}{9477} \] Output:
343/5832*(2+3*x)^8-3724/6561*(2+3*x)^9+11599/7290*(2+3*x)^10-8198/8019*(2+ 3*x)^11+545/2187*(2+3*x)^12-200/9477*(2+3*x)^13
Time = 0.00 (sec) , antiderivative size = 78, normalized size of antiderivative = 1.16 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=1152 x+4512 x^2+\frac {16160 x^3}{3}-13644 x^4-\frac {249864 x^5}{5}-\frac {90794 x^6}{3}+102378 x^7+\frac {1642815 x^8}{8}+69054 x^9-\frac {2005641 x^{10}}{10}-\frac {3168234 x^{11}}{11}-159165 x^{12}-\frac {437400 x^{13}}{13} \] Input:
Integrate[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^2,x]
Output:
1152*x + 4512*x^2 + (16160*x^3)/3 - 13644*x^4 - (249864*x^5)/5 - (90794*x^ 6)/3 + 102378*x^7 + (1642815*x^8)/8 + 69054*x^9 - (2005641*x^10)/10 - (316 8234*x^11)/11 - 159165*x^12 - (437400*x^13)/13
Time = 0.28 (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.
\(\displaystyle \int (1-2 x)^3 (3 x+2)^7 (5 x+3)^2 \, dx\) |
\(\Big \downarrow \) 99 |
\(\displaystyle \int \left (-\frac {200}{243} (3 x+2)^{12}+\frac {2180}{243} (3 x+2)^{11}-\frac {8198}{243} (3 x+2)^{10}+\frac {11599}{243} (3 x+2)^9-\frac {3724}{243} (3 x+2)^8+\frac {343}{243} (3 x+2)^7\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -\frac {200 (3 x+2)^{13}}{9477}+\frac {545 (3 x+2)^{12}}{2187}-\frac {8198 (3 x+2)^{11}}{8019}+\frac {11599 (3 x+2)^{10}}{7290}-\frac {3724 (3 x+2)^9}{6561}+\frac {343 (3 x+2)^8}{5832}\) |
Input:
Int[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^2,x]
Output:
(343*(2 + 3*x)^8)/5832 - (3724*(2 + 3*x)^9)/6561 + (11599*(2 + 3*x)^10)/72 90 - (8198*(2 + 3*x)^11)/8019 + (545*(2 + 3*x)^12)/2187 - (200*(2 + 3*x)^1 3)/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 | \(-\frac {x \left (577368000 x^{12}+2731271400 x^{11}+4942445040 x^{10}+3441679956 x^{9}-1184966640 x^{8}-3523838175 x^{7}-1756806480 x^{6}+519341680 x^{5}+857533248 x^{4}+234131040 x^{3}-92435200 x^{2}-77425920 x -19768320\right )}{17160}\) | \(64\) |
default | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
norman | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
risch | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
parallelrisch | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
orering | \(\frac {x \left (577368000 x^{12}+2731271400 x^{11}+4942445040 x^{10}+3441679956 x^{9}-1184966640 x^{8}-3523838175 x^{7}-1756806480 x^{6}+519341680 x^{5}+857533248 x^{4}+234131040 x^{3}-92435200 x^{2}-77425920 x -19768320\right ) \left (1-2 x \right )^{3}}{17160 \left (-1+2 x \right )^{3}}\) | \(78\) |
Input:
int((1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x,method=_RETURNVERBOSE)
Output:
-1/17160*x*(577368000*x^12+2731271400*x^11+4942445040*x^10+3441679956*x^9- 1184966640*x^8-3523838175*x^7-1756806480*x^6+519341680*x^5+857533248*x^4+2 34131040*x^3-92435200*x^2-77425920*x-19768320)
Time = 0.07 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400}{13} \, x^{13} - 159165 \, x^{12} - \frac {3168234}{11} \, x^{11} - \frac {2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac {1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac {90794}{3} \, x^{6} - \frac {249864}{5} \, x^{5} - 13644 \, x^{4} + \frac {16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \] Input:
integrate((1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x, algorithm="fricas")
Output:
-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054* x^9 + 1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^3 + 4512*x^2 + 1152*x
Time = 0.03 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.12 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=- \frac {437400 x^{13}}{13} - 159165 x^{12} - \frac {3168234 x^{11}}{11} - \frac {2005641 x^{10}}{10} + 69054 x^{9} + \frac {1642815 x^{8}}{8} + 102378 x^{7} - \frac {90794 x^{6}}{3} - \frac {249864 x^{5}}{5} - 13644 x^{4} + \frac {16160 x^{3}}{3} + 4512 x^{2} + 1152 x \] Input:
integrate((1-2*x)**3*(2+3*x)**7*(3+5*x)**2,x)
Output:
-437400*x**13/13 - 159165*x**12 - 3168234*x**11/11 - 2005641*x**10/10 + 69 054*x**9 + 1642815*x**8/8 + 102378*x**7 - 90794*x**6/3 - 249864*x**5/5 - 1 3644*x**4 + 16160*x**3/3 + 4512*x**2 + 1152*x
Time = 0.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400}{13} \, x^{13} - 159165 \, x^{12} - \frac {3168234}{11} \, x^{11} - \frac {2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac {1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac {90794}{3} \, x^{6} - \frac {249864}{5} \, x^{5} - 13644 \, x^{4} + \frac {16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \] Input:
integrate((1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x, algorithm="maxima")
Output:
-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054* x^9 + 1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^3 + 4512*x^2 + 1152*x
Time = 0.12 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400}{13} \, x^{13} - 159165 \, x^{12} - \frac {3168234}{11} \, x^{11} - \frac {2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac {1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac {90794}{3} \, x^{6} - \frac {249864}{5} \, x^{5} - 13644 \, x^{4} + \frac {16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \] Input:
integrate((1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x, algorithm="giac")
Output:
-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054* x^9 + 1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^3 + 4512*x^2 + 1152*x
Time = 0.05 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400\,x^{13}}{13}-159165\,x^{12}-\frac {3168234\,x^{11}}{11}-\frac {2005641\,x^{10}}{10}+69054\,x^9+\frac {1642815\,x^8}{8}+102378\,x^7-\frac {90794\,x^6}{3}-\frac {249864\,x^5}{5}-13644\,x^4+\frac {16160\,x^3}{3}+4512\,x^2+1152\,x \] Input:
int(-(2*x - 1)^3*(3*x + 2)^7*(5*x + 3)^2,x)
Output:
1152*x + 4512*x^2 + (16160*x^3)/3 - 13644*x^4 - (249864*x^5)/5 - (90794*x^ 6)/3 + 102378*x^7 + (1642815*x^8)/8 + 69054*x^9 - (2005641*x^10)/10 - (316 8234*x^11)/11 - 159165*x^12 - (437400*x^13)/13
Time = 0.15 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=\frac {x \left (-577368000 x^{12}-2731271400 x^{11}-4942445040 x^{10}-3441679956 x^{9}+1184966640 x^{8}+3523838175 x^{7}+1756806480 x^{6}-519341680 x^{5}-857533248 x^{4}-234131040 x^{3}+92435200 x^{2}+77425920 x +19768320\right )}{17160} \] Input:
int((1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x)
Output:
(x*( - 577368000*x**12 - 2731271400*x**11 - 4942445040*x**10 - 3441679956* x**9 + 1184966640*x**8 + 3523838175*x**7 + 1756806480*x**6 - 519341680*x** 5 - 857533248*x**4 - 234131040*x**3 + 92435200*x**2 + 77425920*x + 1976832 0))/17160