\(\int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx\) [1271]

Optimal result

Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^{10}}{7290}+\frac {763 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{8748}+\frac {8285 (2+3 x)^{13}}{9477}-\frac {1900 (2+3 x)^{14}}{5103}+\frac {100 (2+3 x)^{15}}{2187} \]

[Out]

-49/7290*(2+3*x)^10+763/8019*(2+3*x)^11-4099/8748*(2+3*x)^12+8285/9477*(2+3*x)^13-1900/5103*(2+3*x)^14+100/218
7*(2+3*x)^15

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=\frac {100 (3 x+2)^{15}}{2187}-\frac {1900 (3 x+2)^{14}}{5103}+\frac {8285 (3 x+2)^{13}}{9477}-\frac {4099 (3 x+2)^{12}}{8748}+\frac {763 (3 x+2)^{11}}{8019}-\frac {49 (3 x+2)^{10}}{7290} \]

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^10)/7290 + (763*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/8748 + (8285*(2 + 3*x)^13)/9477 - (190
0*(2 + 3*x)^14)/5103 + (100*(2 + 3*x)^15)/2187

Rule 90

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(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]))

Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{243} (2+3 x)^9+\frac {763}{243} (2+3 x)^{10}-\frac {4099}{243} (2+3 x)^{11}+\frac {8285}{243} (2+3 x)^{12}-\frac {3800}{243} (2+3 x)^{13}+\frac {500}{243} (2+3 x)^{14}\right ) \, dx \\ & = -\frac {49 (2+3 x)^{10}}{7290}+\frac {763 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{8748}+\frac {8285 (2+3 x)^{13}}{9477}-\frac {1900 (2+3 x)^{14}}{5103}+\frac {100 (2+3 x)^{15}}{2187} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 90, normalized size of antiderivative = 1.34 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=13824 x+100224 x^2+400128 x^3+871936 x^4+\frac {2732864 x^5}{5}-\frac {7363312 x^6}{3}-\frac {55216512 x^7}{7}-9703638 x^8-180666 x^9+\frac {182657511 x^{10}}{10}+\frac {342976275 x^{11}}{11}+\frac {113029263 x^{12}}{4}+\frac {200077695 x^{13}}{13}+\frac {33461100 x^{14}}{7}+656100 x^{15} \]

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]

[Out]

13824*x + 100224*x^2 + 400128*x^3 + 871936*x^4 + (2732864*x^5)/5 - (7363312*x^6)/3 - (55216512*x^7)/7 - 970363
8*x^8 - 180666*x^9 + (182657511*x^10)/10 + (342976275*x^11)/11 + (113029263*x^12)/4 + (200077695*x^13)/13 + (3
3461100*x^14)/7 + 656100*x^15

Maple [A] (verified)

Time = 2.28 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.10

method	result	size
gosper	\(\frac {x \left (39405366000 x^{14}[phone] x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] x^{9}-10850799960 x^{8}-582800498280 x^{7}-473757672960 x^{6}-147413506240 x^{5}[phone] x^{4}[phone] x^{3}[phone] x^{2}[phone] x [phone]\right )}{60060}\)	\(74\)
default	\(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\)	\(75\)
norman	\(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\)	\(75\)
risch	\(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\)	\(75\)
parallelrisch	\(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\)	\(75\)

[In]

int((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

1/60060*x*(39405366000*x^14+287096238000*x^13+924358950900*x^12+1697134383945*x^11+1872650461500*x^10+10970410
11066*x^9-10850799960*x^8-582800498280*x^7-473757672960*x^6-147413506240*x^5+32827162368*x^4+52368476160*x^3+2
4031687680*x^2+6019453440*x+830269440)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.10 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm="fricas")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 -
180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*
x^2 + 13824*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 87, normalized size of antiderivative = 1.30 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=656100 x^{15} + \frac {33461100 x^{14}}{7} + \frac {200077695 x^{13}}{13} + \frac {113029263 x^{12}}{4} + \frac {342976275 x^{11}}{11} + \frac {182657511 x^{10}}{10} - 180666 x^{9} - 9703638 x^{8} - \frac {55216512 x^{7}}{7} - \frac {7363312 x^{6}}{3} + \frac {2732864 x^{5}}{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \]

[In]

integrate((1-2*x)**2*(2+3*x)**9*(3+5*x)**3,x)

[Out]

656100*x**15 + 33461100*x**14/7 + 200077695*x**13/13 + 113029263*x**12/4 + 342976275*x**11/11 + 182657511*x**1
0/10 - 180666*x**9 - 9703638*x**8 - 55216512*x**7/7 - 7363312*x**6/3 + 2732864*x**5/5 + 871936*x**4 + 400128*x
**3 + 100224*x**2 + 13824*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.10 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm="maxima")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 -
180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*
x^2 + 13824*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.10 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm="giac")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 -
180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*
x^2 + 13824*x

Mupad [B] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.10 \[ \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx=656100\,x^{15}+\frac {33461100\,x^{14}}{7}+\frac {200077695\,x^{13}}{13}+\frac {113029263\,x^{12}}{4}+\frac {342976275\,x^{11}}{11}+\frac {182657511\,x^{10}}{10}-180666\,x^9-9703638\,x^8-\frac {55216512\,x^7}{7}-\frac {7363312\,x^6}{3}+\frac {2732864\,x^5}{5}+871936\,x^4+400128\,x^3+100224\,x^2+13824\,x \]

[In]

int((2*x - 1)^2*(3*x + 2)^9*(5*x + 3)^3,x)

[Out]

13824*x + 100224*x^2 + 400128*x^3 + 871936*x^4 + (2732864*x^5)/5 - (7363312*x^6)/3 - (55216512*x^7)/7 - 970363
8*x^8 - 180666*x^9 + (182657511*x^10)/10 + (342976275*x^11)/11 + (113029263*x^12)/4 + (200077695*x^13)/13 + (3
3461100*x^14)/7 + 656100*x^15