3.12.32 \(\int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac {100 (3 x+2)^{15}}{2187}-\frac {1900 (3 x+2)^{14}}{5103}+\frac {8285 (3 x+2)^{13}}{9477}-\frac {4099 (3 x+2)^{12}}{8748}+\frac {763 (3 x+2)^{11}}{8019}-\frac {49 (3 x+2)^{10}}{7290} \]

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Rubi [A]  time = 0.03, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} \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} \end {gather*}

Antiderivative was successfully verified.

[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 88

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*} \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx &=\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*}

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Mathematica [A]  time = 0.00, size = 90, normalized size = 1.34 \begin {gather*} 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 \end {gather*}

Antiderivative was successfully verified.

[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

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.56, size = 74, normalized size = 1.10 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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giac [A]  time = 0.84, size = 74, normalized size = 1.10 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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maple [A]  time = 0.00, size = 75, normalized size = 1.12 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[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

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maxima [A]  time = 0.47, size = 74, normalized size = 1.10 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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mupad [B]  time = 0.12, size = 74, normalized size = 1.10 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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sympy [A]  time = 0.09, size = 87, normalized size = 1.30 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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