3.13.18 \(\int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ -\frac {50 (3 x+2)^{12}}{2187}+\frac {2180 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{3645}+\frac {11599 (3 x+2)^9}{6561}-\frac {931 (3 x+2)^8}{1458}+\frac {49}{729} (3 x+2)^7 \]

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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 {50 (3 x+2)^{12}}{2187}+\frac {2180 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{3645}+\frac {11599 (3 x+2)^9}{6561}-\frac {931 (3 x+2)^8}{1458}+\frac {49}{729} (3 x+2)^7 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

(49*(2 + 3*x)^7)/729 - (931*(2 + 3*x)^8)/1458 + (11599*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/3645 + (2180*(2
+ 3*x)^11)/8019 - (50*(2 + 3*x)^12)/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)^3 (2+3 x)^6 (3+5 x)^2 \, dx &=\int \left (\frac {343}{243} (2+3 x)^6-\frac {3724}{243} (2+3 x)^7+\frac {11599}{243} (2+3 x)^8-\frac {8198}{243} (2+3 x)^9+\frac {2180}{243} (2+3 x)^{10}-\frac {200}{243} (2+3 x)^{11}\right ) \, dx\\ &=\frac {49}{729} (2+3 x)^7-\frac {931 (2+3 x)^8}{1458}+\frac {11599 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{3645}+\frac {2180 (2+3 x)^{11}}{8019}-\frac {50 (2+3 x)^{12}}{2187}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 71, normalized size = 1.06 \begin {gather*} -12150 x^{12}-\frac {539460 x^{11}}{11}-\frac {348219 x^{10}}{5}-22695 x^9+\frac {85833 x^8}{2}+45531 x^7+\frac {13202 x^6}{3}-\frac {78132 x^5}{5}-7800 x^4+\frac {2608 x^3}{3}+1824 x^2+576 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

576*x + 1824*x^2 + (2608*x^3)/3 - 7800*x^4 - (78132*x^5)/5 + (13202*x^6)/3 + 45531*x^7 + (85833*x^8)/2 - 22695
*x^9 - (348219*x^10)/5 - (539460*x^11)/11 - 12150*x^12

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2, x]

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fricas [A]  time = 1.08, size = 59, normalized size = 0.88 \begin {gather*} -12150 x^{12} - \frac {539460}{11} x^{11} - \frac {348219}{5} x^{10} - 22695 x^{9} + \frac {85833}{2} x^{8} + 45531 x^{7} + \frac {13202}{3} x^{6} - \frac {78132}{5} x^{5} - 7800 x^{4} + \frac {2608}{3} x^{3} + 1824 x^{2} + 576 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^2,x, algorithm="fricas")

[Out]

-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x^7 + 13202/3*x^6 - 78132/5*x^5
- 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x

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giac [A]  time = 0.95, size = 59, normalized size = 0.88 \begin {gather*} -12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^2,x, algorithm="giac")

[Out]

-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x^7 + 13202/3*x^6 - 78132/5*x^5
- 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x

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maple [A]  time = 0.00, size = 60, normalized size = 0.90 \begin {gather*} -12150 x^{12}-\frac {539460}{11} x^{11}-\frac {348219}{5} x^{10}-22695 x^{9}+\frac {85833}{2} x^{8}+45531 x^{7}+\frac {13202}{3} x^{6}-\frac {78132}{5} x^{5}-7800 x^{4}+\frac {2608}{3} x^{3}+1824 x^{2}+576 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(3*x+2)^6*(5*x+3)^2,x)

[Out]

-12150*x^12-539460/11*x^11-348219/5*x^10-22695*x^9+85833/2*x^8+45531*x^7+13202/3*x^6-78132/5*x^5-7800*x^4+2608
/3*x^3+1824*x^2+576*x

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maxima [A]  time = 0.50, size = 59, normalized size = 0.88 \begin {gather*} -12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^2,x, algorithm="maxima")

[Out]

-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x^7 + 13202/3*x^6 - 78132/5*x^5
- 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x

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mupad [B]  time = 0.06, size = 59, normalized size = 0.88 \begin {gather*} -12150\,x^{12}-\frac {539460\,x^{11}}{11}-\frac {348219\,x^{10}}{5}-22695\,x^9+\frac {85833\,x^8}{2}+45531\,x^7+\frac {13202\,x^6}{3}-\frac {78132\,x^5}{5}-7800\,x^4+\frac {2608\,x^3}{3}+1824\,x^2+576\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(3*x + 2)^6*(5*x + 3)^2,x)

[Out]

576*x + 1824*x^2 + (2608*x^3)/3 - 7800*x^4 - (78132*x^5)/5 + (13202*x^6)/3 + 45531*x^7 + (85833*x^8)/2 - 22695
*x^9 - (348219*x^10)/5 - (539460*x^11)/11 - 12150*x^12

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sympy [A]  time = 0.08, size = 68, normalized size = 1.01 \begin {gather*} - 12150 x^{12} - \frac {539460 x^{11}}{11} - \frac {348219 x^{10}}{5} - 22695 x^{9} + \frac {85833 x^{8}}{2} + 45531 x^{7} + \frac {13202 x^{6}}{3} - \frac {78132 x^{5}}{5} - 7800 x^{4} + \frac {2608 x^{3}}{3} + 1824 x^{2} + 576 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**6*(3+5*x)**2,x)

[Out]

-12150*x**12 - 539460*x**11/11 - 348219*x**10/5 - 22695*x**9 + 85833*x**8/2 + 45531*x**7 + 13202*x**6/3 - 7813
2*x**5/5 - 7800*x**4 + 2608*x**3/3 + 1824*x**2 + 576*x

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