3.11.19 \(\int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ -\frac {25}{486} (3 x+2)^{12}+\frac {65}{297} (3 x+2)^{11}-\frac {4}{45} (3 x+2)^{10}+\frac {7}{729} (3 x+2)^9 \]

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Rubi [A]  time = 0.03, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {25}{486} (3 x+2)^{12}+\frac {65}{297} (3 x+2)^{11}-\frac {4}{45} (3 x+2)^{10}+\frac {7}{729} (3 x+2)^9 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

(7*(2 + 3*x)^9)/729 - (4*(2 + 3*x)^10)/45 + (65*(2 + 3*x)^11)/297 - (25*(2 + 3*x)^12)/486

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx &=\int \left (\frac {7}{27} (2+3 x)^8-\frac {8}{3} (2+3 x)^9+\frac {65}{9} (2+3 x)^{10}-\frac {50}{27} (2+3 x)^{11}\right ) \, dx\\ &=\frac {7}{729} (2+3 x)^9-\frac {4}{45} (2+3 x)^{10}+\frac {65}{297} (2+3 x)^{11}-\frac {25}{486} (2+3 x)^{12}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 69, normalized size = 1.53 \begin {gather*} -\frac {54675 x^{12}}{2}-\frac {1979235 x^{11}}{11}-\frac {2614194 x^{10}}{5}-869103 x^9-881442 x^8-507600 x^7-71904 x^6+\frac {679008 x^5}{5}+127168 x^4+\frac {173056 x^3}{3}+15360 x^2+2304 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

2304*x + 15360*x^2 + (173056*x^3)/3 + 127168*x^4 + (679008*x^5)/5 - 71904*x^6 - 507600*x^7 - 881442*x^8 - 8691
03*x^9 - (2614194*x^10)/5 - (1979235*x^11)/11 - (54675*x^12)/2

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2, x]

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fricas [A]  time = 1.20, size = 59, normalized size = 1.31 \begin {gather*} -\frac {54675}{2} x^{12} - \frac {1979235}{11} x^{11} - \frac {2614194}{5} x^{10} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac {679008}{5} x^{5} + 127168 x^{4} + \frac {173056}{3} x^{3} + 15360 x^{2} + 2304 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x)^2,x, algorithm="fricas")

[Out]

-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507600*x^7 - 71904*x^6 + 679008/5
*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 2304*x

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giac [A]  time = 1.20, size = 59, normalized size = 1.31 \begin {gather*} -\frac {54675}{2} \, x^{12} - \frac {1979235}{11} \, x^{11} - \frac {2614194}{5} \, x^{10} - 869103 \, x^{9} - 881442 \, x^{8} - 507600 \, x^{7} - 71904 \, x^{6} + \frac {679008}{5} \, x^{5} + 127168 \, x^{4} + \frac {173056}{3} \, x^{3} + 15360 \, x^{2} + 2304 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x)^2,x, algorithm="giac")

[Out]

-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507600*x^7 - 71904*x^6 + 679008/5
*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 2304*x

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maple [A]  time = 0.00, size = 60, normalized size = 1.33 \begin {gather*} -\frac {54675}{2} x^{12}-\frac {1979235}{11} x^{11}-\frac {2614194}{5} x^{10}-869103 x^{9}-881442 x^{8}-507600 x^{7}-71904 x^{6}+\frac {679008}{5} x^{5}+127168 x^{4}+\frac {173056}{3} x^{3}+15360 x^{2}+2304 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(3*x+2)^8*(5*x+3)^2,x)

[Out]

-54675/2*x^12-1979235/11*x^11-2614194/5*x^10-869103*x^9-881442*x^8-507600*x^7-71904*x^6+679008/5*x^5+127168*x^
4+173056/3*x^3+15360*x^2+2304*x

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maxima [A]  time = 0.54, size = 59, normalized size = 1.31 \begin {gather*} -\frac {54675}{2} \, x^{12} - \frac {1979235}{11} \, x^{11} - \frac {2614194}{5} \, x^{10} - 869103 \, x^{9} - 881442 \, x^{8} - 507600 \, x^{7} - 71904 \, x^{6} + \frac {679008}{5} \, x^{5} + 127168 \, x^{4} + \frac {173056}{3} \, x^{3} + 15360 \, x^{2} + 2304 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x)^2,x, algorithm="maxima")

[Out]

-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507600*x^7 - 71904*x^6 + 679008/5
*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 2304*x

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mupad [B]  time = 0.07, size = 59, normalized size = 1.31 \begin {gather*} -\frac {54675\,x^{12}}{2}-\frac {1979235\,x^{11}}{11}-\frac {2614194\,x^{10}}{5}-869103\,x^9-881442\,x^8-507600\,x^7-71904\,x^6+\frac {679008\,x^5}{5}+127168\,x^4+\frac {173056\,x^3}{3}+15360\,x^2+2304\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)*(3*x + 2)^8*(5*x + 3)^2,x)

[Out]

2304*x + 15360*x^2 + (173056*x^3)/3 + 127168*x^4 + (679008*x^5)/5 - 71904*x^6 - 507600*x^7 - 881442*x^8 - 8691
03*x^9 - (2614194*x^10)/5 - (1979235*x^11)/11 - (54675*x^12)/2

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sympy [A]  time = 0.08, size = 66, normalized size = 1.47 \begin {gather*} - \frac {54675 x^{12}}{2} - \frac {1979235 x^{11}}{11} - \frac {2614194 x^{10}}{5} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac {679008 x^{5}}{5} + 127168 x^{4} + \frac {173056 x^{3}}{3} + 15360 x^{2} + 2304 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)**8*(3+5*x)**2,x)

[Out]

-54675*x**12/2 - 1979235*x**11/11 - 2614194*x**10/5 - 869103*x**9 - 881442*x**8 - 507600*x**7 - 71904*x**6 + 6
79008*x**5/5 + 127168*x**4 + 173056*x**3/3 + 15360*x**2 + 2304*x

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