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

Optimal. Leaf size=78 \[ -\frac {250 (3 x+2)^{12}}{6561}+\frac {3700 (3 x+2)^{11}}{8019}-\frac {1439}{729} (3 x+2)^{10}+\frac {66193 (3 x+2)^9}{19683}-\frac {10073 (3 x+2)^8}{5832}+\frac {259}{729} (3 x+2)^7-\frac {343 (3 x+2)^6}{13122} \]

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Rubi [A]  time = 0.04, antiderivative size = 78, 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 {250 (3 x+2)^{12}}{6561}+\frac {3700 (3 x+2)^{11}}{8019}-\frac {1439}{729} (3 x+2)^{10}+\frac {66193 (3 x+2)^9}{19683}-\frac {10073 (3 x+2)^8}{5832}+\frac {259}{729} (3 x+2)^7-\frac {343 (3 x+2)^6}{13122} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-343*(2 + 3*x)^6)/13122 + (259*(2 + 3*x)^7)/729 - (10073*(2 + 3*x)^8)/5832 + (66193*(2 + 3*x)^9)/19683 - (143
9*(2 + 3*x)^10)/729 + (3700*(2 + 3*x)^11)/8019 - (250*(2 + 3*x)^12)/6561

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)^5 (3+5 x)^3 \, dx &=\int \left (-\frac {343}{729} (2+3 x)^5+\frac {1813}{243} (2+3 x)^6-\frac {10073}{243} (2+3 x)^7+\frac {66193}{729} (2+3 x)^8-\frac {14390}{243} (2+3 x)^9+\frac {3700}{243} (2+3 x)^{10}-\frac {1000}{729} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {343 (2+3 x)^6}{13122}+\frac {259}{729} (2+3 x)^7-\frac {10073 (2+3 x)^8}{5832}+\frac {66193 (2+3 x)^9}{19683}-\frac {1439}{729} (2+3 x)^{10}+\frac {3700 (2+3 x)^{11}}{8019}-\frac {250 (2+3 x)^{12}}{6561}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 65, normalized size = 0.83 \begin {gather*} -20250 x^{12}-\frac {882900 x^{11}}{11}-111159 x^{10}-32867 x^9+\frac {565167 x^8}{8}+71107 x^7+\frac {10297 x^6}{2}-24882 x^5-11798 x^4+1536 x^3+2808 x^2+864 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

864*x + 2808*x^2 + 1536*x^3 - 11798*x^4 - 24882*x^5 + (10297*x^6)/2 + 71107*x^7 + (565167*x^8)/8 - 32867*x^9 -
111159*x^10 - (882900*x^11)/11 - 20250*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)^5 (3+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.00, size = 59, normalized size = 0.76 \begin {gather*} -20250 x^{12} - \frac {882900}{11} x^{11} - 111159 x^{10} - 32867 x^{9} + \frac {565167}{8} x^{8} + 71107 x^{7} + \frac {10297}{2} x^{6} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 2808 x^{2} + 864 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^7 + 10297/2*x^6 - 24882*x^5 -
11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x

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giac [A]  time = 0.92, size = 59, normalized size = 0.76 \begin {gather*} -20250 \, x^{12} - \frac {882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac {565167}{8} \, x^{8} + 71107 \, x^{7} + \frac {10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^7 + 10297/2*x^6 - 24882*x^5 -
11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x

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maple [A]  time = 0.00, size = 60, normalized size = 0.77 \begin {gather*} -20250 x^{12}-\frac {882900}{11} x^{11}-111159 x^{10}-32867 x^{9}+\frac {565167}{8} x^{8}+71107 x^{7}+\frac {10297}{2} x^{6}-24882 x^{5}-11798 x^{4}+1536 x^{3}+2808 x^{2}+864 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20250*x^12-882900/11*x^11-111159*x^10-32867*x^9+565167/8*x^8+71107*x^7+10297/2*x^6-24882*x^5-11798*x^4+1536*x
^3+2808*x^2+864*x

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maxima [A]  time = 0.59, size = 59, normalized size = 0.76 \begin {gather*} -20250 \, x^{12} - \frac {882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac {565167}{8} \, x^{8} + 71107 \, x^{7} + \frac {10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^7 + 10297/2*x^6 - 24882*x^5 -
11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x

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mupad [B]  time = 0.07, size = 59, normalized size = 0.76 \begin {gather*} -20250\,x^{12}-\frac {882900\,x^{11}}{11}-111159\,x^{10}-32867\,x^9+\frac {565167\,x^8}{8}+71107\,x^7+\frac {10297\,x^6}{2}-24882\,x^5-11798\,x^4+1536\,x^3+2808\,x^2+864\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

864*x + 2808*x^2 + 1536*x^3 - 11798*x^4 - 24882*x^5 + (10297*x^6)/2 + 71107*x^7 + (565167*x^8)/8 - 32867*x^9 -
111159*x^10 - (882900*x^11)/11 - 20250*x^12

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sympy [A]  time = 0.08, size = 63, normalized size = 0.81 \begin {gather*} - 20250 x^{12} - \frac {882900 x^{11}}{11} - 111159 x^{10} - 32867 x^{9} + \frac {565167 x^{8}}{8} + 71107 x^{7} + \frac {10297 x^{6}}{2} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 2808 x^{2} + 864 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20250*x**12 - 882900*x**11/11 - 111159*x**10 - 32867*x**9 + 565167*x**8/8 + 71107*x**7 + 10297*x**6/2 - 24882
*x**5 - 11798*x**4 + 1536*x**3 + 2808*x**2 + 864*x

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