3.1374 \(\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^3 \, dx\)

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

[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

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Rubi [A]  time = 0.0386395, antiderivative size = 78, normalized size of antiderivative = 1., 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} \[ -\frac{250 (3 x+2)^{12}}{6561}+\frac{3700 (3 x+2)^{11}}{8019}-\frac{1439}{729} (3 x+2)^{10}+\frac{66193 (3 x+2)^9}{19683}-\frac{10073 (3 x+2)^8}{5832}+\frac{259}{729} (3 x+2)^7-\frac{343 (3 x+2)^6}{13122} \]

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*}

Mathematica [A]  time = 0.0023445, size = 65, normalized size = 0.83 \[ -20250 x^{12}-\frac{882900 x^{11}}{11}-111159 x^{10}-32867 x^9+\frac{565167 x^8}{8}+71107 x^7+\frac{10297 x^6}{2}-24882 x^5-11798 x^4+1536 x^3+2808 x^2+864 x \]

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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Maple [A]  time = 0.002, size = 60, normalized size = 0.8 \begin{align*} -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{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^5*(3+5*x)^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 = 1.04001, size = 80, normalized size = 1.03 \begin{align*} -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{align*}

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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Fricas [A]  time = 1.11419, size = 204, normalized size = 2.62 \begin{align*} -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{align*}

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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Sympy [A]  time = 0.072811, size = 63, normalized size = 0.81 \begin{align*} - 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{align*}

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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Giac [A]  time = 2.98389, size = 80, normalized size = 1.03 \begin{align*} -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{align*}

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