3.1375 \(\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^3 \, dx\)

Optimal. Leaf size=62 \[ -\frac{81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac{41619 x^8}{8}+22949 x^7+\frac{19607 x^6}{2}-\frac{28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x \]

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9
- 24030*x^10 - (81000*x^11)/11

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Rubi [A]  time = 0.0309639, antiderivative size = 62, 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} \[ -\frac{81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac{41619 x^8}{8}+22949 x^7+\frac{19607 x^6}{2}-\frac{28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9
- 24030*x^10 - (81000*x^11)/11

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)^4 (3+5 x)^3 \, dx &=\int \left (432+2160 x-936 x^2-22192 x^3-28917 x^4+58821 x^5+160643 x^6+41619 x^7-210330 x^8-240300 x^9-81000 x^{10}\right ) \, dx\\ &=432 x+1080 x^2-312 x^3-5548 x^4-\frac{28917 x^5}{5}+\frac{19607 x^6}{2}+22949 x^7+\frac{41619 x^8}{8}-23370 x^9-24030 x^{10}-\frac{81000 x^{11}}{11}\\ \end{align*}

Mathematica [A]  time = 0.0022843, size = 62, normalized size = 1. \[ -\frac{81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac{41619 x^8}{8}+22949 x^7+\frac{19607 x^6}{2}-\frac{28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9
- 24030*x^10 - (81000*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 0.9 \begin{align*} 432\,x+1080\,{x}^{2}-312\,{x}^{3}-5548\,{x}^{4}-{\frac{28917\,{x}^{5}}{5}}+{\frac{19607\,{x}^{6}}{2}}+22949\,{x}^{7}+{\frac{41619\,{x}^{8}}{8}}-23370\,{x}^{9}-24030\,{x}^{10}-{\frac{81000\,{x}^{11}}{11}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x)

[Out]

432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^
11

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Maxima [A]  time = 1.00681, size = 73, normalized size = 1.18 \begin{align*} -\frac{81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac{41619}{8} \, x^{8} + 22949 \, x^{7} + \frac{19607}{2} \, x^{6} - \frac{28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm="maxima")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312
*x^3 + 1080*x^2 + 432*x

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Fricas [A]  time = 1.12929, size = 182, normalized size = 2.94 \begin{align*} -\frac{81000}{11} x^{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619}{8} x^{8} + 22949 x^{7} + \frac{19607}{2} x^{6} - \frac{28917}{5} x^{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm="fricas")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312
*x^3 + 1080*x^2 + 432*x

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Sympy [A]  time = 0.069873, size = 60, normalized size = 0.97 \begin{align*} - \frac{81000 x^{11}}{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619 x^{8}}{8} + 22949 x^{7} + \frac{19607 x^{6}}{2} - \frac{28917 x^{5}}{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**3,x)

[Out]

-81000*x**11/11 - 24030*x**10 - 23370*x**9 + 41619*x**8/8 + 22949*x**7 + 19607*x**6/2 - 28917*x**5/5 - 5548*x*
*4 - 312*x**3 + 1080*x**2 + 432*x

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Giac [A]  time = 2.47742, size = 73, normalized size = 1.18 \begin{align*} -\frac{81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac{41619}{8} \, x^{8} + 22949 \, x^{7} + \frac{19607}{2} \, x^{6} - \frac{28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm="giac")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312
*x^3 + 1080*x^2 + 432*x