3.1277 \(\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=52 \[ 1500 x^9+4725 x^8+\frac{33255 x^7}{7}+\frac{121 x^6}{6}-\frac{15709 x^5}{5}-\frac{7145 x^4}{4}+258 x^3+594 x^2+216 x \]

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9

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Rubi [A]  time = 0.0228307, antiderivative size = 52, 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} \[ 1500 x^9+4725 x^8+\frac{33255 x^7}{7}+\frac{121 x^6}{6}-\frac{15709 x^5}{5}-\frac{7145 x^4}{4}+258 x^3+594 x^2+216 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9

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)^2 (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+1188 x+774 x^2-7145 x^3-15709 x^4+121 x^5+33255 x^6+37800 x^7+13500 x^8\right ) \, dx\\ &=216 x+594 x^2+258 x^3-\frac{7145 x^4}{4}-\frac{15709 x^5}{5}+\frac{121 x^6}{6}+\frac{33255 x^7}{7}+4725 x^8+1500 x^9\\ \end{align*}

Mathematica [A]  time = 0.0025069, size = 52, normalized size = 1. \[ 1500 x^9+4725 x^8+\frac{33255 x^7}{7}+\frac{121 x^6}{6}-\frac{15709 x^5}{5}-\frac{7145 x^4}{4}+258 x^3+594 x^2+216 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9

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Maple [A]  time = 0.001, size = 45, normalized size = 0.9 \begin{align*} 216\,x+594\,{x}^{2}+258\,{x}^{3}-{\frac{7145\,{x}^{4}}{4}}-{\frac{15709\,{x}^{5}}{5}}+{\frac{121\,{x}^{6}}{6}}+{\frac{33255\,{x}^{7}}{7}}+4725\,{x}^{8}+1500\,{x}^{9} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

216*x+594*x^2+258*x^3-7145/4*x^4-15709/5*x^5+121/6*x^6+33255/7*x^7+4725*x^8+1500*x^9

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Maxima [A]  time = 1.17876, size = 59, normalized size = 1.13 \begin{align*} 1500 \, x^{9} + 4725 \, x^{8} + \frac{33255}{7} \, x^{7} + \frac{121}{6} \, x^{6} - \frac{15709}{5} \, x^{5} - \frac{7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x

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Fricas [A]  time = 1.57935, size = 138, normalized size = 2.65 \begin{align*} 1500 x^{9} + 4725 x^{8} + \frac{33255}{7} x^{7} + \frac{121}{6} x^{6} - \frac{15709}{5} x^{5} - \frac{7145}{4} x^{4} + 258 x^{3} + 594 x^{2} + 216 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x

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Sympy [A]  time = 0.06618, size = 49, normalized size = 0.94 \begin{align*} 1500 x^{9} + 4725 x^{8} + \frac{33255 x^{7}}{7} + \frac{121 x^{6}}{6} - \frac{15709 x^{5}}{5} - \frac{7145 x^{4}}{4} + 258 x^{3} + 594 x^{2} + 216 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1500*x**9 + 4725*x**8 + 33255*x**7/7 + 121*x**6/6 - 15709*x**5/5 - 7145*x**4/4 + 258*x**3 + 594*x**2 + 216*x

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Giac [A]  time = 2.92671, size = 59, normalized size = 1.13 \begin{align*} 1500 \, x^{9} + 4725 \, x^{8} + \frac{33255}{7} \, x^{7} + \frac{121}{6} \, x^{6} - \frac{15709}{5} \, x^{5} - \frac{7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x