3.1360 \(\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^
9

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Rubi [A]  time = 0.0230412, antiderivative size = 56, 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} \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*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)^3 (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (72+132 x-754 x^2-1641 x^3+2262 x^4+6743 x^5-234 x^6-9180 x^7-5400 x^8\right ) \, dx\\ &=72 x+66 x^2-\frac{754 x^3}{3}-\frac{1641 x^4}{4}+\frac{2262 x^5}{5}+\frac{6743 x^6}{6}-\frac{234 x^7}{7}-\frac{2295 x^8}{2}-600 x^9\\ \end{align*}

Mathematica [A]  time = 0.0022935, size = 56, normalized size = 1. \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^
9

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Maple [A]  time = 0.001, size = 45, normalized size = 0.8 \begin{align*} 72\,x+66\,{x}^{2}-{\frac{754\,{x}^{3}}{3}}-{\frac{1641\,{x}^{4}}{4}}+{\frac{2262\,{x}^{5}}{5}}+{\frac{6743\,{x}^{6}}{6}}-{\frac{234\,{x}^{7}}{7}}-{\frac{2295\,{x}^{8}}{2}}-600\,{x}^{9} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

72*x+66*x^2-754/3*x^3-1641/4*x^4+2262/5*x^5+6743/6*x^6-234/7*x^7-2295/2*x^8-600*x^9

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Maxima [A]  time = 1.01818, size = 59, normalized size = 1.05 \begin{align*} -600 \, x^{9} - \frac{2295}{2} \, x^{8} - \frac{234}{7} \, x^{7} + \frac{6743}{6} \, x^{6} + \frac{2262}{5} \, x^{5} - \frac{1641}{4} \, x^{4} - \frac{754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x

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Fricas [A]  time = 1.18955, size = 138, normalized size = 2.46 \begin{align*} -600 x^{9} - \frac{2295}{2} x^{8} - \frac{234}{7} x^{7} + \frac{6743}{6} x^{6} + \frac{2262}{5} x^{5} - \frac{1641}{4} x^{4} - \frac{754}{3} x^{3} + 66 x^{2} + 72 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x

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Sympy [A]  time = 0.06655, size = 53, normalized size = 0.95 \begin{align*} - 600 x^{9} - \frac{2295 x^{8}}{2} - \frac{234 x^{7}}{7} + \frac{6743 x^{6}}{6} + \frac{2262 x^{5}}{5} - \frac{1641 x^{4}}{4} - \frac{754 x^{3}}{3} + 66 x^{2} + 72 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600*x**9 - 2295*x**8/2 - 234*x**7/7 + 6743*x**6/6 + 2262*x**5/5 - 1641*x**4/4 - 754*x**3/3 + 66*x**2 + 72*x

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Giac [A]  time = 2.98643, size = 59, normalized size = 1.05 \begin{align*} -600 \, x^{9} - \frac{2295}{2} \, x^{8} - \frac{234}{7} \, x^{7} + \frac{6743}{6} \, x^{6} + \frac{2262}{5} \, x^{5} - \frac{1641}{4} \, x^{4} - \frac{754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x