3.1180 \(\int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=49 \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4

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Rubi [A]  time = 0.0192387, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+1620 x+4014 x^2+883 x^3-13943 x^4-27765 x^5-22275 x^6-6750 x^7\right ) \, dx\\ &=216 x+810 x^2+1338 x^3+\frac{883 x^4}{4}-\frac{13943 x^5}{5}-\frac{9255 x^6}{2}-\frac{22275 x^7}{7}-\frac{3375 x^8}{4}\\ \end{align*}

Mathematica [A]  time = 0.0009678, size = 49, normalized size = 1. \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4

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Maple [A]  time = 0.002, size = 40, normalized size = 0.8 \begin{align*} 216\,x+810\,{x}^{2}+1338\,{x}^{3}+{\frac{883\,{x}^{4}}{4}}-{\frac{13943\,{x}^{5}}{5}}-{\frac{9255\,{x}^{6}}{2}}-{\frac{22275\,{x}^{7}}{7}}-{\frac{3375\,{x}^{8}}{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

216*x+810*x^2+1338*x^3+883/4*x^4-13943/5*x^5-9255/2*x^6-22275/7*x^7-3375/4*x^8

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Maxima [A]  time = 1.07152, size = 53, normalized size = 1.08 \begin{align*} -\frac{3375}{4} \, x^{8} - \frac{22275}{7} \, x^{7} - \frac{9255}{2} \, x^{6} - \frac{13943}{5} \, x^{5} + \frac{883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x

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Fricas [A]  time = 1.59017, size = 128, normalized size = 2.61 \begin{align*} -\frac{3375}{4} x^{8} - \frac{22275}{7} x^{7} - \frac{9255}{2} x^{6} - \frac{13943}{5} x^{5} + \frac{883}{4} x^{4} + 1338 x^{3} + 810 x^{2} + 216 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x

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Sympy [A]  time = 0.064308, size = 46, normalized size = 0.94 \begin{align*} - \frac{3375 x^{8}}{4} - \frac{22275 x^{7}}{7} - \frac{9255 x^{6}}{2} - \frac{13943 x^{5}}{5} + \frac{883 x^{4}}{4} + 1338 x^{3} + 810 x^{2} + 216 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375*x**8/4 - 22275*x**7/7 - 9255*x**6/2 - 13943*x**5/5 + 883*x**4/4 + 1338*x**3 + 810*x**2 + 216*x

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Giac [A]  time = 2.83056, size = 53, normalized size = 1.08 \begin{align*} -\frac{3375}{4} \, x^{8} - \frac{22275}{7} \, x^{7} - \frac{9255}{2} \, x^{6} - \frac{13943}{5} \, x^{5} + \frac{883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x