3.1145 \(\int (1-2 x) (2+3 x)^6 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7 \]

[Out]

-(2 + 3*x)^7/27 + (37*(2 + 3*x)^8)/216 - (10*(2 + 3*x)^9)/243

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Rubi [A]  time = 0.0193035, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x),x]

[Out]

-(2 + 3*x)^7/27 + (37*(2 + 3*x)^8)/216 - (10*(2 + 3*x)^9)/243

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)^6 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^6+\frac{37}{9} (2+3 x)^7-\frac{10}{9} (2+3 x)^8\right ) \, dx\\ &=-\frac{1}{27} (2+3 x)^7+\frac{37}{216} (2+3 x)^8-\frac{10}{243} (2+3 x)^9\\ \end{align*}

Mathematica [A]  time = 0.0023265, size = 48, normalized size = 1.41 \[ -810 x^9-\frac{29889 x^8}{8}-7047 x^7-6552 x^6-2268 x^5+1260 x^4+\frac{5264 x^3}{3}+832 x^2+192 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x),x]

[Out]

192*x + 832*x^2 + (5264*x^3)/3 + 1260*x^4 - 2268*x^5 - 6552*x^6 - 7047*x^7 - (29889*x^8)/8 - 810*x^9

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Maple [A]  time = 0.001, size = 45, normalized size = 1.3 \begin{align*} -810\,{x}^{9}-{\frac{29889\,{x}^{8}}{8}}-7047\,{x}^{7}-6552\,{x}^{6}-2268\,{x}^{5}+1260\,{x}^{4}+{\frac{5264\,{x}^{3}}{3}}+832\,{x}^{2}+192\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(2+3*x)^6*(3+5*x),x)

[Out]

-810*x^9-29889/8*x^8-7047*x^7-6552*x^6-2268*x^5+1260*x^4+5264/3*x^3+832*x^2+192*x

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Maxima [A]  time = 1.1865, size = 59, normalized size = 1.74 \begin{align*} -810 \, x^{9} - \frac{29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac{5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^6*(3+5*x),x, algorithm="maxima")

[Out]

-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3 + 832*x^2 + 192*x

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Fricas [A]  time = 1.28706, size = 134, normalized size = 3.94 \begin{align*} -810 x^{9} - \frac{29889}{8} x^{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264}{3} x^{3} + 832 x^{2} + 192 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^6*(3+5*x),x, algorithm="fricas")

[Out]

-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3 + 832*x^2 + 192*x

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Sympy [A]  time = 0.065316, size = 46, normalized size = 1.35 \begin{align*} - 810 x^{9} - \frac{29889 x^{8}}{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264 x^{3}}{3} + 832 x^{2} + 192 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)**6*(3+5*x),x)

[Out]

-810*x**9 - 29889*x**8/8 - 7047*x**7 - 6552*x**6 - 2268*x**5 + 1260*x**4 + 5264*x**3/3 + 832*x**2 + 192*x

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Giac [A]  time = 2.5213, size = 59, normalized size = 1.74 \begin{align*} -810 \, x^{9} - \frac{29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac{5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^6*(3+5*x),x, algorithm="giac")

[Out]

-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3 + 832*x^2 + 192*x