3.1341 \(\int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458} \]

[Out]

(-343*(2 + 3*x)^6)/1458 + (287*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/324 + (428*(2 + 3*x)^9)/2187 - (4*(2 + 3*x
)^10)/243

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Rubi [A]  time = 0.0237418, antiderivative size = 56, 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} \[ -\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-343*(2 + 3*x)^6)/1458 + (287*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/324 + (428*(2 + 3*x)^9)/2187 - (4*(2 + 3*x
)^10)/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)^3 (2+3 x)^5 (3+5 x) \, dx &=\int \left (-\frac{343}{81} (2+3 x)^5+\frac{2009}{81} (2+3 x)^6-\frac{518}{27} (2+3 x)^7+\frac{428}{81} (2+3 x)^8-\frac{40}{81} (2+3 x)^9\right ) \, dx\\ &=-\frac{343 (2+3 x)^6}{1458}+\frac{287}{243} (2+3 x)^7-\frac{259}{324} (2+3 x)^8+\frac{428 (2+3 x)^9}{2187}-\frac{4}{243} (2+3 x)^{10}\\ \end{align*}

Mathematica [A]  time = 0.0021923, size = 53, normalized size = 0.95 \[ -972 x^{10}-2628 x^9-\frac{6291 x^8}{4}+1683 x^7+\frac{4333 x^6}{2}+14 x^5-882 x^4-256 x^3+152 x^2+96 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

96*x + 152*x^2 - 256*x^3 - 882*x^4 + 14*x^5 + (4333*x^6)/2 + 1683*x^7 - (6291*x^8)/4 - 2628*x^9 - 972*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 0.9 \begin{align*} -972\,{x}^{10}-2628\,{x}^{9}-{\frac{6291\,{x}^{8}}{4}}+1683\,{x}^{7}+{\frac{4333\,{x}^{6}}{2}}+14\,{x}^{5}-882\,{x}^{4}-256\,{x}^{3}+152\,{x}^{2}+96\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-972*x^10-2628*x^9-6291/4*x^8+1683*x^7+4333/2*x^6+14*x^5-882*x^4-256*x^3+152*x^2+96*x

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Maxima [A]  time = 2.18748, size = 66, normalized size = 1.18 \begin{align*} -972 \, x^{10} - 2628 \, x^{9} - \frac{6291}{4} \, x^{8} + 1683 \, x^{7} + \frac{4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x

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Fricas [A]  time = 1.16307, size = 142, normalized size = 2.54 \begin{align*} -972 x^{10} - 2628 x^{9} - \frac{6291}{4} x^{8} + 1683 x^{7} + \frac{4333}{2} x^{6} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x

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Sympy [A]  time = 0.067272, size = 51, normalized size = 0.91 \begin{align*} - 972 x^{10} - 2628 x^{9} - \frac{6291 x^{8}}{4} + 1683 x^{7} + \frac{4333 x^{6}}{2} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-972*x**10 - 2628*x**9 - 6291*x**8/4 + 1683*x**7 + 4333*x**6/2 + 14*x**5 - 882*x**4 - 256*x**3 + 152*x**2 + 96
*x

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Giac [A]  time = 2.56065, size = 66, normalized size = 1.18 \begin{align*} -972 \, x^{10} - 2628 \, x^{9} - \frac{6291}{4} \, x^{8} + 1683 \, x^{7} + \frac{4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x