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

Optimal. Leaf size=45 \[ -135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 x \]

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Rubi [A]  time = 0.02, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 2*x^2 - 86*x^3 - (117*x^4)/4 + (949*x^5)/5 + 111*x^6 - (1188*x^7)/7 - 135*x^8

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)^3 (3+5 x) \, dx &=\int \left (24+4 x-258 x^2-117 x^3+949 x^4+666 x^5-1188 x^6-1080 x^7\right ) \, dx\\ &=24 x+2 x^2-86 x^3-\frac {117 x^4}{4}+\frac {949 x^5}{5}+111 x^6-\frac {1188 x^7}{7}-135 x^8\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 45, normalized size = 1.00 \begin {gather*} -135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 2*x^2 - 86*x^3 - (117*x^4)/4 + (949*x^5)/5 + 111*x^6 - (1188*x^7)/7 - 135*x^8

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.80, size = 39, normalized size = 0.87 \begin {gather*} -135 x^{8} - \frac {1188}{7} x^{7} + 111 x^{6} + \frac {949}{5} x^{5} - \frac {117}{4} x^{4} - 86 x^{3} + 2 x^{2} + 24 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x

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giac [A]  time = 1.01, size = 39, normalized size = 0.87 \begin {gather*} -135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x

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maple [A]  time = 0.00, size = 40, normalized size = 0.89 \begin {gather*} -135 x^{8}-\frac {1188}{7} x^{7}+111 x^{6}+\frac {949}{5} x^{5}-\frac {117}{4} x^{4}-86 x^{3}+2 x^{2}+24 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

24*x+2*x^2-86*x^3-117/4*x^4+949/5*x^5+111*x^6-1188/7*x^7-135*x^8

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maxima [A]  time = 0.61, size = 39, normalized size = 0.87 \begin {gather*} -135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x

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mupad [B]  time = 0.03, size = 39, normalized size = 0.87 \begin {gather*} -135\,x^8-\frac {1188\,x^7}{7}+111\,x^6+\frac {949\,x^5}{5}-\frac {117\,x^4}{4}-86\,x^3+2\,x^2+24\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

24*x + 2*x^2 - 86*x^3 - (117*x^4)/4 + (949*x^5)/5 + 111*x^6 - (1188*x^7)/7 - 135*x^8

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sympy [A]  time = 0.07, size = 42, normalized size = 0.93 \begin {gather*} - 135 x^{8} - \frac {1188 x^{7}}{7} + 111 x^{6} + \frac {949 x^{5}}{5} - \frac {117 x^{4}}{4} - 86 x^{3} + 2 x^{2} + 24 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x**8 - 1188*x**7/7 + 111*x**6 + 949*x**5/5 - 117*x**4/4 - 86*x**3 + 2*x**2 + 24*x

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