3.1379 \(\int (1-2 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=40 \[ -\frac{1000 x^7}{7}-50 x^6+174 x^5+\frac{179 x^4}{4}-87 x^3-\frac{27 x^2}{2}+27 x \]

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7

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Rubi [A]  time = 0.0153185, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{1000 x^7}{7}-50 x^6+174 x^5+\frac{179 x^4}{4}-87 x^3-\frac{27 x^2}{2}+27 x \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(3 + 5*x)^3,x]

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin{align*} \int (1-2 x)^3 (3+5 x)^3 \, dx &=\int \left (27-27 x-261 x^2+179 x^3+870 x^4-300 x^5-1000 x^6\right ) \, dx\\ &=27 x-\frac{27 x^2}{2}-87 x^3+\frac{179 x^4}{4}+174 x^5-50 x^6-\frac{1000 x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0014171, size = 40, normalized size = 1. \[ -\frac{1000 x^7}{7}-50 x^6+174 x^5+\frac{179 x^4}{4}-87 x^3-\frac{27 x^2}{2}+27 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(3 + 5*x)^3,x]

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.9 \begin{align*} 27\,x-{\frac{27\,{x}^{2}}{2}}-87\,{x}^{3}+{\frac{179\,{x}^{4}}{4}}+174\,{x}^{5}-50\,{x}^{6}-{\frac{1000\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

27*x-27/2*x^2-87*x^3+179/4*x^4+174*x^5-50*x^6-1000/7*x^7

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Maxima [A]  time = 1.03923, size = 46, normalized size = 1.15 \begin{align*} -\frac{1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac{179}{4} \, x^{4} - 87 \, x^{3} - \frac{27}{2} \, x^{2} + 27 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

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Fricas [A]  time = 1.0898, size = 96, normalized size = 2.4 \begin{align*} -\frac{1000}{7} x^{7} - 50 x^{6} + 174 x^{5} + \frac{179}{4} x^{4} - 87 x^{3} - \frac{27}{2} x^{2} + 27 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

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Sympy [A]  time = 0.062115, size = 37, normalized size = 0.92 \begin{align*} - \frac{1000 x^{7}}{7} - 50 x^{6} + 174 x^{5} + \frac{179 x^{4}}{4} - 87 x^{3} - \frac{27 x^{2}}{2} + 27 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000*x**7/7 - 50*x**6 + 174*x**5 + 179*x**4/4 - 87*x**3 - 27*x**2/2 + 27*x

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Giac [A]  time = 3.08409, size = 46, normalized size = 1.15 \begin{align*} -\frac{1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac{179}{4} \, x^{4} - 87 \, x^{3} - \frac{27}{2} \, x^{2} + 27 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x