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

Optimal. Leaf size=47 \[ -375 x^8-\frac {2900 x^7}{7}+335 x^6+\frac {2277 x^5}{5}-\frac {425 x^4}{4}-201 x^3+\frac {27 x^2}{2}+54 x \]

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Rubi [A]  time = 0.02, antiderivative size = 47, 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*} -375 x^8-\frac {2900 x^7}{7}+335 x^6+\frac {2277 x^5}{5}-\frac {425 x^4}{4}-201 x^3+\frac {27 x^2}{2}+54 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*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+5 x)^3 \, dx &=\int \left (54+27 x-603 x^2-425 x^3+2277 x^4+2010 x^5-2900 x^6-3000 x^7\right ) \, dx\\ &=54 x+\frac {27 x^2}{2}-201 x^3-\frac {425 x^4}{4}+\frac {2277 x^5}{5}+335 x^6-\frac {2900 x^7}{7}-375 x^8\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 47, normalized size = 1.00 \begin {gather*} -375 x^8-\frac {2900 x^7}{7}+335 x^6+\frac {2277 x^5}{5}-\frac {425 x^4}{4}-201 x^3+\frac {27 x^2}{2}+54 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*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+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.13, size = 39, normalized size = 0.83 \begin {gather*} -375 x^{8} - \frac {2900}{7} x^{7} + 335 x^{6} + \frac {2277}{5} x^{5} - \frac {425}{4} x^{4} - 201 x^{3} + \frac {27}{2} x^{2} + 54 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x

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giac [A]  time = 0.81, size = 39, normalized size = 0.83 \begin {gather*} -375 \, x^{8} - \frac {2900}{7} \, x^{7} + 335 \, x^{6} + \frac {2277}{5} \, x^{5} - \frac {425}{4} \, x^{4} - 201 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x

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maple [A]  time = 0.00, size = 40, normalized size = 0.85 \begin {gather*} -375 x^{8}-\frac {2900}{7} x^{7}+335 x^{6}+\frac {2277}{5} x^{5}-\frac {425}{4} x^{4}-201 x^{3}+\frac {27}{2} x^{2}+54 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

54*x+27/2*x^2-201*x^3-425/4*x^4+2277/5*x^5+335*x^6-2900/7*x^7-375*x^8

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maxima [A]  time = 0.46, size = 39, normalized size = 0.83 \begin {gather*} -375 \, x^{8} - \frac {2900}{7} \, x^{7} + 335 \, x^{6} + \frac {2277}{5} \, x^{5} - \frac {425}{4} \, x^{4} - 201 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x

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mupad [B]  time = 0.03, size = 39, normalized size = 0.83 \begin {gather*} -375\,x^8-\frac {2900\,x^7}{7}+335\,x^6+\frac {2277\,x^5}{5}-\frac {425\,x^4}{4}-201\,x^3+\frac {27\,x^2}{2}+54\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*x^8

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sympy [A]  time = 0.07, size = 44, normalized size = 0.94 \begin {gather*} - 375 x^{8} - \frac {2900 x^{7}}{7} + 335 x^{6} + \frac {2277 x^{5}}{5} - \frac {425 x^{4}}{4} - 201 x^{3} + \frac {27 x^{2}}{2} + 54 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375*x**8 - 2900*x**7/7 + 335*x**6 + 2277*x**5/5 - 425*x**4/4 - 201*x**3 + 27*x**2/2 + 54*x

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