3.1378 \(\int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx\)

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

[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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Rubi [A]  time = 0.0181664, antiderivative size = 47, 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} \[ -375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x \]

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*}

Mathematica [A]  time = 0.0010069, size = 47, normalized size = 1. \[ -375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x \]

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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Maple [A]  time = 0.001, size = 40, normalized size = 0.9 \begin{align*} 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*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)*(3+5*x)^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 = 1.03634, size = 53, normalized size = 1.13 \begin{align*} -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{align*}

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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Fricas [A]  time = 1.00643, size = 116, normalized size = 2.47 \begin{align*} -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{align*}

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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Sympy [A]  time = 0.063234, size = 44, normalized size = 0.94 \begin{align*} - 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{align*}

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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Giac [A]  time = 2.46492, size = 53, normalized size = 1.13 \begin{align*} -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{align*}

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