3.1344 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=40 \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

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Rubi [A]  time = 0.0172792, antiderivative size = 40, 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} \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

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)^2 (3+5 x) \, dx &=\int \left (12-16 x-105 x^2+99 x^3+326 x^4-156 x^5-360 x^6\right ) \, dx\\ &=12 x-8 x^2-35 x^3+\frac{99 x^4}{4}+\frac{326 x^5}{5}-26 x^6-\frac{360 x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0008698, size = 40, normalized size = 1. \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

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Maple [A]  time = 0., size = 35, normalized size = 0.9 \begin{align*} 12\,x-8\,{x}^{2}-35\,{x}^{3}+{\frac{99\,{x}^{4}}{4}}+{\frac{326\,{x}^{5}}{5}}-26\,{x}^{6}-{\frac{360\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7

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Maxima [A]  time = 1.14528, size = 46, normalized size = 1.15 \begin{align*} -\frac{360}{7} \, x^{7} - 26 \, x^{6} + \frac{326}{5} \, x^{5} + \frac{99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

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Fricas [A]  time = 1.19916, size = 92, normalized size = 2.3 \begin{align*} -\frac{360}{7} x^{7} - 26 x^{6} + \frac{326}{5} x^{5} + \frac{99}{4} x^{4} - 35 x^{3} - 8 x^{2} + 12 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

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Sympy [A]  time = 0.060783, size = 37, normalized size = 0.92 \begin{align*} - \frac{360 x^{7}}{7} - 26 x^{6} + \frac{326 x^{5}}{5} + \frac{99 x^{4}}{4} - 35 x^{3} - 8 x^{2} + 12 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360*x**7/7 - 26*x**6 + 326*x**5/5 + 99*x**4/4 - 35*x**3 - 8*x**2 + 12*x

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Giac [A]  time = 1.98691, size = 46, normalized size = 1.15 \begin{align*} -\frac{360}{7} \, x^{7} - 26 \, x^{6} + \frac{326}{5} \, x^{5} + \frac{99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x