3.1260 \(\int (1-2 x)^2 (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=35 \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]

[Out]

18*x + (15*x^2)/2 - (136*x^3)/3 - (137*x^4)/4 + 52*x^5 + 50*x^6

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Rubi [A]  time = 0.0138977, antiderivative size = 35, 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} \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

18*x + (15*x^2)/2 - (136*x^3)/3 - (137*x^4)/4 + 52*x^5 + 50*x^6

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)^2 (2+3 x) (3+5 x)^2 \, dx &=\int \left (18+15 x-136 x^2-137 x^3+260 x^4+300 x^5\right ) \, dx\\ &=18 x+\frac{15 x^2}{2}-\frac{136 x^3}{3}-\frac{137 x^4}{4}+52 x^5+50 x^6\\ \end{align*}

Mathematica [A]  time = 0.0007696, size = 35, normalized size = 1. \[ 50 x^6+52 x^5-\frac{137 x^4}{4}-\frac{136 x^3}{3}+\frac{15 x^2}{2}+18 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

18*x + (15*x^2)/2 - (136*x^3)/3 - (137*x^4)/4 + 52*x^5 + 50*x^6

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Maple [A]  time = 0.001, size = 30, normalized size = 0.9 \begin{align*} 18\,x+{\frac{15\,{x}^{2}}{2}}-{\frac{136\,{x}^{3}}{3}}-{\frac{137\,{x}^{4}}{4}}+52\,{x}^{5}+50\,{x}^{6} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18*x+15/2*x^2-136/3*x^3-137/4*x^4+52*x^5+50*x^6

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Maxima [A]  time = 1.38883, size = 39, normalized size = 1.11 \begin{align*} 50 \, x^{6} + 52 \, x^{5} - \frac{137}{4} \, x^{4} - \frac{136}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x

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Fricas [A]  time = 1.28191, size = 80, normalized size = 2.29 \begin{align*} 50 x^{6} + 52 x^{5} - \frac{137}{4} x^{4} - \frac{136}{3} x^{3} + \frac{15}{2} x^{2} + 18 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x

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Sympy [A]  time = 0.058923, size = 32, normalized size = 0.91 \begin{align*} 50 x^{6} + 52 x^{5} - \frac{137 x^{4}}{4} - \frac{136 x^{3}}{3} + \frac{15 x^{2}}{2} + 18 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

50*x**6 + 52*x**5 - 137*x**4/4 - 136*x**3/3 + 15*x**2/2 + 18*x

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Giac [A]  time = 2.03849, size = 39, normalized size = 1.11 \begin{align*} 50 \, x^{6} + 52 \, x^{5} - \frac{137}{4} \, x^{4} - \frac{136}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x