3.1149 \(\int (1-2 x) (2+3 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=28 \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]

[Out]

12*x + 16*x^2 - (25*x^3)/3 - (129*x^4)/4 - 18*x^5

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Rubi [A]  time = 0.012096, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

12*x + 16*x^2 - (25*x^3)/3 - (129*x^4)/4 - 18*x^5

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+3 x)^2 (3+5 x) \, dx &=\int \left (12+32 x-25 x^2-129 x^3-90 x^4\right ) \, dx\\ &=12 x+16 x^2-\frac{25 x^3}{3}-\frac{129 x^4}{4}-18 x^5\\ \end{align*}

Mathematica [A]  time = 0.0008591, size = 28, normalized size = 1. \[ -18 x^5-\frac{129 x^4}{4}-\frac{25 x^3}{3}+16 x^2+12 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

12*x + 16*x^2 - (25*x^3)/3 - (129*x^4)/4 - 18*x^5

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Maple [A]  time = 0.001, size = 25, normalized size = 0.9 \begin{align*} 12\,x+16\,{x}^{2}-{\frac{25\,{x}^{3}}{3}}-{\frac{129\,{x}^{4}}{4}}-18\,{x}^{5} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x+16*x^2-25/3*x^3-129/4*x^4-18*x^5

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Maxima [A]  time = 1.2363, size = 32, normalized size = 1.14 \begin{align*} -18 \, x^{5} - \frac{129}{4} \, x^{4} - \frac{25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x

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Fricas [A]  time = 1.27884, size = 65, normalized size = 2.32 \begin{align*} -18 x^{5} - \frac{129}{4} x^{4} - \frac{25}{3} x^{3} + 16 x^{2} + 12 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x

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Sympy [A]  time = 0.055785, size = 26, normalized size = 0.93 \begin{align*} - 18 x^{5} - \frac{129 x^{4}}{4} - \frac{25 x^{3}}{3} + 16 x^{2} + 12 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-18*x**5 - 129*x**4/4 - 25*x**3/3 + 16*x**2 + 12*x

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Giac [A]  time = 1.77552, size = 32, normalized size = 1.14 \begin{align*} -18 \, x^{5} - \frac{129}{4} \, x^{4} - \frac{25}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x