3.1164 \(\int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=31 \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6

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Rubi [A]  time = 0.014905, antiderivative size = 31, 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} \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*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+3 x)^2 (3+5 x)^2 \, dx &=\int \left (36+156 x+85 x^2-512 x^3-915 x^4-450 x^5\right ) \, dx\\ &=36 x+78 x^2+\frac{85 x^3}{3}-128 x^4-183 x^5-75 x^6\\ \end{align*}

Mathematica [A]  time = 0.0009216, size = 31, normalized size = 1. \[ -75 x^6-183 x^5-128 x^4+\frac{85 x^3}{3}+78 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6

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Maple [A]  time = 0., size = 30, normalized size = 1. \begin{align*} 36\,x+78\,{x}^{2}+{\frac{85\,{x}^{3}}{3}}-128\,{x}^{4}-183\,{x}^{5}-75\,{x}^{6} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

36*x+78*x^2+85/3*x^3-128*x^4-183*x^5-75*x^6

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Maxima [A]  time = 1.10817, size = 39, normalized size = 1.26 \begin{align*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac{85}{3} \, x^{3} + 78 \, x^{2} + 36 \, 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)^2,x, algorithm="maxima")

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

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Fricas [A]  time = 1.45327, size = 76, normalized size = 2.45 \begin{align*} -75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85}{3} x^{3} + 78 x^{2} + 36 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)^2,x, algorithm="fricas")

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

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Sympy [A]  time = 0.058688, size = 29, normalized size = 0.94 \begin{align*} - 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85 x^{3}}{3} + 78 x^{2} + 36 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)**2,x)

[Out]

-75*x**6 - 183*x**5 - 128*x**4 + 85*x**3/3 + 78*x**2 + 36*x

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Giac [A]  time = 2.61112, size = 39, normalized size = 1.26 \begin{align*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac{85}{3} \, x^{3} + 78 \, x^{2} + 36 \, 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)^2,x, algorithm="giac")

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x