3.1148 \(\int (1-2 x) (2+3 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{5}{81} (3 x+2)^6+\frac{37}{135} (3 x+2)^5-\frac{7}{108} (3 x+2)^4 \]

[Out]

(-7*(2 + 3*x)^4)/108 + (37*(2 + 3*x)^5)/135 - (5*(2 + 3*x)^6)/81

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Rubi [A]  time = 0.0144945, antiderivative size = 34, 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} \[ -\frac{5}{81} (3 x+2)^6+\frac{37}{135} (3 x+2)^5-\frac{7}{108} (3 x+2)^4 \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-7*(2 + 3*x)^4)/108 + (37*(2 + 3*x)^5)/135 - (5*(2 + 3*x)^6)/81

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)^3 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^3+\frac{37}{9} (2+3 x)^4-\frac{10}{9} (2+3 x)^5\right ) \, dx\\ &=-\frac{7}{108} (2+3 x)^4+\frac{37}{135} (2+3 x)^5-\frac{5}{81} (2+3 x)^6\\ \end{align*}

Mathematica [A]  time = 0.0009359, size = 35, normalized size = 1.03 \[ -45 x^6-\frac{567 x^5}{5}-\frac{333 x^4}{4}+\frac{46 x^3}{3}+50 x^2+24 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 50*x^2 + (46*x^3)/3 - (333*x^4)/4 - (567*x^5)/5 - 45*x^6

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Maple [A]  time = 0., size = 30, normalized size = 0.9 \begin{align*} -45\,{x}^{6}-{\frac{567\,{x}^{5}}{5}}-{\frac{333\,{x}^{4}}{4}}+{\frac{46\,{x}^{3}}{3}}+50\,{x}^{2}+24\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-45*x^6-567/5*x^5-333/4*x^4+46/3*x^3+50*x^2+24*x

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Maxima [A]  time = 1.09581, size = 39, normalized size = 1.15 \begin{align*} -45 \, x^{6} - \frac{567}{5} \, x^{5} - \frac{333}{4} \, x^{4} + \frac{46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-45*x^6 - 567/5*x^5 - 333/4*x^4 + 46/3*x^3 + 50*x^2 + 24*x

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Fricas [A]  time = 1.28403, size = 81, normalized size = 2.38 \begin{align*} -45 x^{6} - \frac{567}{5} x^{5} - \frac{333}{4} x^{4} + \frac{46}{3} x^{3} + 50 x^{2} + 24 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-45*x^6 - 567/5*x^5 - 333/4*x^4 + 46/3*x^3 + 50*x^2 + 24*x

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Sympy [A]  time = 0.058004, size = 32, normalized size = 0.94 \begin{align*} - 45 x^{6} - \frac{567 x^{5}}{5} - \frac{333 x^{4}}{4} + \frac{46 x^{3}}{3} + 50 x^{2} + 24 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-45*x**6 - 567*x**5/5 - 333*x**4/4 + 46*x**3/3 + 50*x**2 + 24*x

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Giac [A]  time = 3.48673, size = 39, normalized size = 1.15 \begin{align*} -45 \, x^{6} - \frac{567}{5} \, x^{5} - \frac{333}{4} \, x^{4} + \frac{46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-45*x^6 - 567/5*x^5 - 333/4*x^4 + 46/3*x^3 + 50*x^2 + 24*x