3.1347 \(\int \frac{(1-2 x)^3 (3+5 x)}{2+3 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{10 x^4}{3}+\frac{188 x^3}{27}-\frac{161 x^2}{27}+\frac{293 x}{81}-\frac{343}{243} \log (3 x+2) \]

[Out]

(293*x)/81 - (161*x^2)/27 + (188*x^3)/27 - (10*x^4)/3 - (343*Log[2 + 3*x])/243

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Rubi [A]  time = 0.0133814, antiderivative size = 37, 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} \[ -\frac{10 x^4}{3}+\frac{188 x^3}{27}-\frac{161 x^2}{27}+\frac{293 x}{81}-\frac{343}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(293*x)/81 - (161*x^2)/27 + (188*x^3)/27 - (10*x^4)/3 - (343*Log[2 + 3*x])/243

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 \frac{(1-2 x)^3 (3+5 x)}{2+3 x} \, dx &=\int \left (\frac{293}{81}-\frac{322 x}{27}+\frac{188 x^2}{9}-\frac{40 x^3}{3}-\frac{343}{81 (2+3 x)}\right ) \, dx\\ &=\frac{293 x}{81}-\frac{161 x^2}{27}+\frac{188 x^3}{27}-\frac{10 x^4}{3}-\frac{343}{243} \log (2+3 x)\\ \end{align*}

Mathematica [A]  time = 0.0114267, size = 32, normalized size = 0.86 \[ \frac{1}{729} \left (-2430 x^4+5076 x^3-4347 x^2+2637 x-1029 \log (3 x+2)+5674\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(5674 + 2637*x - 4347*x^2 + 5076*x^3 - 2430*x^4 - 1029*Log[2 + 3*x])/729

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Maple [A]  time = 0.003, size = 28, normalized size = 0.8 \begin{align*}{\frac{293\,x}{81}}-{\frac{161\,{x}^{2}}{27}}+{\frac{188\,{x}^{3}}{27}}-{\frac{10\,{x}^{4}}{3}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

293/81*x-161/27*x^2+188/27*x^3-10/3*x^4-343/243*ln(2+3*x)

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Maxima [A]  time = 1.03237, size = 36, normalized size = 0.97 \begin{align*} -\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{243} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10/3*x^4 + 188/27*x^3 - 161/27*x^2 + 293/81*x - 343/243*log(3*x + 2)

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Fricas [A]  time = 1.26892, size = 96, normalized size = 2.59 \begin{align*} -\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{243} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10/3*x^4 + 188/27*x^3 - 161/27*x^2 + 293/81*x - 343/243*log(3*x + 2)

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Sympy [A]  time = 0.087991, size = 34, normalized size = 0.92 \begin{align*} - \frac{10 x^{4}}{3} + \frac{188 x^{3}}{27} - \frac{161 x^{2}}{27} + \frac{293 x}{81} - \frac{343 \log{\left (3 x + 2 \right )}}{243} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x**4/3 + 188*x**3/27 - 161*x**2/27 + 293*x/81 - 343*log(3*x + 2)/243

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Giac [A]  time = 2.73058, size = 38, normalized size = 1.03 \begin{align*} -\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10/3*x^4 + 188/27*x^3 - 161/27*x^2 + 293/81*x - 343/243*log(abs(3*x + 2))