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]

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

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Rubi [A]  time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}

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Mathematica [A]  time = 0.02, 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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fricas [A]  time = 0.60, size = 27, normalized size = 0.73 \[ -\frac {10}{3} \, x^{4} + \frac {188}{27} \, x^{3} - \frac {161}{27} \, x^{2} + \frac {293}{81} \, x - \frac {343}{243} \, \log \left (3 \, x + 2\right ) \]

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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giac [A]  time = 1.03, size = 28, normalized size = 0.76 \[ -\frac {10}{3} \, x^{4} + \frac {188}{27} \, x^{3} - \frac {161}{27} \, x^{2} + \frac {293}{81} \, x - \frac {343}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]

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))

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maple [A]  time = 0.00, size = 28, normalized size = 0.76 \[ -\frac {10 x^{4}}{3}+\frac {188 x^{3}}{27}-\frac {161 x^{2}}{27}+\frac {293 x}{81}-\frac {343 \ln \left (3 x +2\right )}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.46, size = 27, normalized size = 0.73 \[ -\frac {10}{3} \, x^{4} + \frac {188}{27} \, x^{3} - \frac {161}{27} \, x^{2} + \frac {293}{81} \, x - \frac {343}{243} \, \log \left (3 \, x + 2\right ) \]

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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mupad [B]  time = 0.03, size = 25, normalized size = 0.68 \[ \frac {293\,x}{81}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {161\,x^2}{27}+\frac {188\,x^3}{27}-\frac {10\,x^4}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.09, size = 34, normalized size = 0.92 \[ - \frac {10 x^{4}}{3} + \frac {188 x^{3}}{27} - \frac {161 x^{2}}{27} + \frac {293 x}{81} - \frac {343 \log {\left (3 x + 2 \right )}}{243} \]

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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