3.1167 \(\int \frac{(1-2 x) (3+5 x)^3}{2+3 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{125 x^4}{6}-\frac{475 x^3}{27}+\frac{545 x^2}{54}+\frac{1097 x}{81}-\frac{7}{243} \log (3 x+2) \]

[Out]

(1097*x)/81 + (545*x^2)/54 - (475*x^3)/27 - (125*x^4)/6 - (7*Log[2 + 3*x])/243

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Rubi [A]  time = 0.0354103, 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 \[ -\frac{125 x^4}{6}-\frac{475 x^3}{27}+\frac{545 x^2}{54}+\frac{1097 x}{81}-\frac{7}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(1097*x)/81 + (545*x^2)/54 - (475*x^3)/27 - (125*x^4)/6 - (7*Log[2 + 3*x])/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{125 x^{4}}{6} - \frac{475 x^{3}}{27} - \frac{7 \log{\left (3 x + 2 \right )}}{243} + \int \frac{1097}{81}\, dx + \frac{545 \int x\, dx}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)**3/(2+3*x),x)

[Out]

-125*x**4/6 - 475*x**3/27 - 7*log(3*x + 2)/243 + Integral(1097/81, x) + 545*Inte
gral(x, x)/27

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Mathematica [A]  time = 0.0178861, size = 32, normalized size = 0.86 \[ \frac{-30375 x^4-25650 x^3+14715 x^2+19746 x-42 \log (3 x+2)+5024}{1458} \]

Antiderivative was successfully verified.

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

[Out]

(5024 + 19746*x + 14715*x^2 - 25650*x^3 - 30375*x^4 - 42*Log[2 + 3*x])/1458

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Maple [A]  time = 0.005, size = 28, normalized size = 0.8 \[{\frac{1097\,x}{81}}+{\frac{545\,{x}^{2}}{54}}-{\frac{475\,{x}^{3}}{27}}-{\frac{125\,{x}^{4}}{6}}-{\frac{7\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1097/81*x+545/54*x^2-475/27*x^3-125/6*x^4-7/243*ln(2+3*x)

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Maxima [A]  time = 1.32649, size = 36, normalized size = 0.97 \[ -\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/6*x^4 - 475/27*x^3 + 545/54*x^2 + 1097/81*x - 7/243*log(3*x + 2)

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Fricas [A]  time = 0.211039, size = 36, normalized size = 0.97 \[ -\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/6*x^4 - 475/27*x^3 + 545/54*x^2 + 1097/81*x - 7/243*log(3*x + 2)

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Sympy [A]  time = 0.166831, size = 34, normalized size = 0.92 \[ - \frac{125 x^{4}}{6} - \frac{475 x^{3}}{27} + \frac{545 x^{2}}{54} + \frac{1097 x}{81} - \frac{7 \log{\left (3 x + 2 \right )}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x**4/6 - 475*x**3/27 + 545*x**2/54 + 1097*x/81 - 7*log(3*x + 2)/243

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GIAC/XCAS [A]  time = 0.207973, size = 38, normalized size = 1.03 \[ -\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/6*x^4 - 475/27*x^3 + 545/54*x^2 + 1097/81*x - 7/243*ln(abs(3*x + 2))