3.1230 \(\int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=38 \[ \frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2) \]

[Out]

(20*x)/27 + 49/(162*(2 + 3*x)^2) - 91/(27*(2 + 3*x)) - (16*Log[2 + 3*x])/9

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Rubi [A]  time = 0.046529, antiderivative size = 38, 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 \[ \frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(20*x)/27 + 49/(162*(2 + 3*x)^2) - 91/(27*(2 + 3*x)) - (16*Log[2 + 3*x])/9

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{16 \log{\left (3 x + 2 \right )}}{9} + \int \frac{20}{27}\, dx - \frac{91}{27 \left (3 x + 2\right )} + \frac{49}{162 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-16*log(3*x + 2)/9 + Integral(20/27, x) - 91/(27*(3*x + 2)) + 49/(162*(3*x + 2)*
*2)

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Mathematica [A]  time = 0.0205816, size = 41, normalized size = 1.08 \[ \frac{1080 x^3+900 x^2-1878 x-288 (3 x+2)^2 \log (6 x+4)-1283}{162 (3 x+2)^2} \]

Antiderivative was successfully verified.

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

[Out]

(-1283 - 1878*x + 900*x^2 + 1080*x^3 - 288*(2 + 3*x)^2*Log[4 + 6*x])/(162*(2 + 3
*x)^2)

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Maple [A]  time = 0.012, size = 31, normalized size = 0.8 \[{\frac{20\,x}{27}}+{\frac{49}{162\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{91}{54+81\,x}}-{\frac{16\,\ln \left ( 2+3\,x \right ) }{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/27*x+49/162/(2+3*x)^2-91/27/(2+3*x)-16/9*ln(2+3*x)

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Maxima [A]  time = 1.34441, size = 42, normalized size = 1.11 \[ \frac{20}{27} \, x - \frac{7 \,{\left (234 \, x + 149\right )}}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{16}{9} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/27*x - 7/162*(234*x + 149)/(9*x^2 + 12*x + 4) - 16/9*log(3*x + 2)

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Fricas [A]  time = 0.214781, size = 63, normalized size = 1.66 \[ \frac{1080 \, x^{3} + 1440 \, x^{2} - 288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 1158 \, x - 1043}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/162*(1080*x^3 + 1440*x^2 - 288*(9*x^2 + 12*x + 4)*log(3*x + 2) - 1158*x - 1043
)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.271722, size = 29, normalized size = 0.76 \[ \frac{20 x}{27} - \frac{1638 x + 1043}{1458 x^{2} + 1944 x + 648} - \frac{16 \log{\left (3 x + 2 \right )}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x/27 - (1638*x + 1043)/(1458*x**2 + 1944*x + 648) - 16*log(3*x + 2)/9

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GIAC/XCAS [A]  time = 0.20786, size = 36, normalized size = 0.95 \[ \frac{20}{27} \, x - \frac{7 \,{\left (234 \, x + 149\right )}}{162 \,{\left (3 \, x + 2\right )}^{2}} - \frac{16}{9} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/27*x - 7/162*(234*x + 149)/(3*x + 2)^2 - 16/9*ln(abs(3*x + 2))