3.1461 \(\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^3} \, dx\)

Optimal. Leaf size=43 \[ -\frac{103}{1323 (3 x+2)}+\frac{1}{378 (3 x+2)^2}-\frac{1331}{686} \log (1-2 x)-\frac{3469 \log (3 x+2)}{9261} \]

[Out]

1/(378*(2 + 3*x)^2) - 103/(1323*(2 + 3*x)) - (1331*Log[1 - 2*x])/686 - (3469*Log
[2 + 3*x])/9261

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Rubi [A]  time = 0.0495631, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{103}{1323 (3 x+2)}+\frac{1}{378 (3 x+2)^2}-\frac{1331}{686} \log (1-2 x)-\frac{3469 \log (3 x+2)}{9261} \]

Antiderivative was successfully verified.

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

[Out]

1/(378*(2 + 3*x)^2) - 103/(1323*(2 + 3*x)) - (1331*Log[1 - 2*x])/686 - (3469*Log
[2 + 3*x])/9261

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Rubi in Sympy [A]  time = 7.90407, size = 36, normalized size = 0.84 \[ - \frac{1331 \log{\left (- 2 x + 1 \right )}}{686} - \frac{3469 \log{\left (3 x + 2 \right )}}{9261} - \frac{103}{1323 \left (3 x + 2\right )} + \frac{1}{378 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331*log(-2*x + 1)/686 - 3469*log(3*x + 2)/9261 - 103/(1323*(3*x + 2)) + 1/(378
*(3*x + 2)**2)

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Mathematica [A]  time = 0.0361536, size = 35, normalized size = 0.81 \[ \frac{-\frac{21 (206 x+135)}{(3 x+2)^2}-35937 \log (1-2 x)-6938 \log (6 x+4)}{18522} \]

Antiderivative was successfully verified.

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

[Out]

((-21*(135 + 206*x))/(2 + 3*x)^2 - 35937*Log[1 - 2*x] - 6938*Log[4 + 6*x])/18522

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Maple [A]  time = 0.013, size = 36, normalized size = 0.8 \[{\frac{1}{378\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{103}{2646+3969\,x}}-{\frac{3469\,\ln \left ( 2+3\,x \right ) }{9261}}-{\frac{1331\,\ln \left ( -1+2\,x \right ) }{686}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/378/(2+3*x)^2-103/1323/(2+3*x)-3469/9261*ln(2+3*x)-1331/686*ln(-1+2*x)

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Maxima [A]  time = 1.35005, size = 49, normalized size = 1.14 \[ -\frac{206 \, x + 135}{882 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{3469}{9261} \, \log \left (3 \, x + 2\right ) - \frac{1331}{686} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/882*(206*x + 135)/(9*x^2 + 12*x + 4) - 3469/9261*log(3*x + 2) - 1331/686*log(
2*x - 1)

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Fricas [A]  time = 0.215171, size = 74, normalized size = 1.72 \[ -\frac{6938 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 35937 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 4326 \, x + 2835}{18522 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/18522*(6938*(9*x^2 + 12*x + 4)*log(3*x + 2) + 35937*(9*x^2 + 12*x + 4)*log(2*
x - 1) + 4326*x + 2835)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.423903, size = 36, normalized size = 0.84 \[ - \frac{206 x + 135}{7938 x^{2} + 10584 x + 3528} - \frac{1331 \log{\left (x - \frac{1}{2} \right )}}{686} - \frac{3469 \log{\left (x + \frac{2}{3} \right )}}{9261} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(206*x + 135)/(7938*x**2 + 10584*x + 3528) - 1331*log(x - 1/2)/686 - 3469*log(x
+ 2/3)/9261

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GIAC/XCAS [A]  time = 0.209346, size = 45, normalized size = 1.05 \[ -\frac{206 \, x + 135}{882 \,{\left (3 \, x + 2\right )}^{2}} - \frac{3469}{9261} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1331}{686} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/882*(206*x + 135)/(3*x + 2)^2 - 3469/9261*ln(abs(3*x + 2)) - 1331/686*ln(abs(
2*x - 1))