3.1462 \(\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx\)

Optimal. Leaf size=54 \[ \frac{3469}{9261 (3 x+2)}-\frac{103}{2646 (3 x+2)^2}+\frac{1}{567 (3 x+2)^3}-\frac{1331 \log (1-2 x)}{2401}+\frac{1331 \log (3 x+2)}{2401} \]

[Out]

1/(567*(2 + 3*x)^3) - 103/(2646*(2 + 3*x)^2) + 3469/(9261*(2 + 3*x)) - (1331*Log
[1 - 2*x])/2401 + (1331*Log[2 + 3*x])/2401

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Rubi [A]  time = 0.0590669, antiderivative size = 54, 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 \[ \frac{3469}{9261 (3 x+2)}-\frac{103}{2646 (3 x+2)^2}+\frac{1}{567 (3 x+2)^3}-\frac{1331 \log (1-2 x)}{2401}+\frac{1331 \log (3 x+2)}{2401} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^4),x]

[Out]

1/(567*(2 + 3*x)^3) - 103/(2646*(2 + 3*x)^2) + 3469/(9261*(2 + 3*x)) - (1331*Log
[1 - 2*x])/2401 + (1331*Log[2 + 3*x])/2401

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Rubi in Sympy [A]  time = 9.05399, size = 46, normalized size = 0.85 \[ - \frac{1331 \log{\left (- 2 x + 1 \right )}}{2401} + \frac{1331 \log{\left (3 x + 2 \right )}}{2401} + \frac{3469}{9261 \left (3 x + 2\right )} - \frac{103}{2646 \left (3 x + 2\right )^{2}} + \frac{1}{567 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**3/(1-2*x)/(2+3*x)**4,x)

[Out]

-1331*log(-2*x + 1)/2401 + 1331*log(3*x + 2)/2401 + 3469/(9261*(3*x + 2)) - 103/
(2646*(3*x + 2)**2) + 1/(567*(3*x + 2)**3)

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Mathematica [A]  time = 0.0394475, size = 40, normalized size = 0.74 \[ \frac{\frac{7 \left (187326 x^2+243279 x+79028\right )}{(3 x+2)^3}-215622 \log (1-2 x)+215622 \log (6 x+4)}{388962} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^4),x]

[Out]

((7*(79028 + 243279*x + 187326*x^2))/(2 + 3*x)^3 - 215622*Log[1 - 2*x] + 215622*
Log[4 + 6*x])/388962

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Maple [A]  time = 0.011, size = 45, normalized size = 0.8 \[{\frac{1}{567\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{103}{2646\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{3469}{18522+27783\,x}}+{\frac{1331\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{1331\,\ln \left ( -1+2\,x \right ) }{2401}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^3/(1-2*x)/(2+3*x)^4,x)

[Out]

1/567/(2+3*x)^3-103/2646/(2+3*x)^2+3469/9261/(2+3*x)+1331/2401*ln(2+3*x)-1331/24
01*ln(-1+2*x)

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Maxima [A]  time = 1.34286, size = 62, normalized size = 1.15 \[ \frac{187326 \, x^{2} + 243279 \, x + 79028}{55566 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{1331}{2401} \, \log \left (3 \, x + 2\right ) - \frac{1331}{2401} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3/((3*x + 2)^4*(2*x - 1)),x, algorithm="maxima")

[Out]

1/55566*(187326*x^2 + 243279*x + 79028)/(27*x^3 + 54*x^2 + 36*x + 8) + 1331/2401
*log(3*x + 2) - 1331/2401*log(2*x - 1)

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Fricas [A]  time = 0.217309, size = 101, normalized size = 1.87 \[ \frac{1311282 \, x^{2} + 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 1702953 \, x + 553196}{388962 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3/((3*x + 2)^4*(2*x - 1)),x, algorithm="fricas")

[Out]

1/388962*(1311282*x^2 + 215622*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 21562
2*(27*x^3 + 54*x^2 + 36*x + 8)*log(2*x - 1) + 1702953*x + 553196)/(27*x^3 + 54*x
^2 + 36*x + 8)

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Sympy [A]  time = 0.441047, size = 44, normalized size = 0.81 \[ \frac{187326 x^{2} + 243279 x + 79028}{1500282 x^{3} + 3000564 x^{2} + 2000376 x + 444528} - \frac{1331 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{1331 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**3/(1-2*x)/(2+3*x)**4,x)

[Out]

(187326*x**2 + 243279*x + 79028)/(1500282*x**3 + 3000564*x**2 + 2000376*x + 4445
28) - 1331*log(x - 1/2)/2401 + 1331*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.208717, size = 51, normalized size = 0.94 \[ \frac{187326 \, x^{2} + 243279 \, x + 79028}{55566 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1331}{2401} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1331}{2401} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3/((3*x + 2)^4*(2*x - 1)),x, algorithm="giac")

[Out]

1/55566*(187326*x^2 + 243279*x + 79028)/(3*x + 2)^3 + 1331/2401*ln(abs(3*x + 2))
- 1331/2401*ln(abs(2*x - 1))