3.1547 \(\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^2} \, dx\)

Optimal. Leaf size=43 \[ \frac{121}{98 (1-2 x)}-\frac{1}{147 (3 x+2)}+\frac{22}{343} \log (1-2 x)-\frac{22}{343} \log (3 x+2) \]

[Out]

121/(98*(1 - 2*x)) - 1/(147*(2 + 3*x)) + (22*Log[1 - 2*x])/343 - (22*Log[2 + 3*x
])/343

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Rubi [A]  time = 0.0521172, 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 \[ \frac{121}{98 (1-2 x)}-\frac{1}{147 (3 x+2)}+\frac{22}{343} \log (1-2 x)-\frac{22}{343} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

121/(98*(1 - 2*x)) - 1/(147*(2 + 3*x)) + (22*Log[1 - 2*x])/343 - (22*Log[2 + 3*x
])/343

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Rubi in Sympy [A]  time = 7.79651, size = 32, normalized size = 0.74 \[ \frac{22 \log{\left (- 2 x + 1 \right )}}{343} - \frac{22 \log{\left (3 x + 2 \right )}}{343} - \frac{1}{147 \left (3 x + 2\right )} + \frac{121}{98 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

22*log(-2*x + 1)/343 - 22*log(3*x + 2)/343 - 1/(147*(3*x + 2)) + 121/(98*(-2*x +
1))

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Mathematica [A]  time = 0.0443986, size = 38, normalized size = 0.88 \[ \frac{-\frac{7 (1093 x+724)}{6 x^2+x-2}+132 \log (1-2 x)-132 \log (3 x+2)}{2058} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(724 + 1093*x))/(-2 + x + 6*x^2) + 132*Log[1 - 2*x] - 132*Log[2 + 3*x])/205
8

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Maple [A]  time = 0.013, size = 36, normalized size = 0.8 \[ -{\frac{1}{294+441\,x}}-{\frac{22\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{121}{-98+196\,x}}+{\frac{22\,\ln \left ( -1+2\,x \right ) }{343}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/147/(2+3*x)-22/343*ln(2+3*x)-121/98/(-1+2*x)+22/343*ln(-1+2*x)

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Maxima [A]  time = 1.34805, size = 46, normalized size = 1.07 \[ -\frac{1093 \, x + 724}{294 \,{\left (6 \, x^{2} + x - 2\right )}} - \frac{22}{343} \, \log \left (3 \, x + 2\right ) + \frac{22}{343} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/294*(1093*x + 724)/(6*x^2 + x - 2) - 22/343*log(3*x + 2) + 22/343*log(2*x - 1
)

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Fricas [A]  time = 0.20941, size = 66, normalized size = 1.53 \[ -\frac{132 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) - 132 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) + 7651 \, x + 5068}{2058 \,{\left (6 \, x^{2} + x - 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2058*(132*(6*x^2 + x - 2)*log(3*x + 2) - 132*(6*x^2 + x - 2)*log(2*x - 1) + 7
651*x + 5068)/(6*x^2 + x - 2)

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Sympy [A]  time = 0.322092, size = 34, normalized size = 0.79 \[ - \frac{1093 x + 724}{1764 x^{2} + 294 x - 588} + \frac{22 \log{\left (x - \frac{1}{2} \right )}}{343} - \frac{22 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1093*x + 724)/(1764*x**2 + 294*x - 588) + 22*log(x - 1/2)/343 - 22*log(x + 2/3
)/343

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GIAC/XCAS [A]  time = 0.208808, size = 54, normalized size = 1.26 \[ -\frac{1}{147 \,{\left (3 \, x + 2\right )}} + \frac{363}{343 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} + \frac{22}{343} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/147/(3*x + 2) + 363/343/(7/(3*x + 2) - 2) + 22/343*ln(abs(-7/(3*x + 2) + 2))