3.1546 \(\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)} \, dx\)

Optimal. Leaf size=32 \[ \frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2) \]

[Out]

121/(28*(1 - 2*x)) + (407*Log[1 - 2*x])/196 + Log[2 + 3*x]/147

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Rubi [A]  time = 0.0434601, antiderivative size = 32, 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 \[ \frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

121/(28*(1 - 2*x)) + (407*Log[1 - 2*x])/196 + Log[2 + 3*x]/147

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Rubi in Sympy [A]  time = 6.68426, size = 24, normalized size = 0.75 \[ \frac{407 \log{\left (- 2 x + 1 \right )}}{196} + \frac{\log{\left (3 x + 2 \right )}}{147} + \frac{121}{28 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

407*log(-2*x + 1)/196 + log(3*x + 2)/147 + 121/(28*(-2*x + 1))

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Mathematica [A]  time = 0.0249334, size = 40, normalized size = 1.25 \[ -\frac{363}{28 (2 (3 x+2)-7)}+\frac{1}{147} \log (3 x+2)+\frac{407}{196} \log (7-2 (3 x+2)) \]

Antiderivative was successfully verified.

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

[Out]

-363/(28*(-7 + 2*(2 + 3*x))) + Log[2 + 3*x]/147 + (407*Log[7 - 2*(2 + 3*x)])/196

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Maple [A]  time = 0.01, size = 27, normalized size = 0.8 \[{\frac{\ln \left ( 2+3\,x \right ) }{147}}-{\frac{121}{-28+56\,x}}+{\frac{407\,\ln \left ( -1+2\,x \right ) }{196}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/147*ln(2+3*x)-121/28/(-1+2*x)+407/196*ln(-1+2*x)

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Maxima [A]  time = 1.33838, size = 35, normalized size = 1.09 \[ -\frac{121}{28 \,{\left (2 \, x - 1\right )}} + \frac{1}{147} \, \log \left (3 \, x + 2\right ) + \frac{407}{196} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-121/28/(2*x - 1) + 1/147*log(3*x + 2) + 407/196*log(2*x - 1)

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Fricas [A]  time = 0.210355, size = 50, normalized size = 1.56 \[ \frac{4 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) + 1221 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2541}{588 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/588*(4*(2*x - 1)*log(3*x + 2) + 1221*(2*x - 1)*log(2*x - 1) - 2541)/(2*x - 1)

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Sympy [A]  time = 0.309411, size = 24, normalized size = 0.75 \[ \frac{407 \log{\left (x - \frac{1}{2} \right )}}{196} + \frac{\log{\left (x + \frac{2}{3} \right )}}{147} - \frac{121}{56 x - 28} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

407*log(x - 1/2)/196 + log(x + 2/3)/147 - 121/(56*x - 28)

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GIAC/XCAS [A]  time = 0.207518, size = 58, normalized size = 1.81 \[ -\frac{121}{28 \,{\left (2 \, x - 1\right )}} - \frac{25}{12} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{147} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-121/28/(2*x - 1) - 25/12*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) + 1/147*ln(abs(-7/(2*
x - 1) - 3))