3.1577 \(\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=32 \[ \frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (5 x+3) \]

[Out]

49/(44*(1 - 2*x)) + (217*Log[1 - 2*x])/484 + Log[3 + 5*x]/605

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Rubi [A]  time = 0.0415348, 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 \[ \frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(44*(1 - 2*x)) + (217*Log[1 - 2*x])/484 + Log[3 + 5*x]/605

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Rubi in Sympy [A]  time = 6.73767, size = 24, normalized size = 0.75 \[ \frac{217 \log{\left (- 2 x + 1 \right )}}{484} + \frac{\log{\left (5 x + 3 \right )}}{605} + \frac{49}{44 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

217*log(-2*x + 1)/484 + log(5*x + 3)/605 + 49/(44*(-2*x + 1))

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Mathematica [A]  time = 0.0233264, size = 40, normalized size = 1.25 \[ -\frac{245}{44 (2 (5 x+3)-11)}+\frac{1}{605} \log (5 x+3)+\frac{217}{484} \log (11-2 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

-245/(44*(-11 + 2*(3 + 5*x))) + Log[3 + 5*x]/605 + (217*Log[11 - 2*(3 + 5*x)])/4
84

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Maple [A]  time = 0.011, size = 27, normalized size = 0.8 \[{\frac{\ln \left ( 3+5\,x \right ) }{605}}-{\frac{49}{-44+88\,x}}+{\frac{217\,\ln \left ( -1+2\,x \right ) }{484}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/605*ln(3+5*x)-49/44/(-1+2*x)+217/484*ln(-1+2*x)

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Maxima [A]  time = 1.34118, size = 35, normalized size = 1.09 \[ -\frac{49}{44 \,{\left (2 \, x - 1\right )}} + \frac{1}{605} \, \log \left (5 \, x + 3\right ) + \frac{217}{484} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/44/(2*x - 1) + 1/605*log(5*x + 3) + 217/484*log(2*x - 1)

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Fricas [A]  time = 0.205392, size = 50, normalized size = 1.56 \[ \frac{4 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 1085 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2695}{2420 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2420*(4*(2*x - 1)*log(5*x + 3) + 1085*(2*x - 1)*log(2*x - 1) - 2695)/(2*x - 1)

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Sympy [A]  time = 0.307791, size = 24, normalized size = 0.75 \[ \frac{217 \log{\left (x - \frac{1}{2} \right )}}{484} + \frac{\log{\left (x + \frac{3}{5} \right )}}{605} - \frac{49}{88 x - 44} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

217*log(x - 1/2)/484 + log(x + 3/5)/605 - 49/(88*x - 44)

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GIAC/XCAS [A]  time = 0.210465, size = 58, normalized size = 1.81 \[ -\frac{49}{44 \,{\left (2 \, x - 1\right )}} - \frac{9}{20} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{605} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/44/(2*x - 1) - 9/20*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) + 1/605*ln(abs(-11/(2*x
- 1) - 5))