3.1592 \(\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=43 \[ \frac{49}{242 (1-2 x)}-\frac{1}{605 (5 x+3)}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (5 x+3)}{1331} \]

[Out]

49/(242*(1 - 2*x)) - 1/(605*(3 + 5*x)) - (14*Log[1 - 2*x])/1331 + (14*Log[3 + 5*
x])/1331

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Rubi [A]  time = 0.0533914, 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 \[ \frac{49}{242 (1-2 x)}-\frac{1}{605 (5 x+3)}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

49/(242*(1 - 2*x)) - 1/(605*(3 + 5*x)) - (14*Log[1 - 2*x])/1331 + (14*Log[3 + 5*
x])/1331

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Rubi in Sympy [A]  time = 7.79605, size = 32, normalized size = 0.74 \[ - \frac{14 \log{\left (- 2 x + 1 \right )}}{1331} + \frac{14 \log{\left (5 x + 3 \right )}}{1331} - \frac{1}{605 \left (5 x + 3\right )} + \frac{49}{242 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-14*log(-2*x + 1)/1331 + 14*log(5*x + 3)/1331 - 1/(605*(5*x + 3)) + 49/(242*(-2*
x + 1))

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Mathematica [A]  time = 0.0421475, size = 38, normalized size = 0.88 \[ \frac{-\frac{11 (1229 x+733)}{10 x^2+x-3}+140 \log (-5 x-3)-140 \log (1-2 x)}{13310} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(733 + 1229*x))/(-3 + x + 10*x^2) + 140*Log[-3 - 5*x] - 140*Log[1 - 2*x])/
13310

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Maple [A]  time = 0.013, size = 36, normalized size = 0.8 \[ -{\frac{1}{1815+3025\,x}}+{\frac{14\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{49}{-242+484\,x}}-{\frac{14\,\ln \left ( -1+2\,x \right ) }{1331}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/605/(3+5*x)+14/1331*ln(3+5*x)-49/242/(-1+2*x)-14/1331*ln(-1+2*x)

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Maxima [A]  time = 1.35548, size = 46, normalized size = 1.07 \[ -\frac{1229 \, x + 733}{1210 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{14}{1331} \, \log \left (5 \, x + 3\right ) - \frac{14}{1331} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1210*(1229*x + 733)/(10*x^2 + x - 3) + 14/1331*log(5*x + 3) - 14/1331*log(2*x
- 1)

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Fricas [A]  time = 0.204815, size = 66, normalized size = 1.53 \[ \frac{140 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 140 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 13519 \, x - 8063}{13310 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/13310*(140*(10*x^2 + x - 3)*log(5*x + 3) - 140*(10*x^2 + x - 3)*log(2*x - 1) -
13519*x - 8063)/(10*x^2 + x - 3)

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Sympy [A]  time = 0.319484, size = 34, normalized size = 0.79 \[ - \frac{1229 x + 733}{12100 x^{2} + 1210 x - 3630} - \frac{14 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{14 \log{\left (x + \frac{3}{5} \right )}}{1331} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1229*x + 733)/(12100*x**2 + 1210*x - 3630) - 14*log(x - 1/2)/1331 + 14*log(x +
3/5)/1331

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GIAC/XCAS [A]  time = 0.205483, size = 54, normalized size = 1.26 \[ -\frac{1}{605 \,{\left (5 \, x + 3\right )}} + \frac{245}{1331 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{14}{1331} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/605/(5*x + 3) + 245/1331/(11/(5*x + 3) - 2) - 14/1331*ln(abs(-11/(5*x + 3) +
2))