3.1442 \(\int \frac{(3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=23 \[ -\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x) \]

[Out]

(-85*x)/4 - (25*x^2)/4 - (121*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0220107, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/(1 - 2*x),x]

[Out]

(-85*x)/4 - (25*x^2)/4 - (121*Log[1 - 2*x])/8

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{121 \log{\left (- 2 x + 1 \right )}}{8} + \int \left (- \frac{85}{4}\right )\, dx - \frac{25 \int x\, dx}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-121*log(-2*x + 1)/8 + Integral(-85/4, x) - 25*Integral(x, x)/2

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Mathematica [A]  time = 0.00956173, size = 25, normalized size = 1.09 \[ \frac{1}{16} \left (-5 \left (20 x^2+68 x-39\right )-242 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-5*(-39 + 68*x + 20*x^2) - 242*Log[1 - 2*x])/16

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Maple [A]  time = 0.003, size = 18, normalized size = 0.8 \[ -{\frac{25\,{x}^{2}}{4}}-{\frac{85\,x}{4}}-{\frac{121\,\ln \left ( -1+2\,x \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x),x)

[Out]

-25/4*x^2-85/4*x-121/8*ln(-1+2*x)

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Maxima [A]  time = 1.33354, size = 23, normalized size = 1. \[ -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/4*x^2 - 85/4*x - 121/8*log(2*x - 1)

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Fricas [A]  time = 0.216432, size = 23, normalized size = 1. \[ -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/4*x^2 - 85/4*x - 121/8*log(2*x - 1)

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Sympy [A]  time = 0.148875, size = 22, normalized size = 0.96 \[ - \frac{25 x^{2}}{4} - \frac{85 x}{4} - \frac{121 \log{\left (2 x - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**2/(1-2*x),x)

[Out]

-25*x**2/4 - 85*x/4 - 121*log(2*x - 1)/8

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GIAC/XCAS [A]  time = 0.206113, size = 24, normalized size = 1.04 \[ -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/4*x^2 - 85/4*x - 121/8*ln(abs(2*x - 1))