3.1529 \(\int \frac{3+5 x}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=22 \[ \frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x) \]

[Out]

11/(4*(1 - 2*x)) + (5*Log[1 - 2*x])/4

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Rubi [A]  time = 0.0214085, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)/(1 - 2*x)^2,x]

[Out]

11/(4*(1 - 2*x)) + (5*Log[1 - 2*x])/4

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Rubi in Sympy [A]  time = 4.52582, size = 15, normalized size = 0.68 \[ \frac{5 \log{\left (- 2 x + 1 \right )}}{4} + \frac{11}{4 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5*log(-2*x + 1)/4 + 11/(4*(-2*x + 1))

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Mathematica [A]  time = 0.0103047, size = 22, normalized size = 1. \[ \frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

11/(4*(1 - 2*x)) + (5*Log[1 - 2*x])/4

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Maple [A]  time = 0.009, size = 19, normalized size = 0.9 \[ -{\frac{11}{-4+8\,x}}+{\frac{5\,\ln \left ( -1+2\,x \right ) }{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)/(1-2*x)^2,x)

[Out]

-11/4/(-1+2*x)+5/4*ln(-1+2*x)

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Maxima [A]  time = 1.34161, size = 24, normalized size = 1.09 \[ -\frac{11}{4 \,{\left (2 \, x - 1\right )}} + \frac{5}{4} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/4/(2*x - 1) + 5/4*log(2*x - 1)

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Fricas [A]  time = 0.208107, size = 32, normalized size = 1.45 \[ \frac{5 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{4 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*(5*(2*x - 1)*log(2*x - 1) - 11)/(2*x - 1)

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Sympy [A]  time = 0.15906, size = 15, normalized size = 0.68 \[ \frac{5 \log{\left (2 x - 1 \right )}}{4} - \frac{11}{8 x - 4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)/(1-2*x)**2,x)

[Out]

5*log(2*x - 1)/4 - 11/(8*x - 4)

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GIAC/XCAS [A]  time = 0.204957, size = 38, normalized size = 1.73 \[ -\frac{11}{4 \,{\left (2 \, x - 1\right )}} - \frac{5}{4} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/4/(2*x - 1) - 5/4*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)