3.1425 \(\int \frac{3+5 x}{1-2 x} \, dx\)

Optimal. Leaf size=16 \[ -\frac{5 x}{2}-\frac{11}{4} \log (1-2 x) \]

[Out]

(-5*x)/2 - (11*Log[1 - 2*x])/4

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Rubi [A]  time = 0.0179558, antiderivative size = 16, 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 \[ -\frac{5 x}{2}-\frac{11}{4} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)/(1 - 2*x),x]

[Out]

(-5*x)/2 - (11*Log[1 - 2*x])/4

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{11 \log{\left (- 2 x + 1 \right )}}{4} + \int \left (- \frac{5}{2}\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00441257, size = 17, normalized size = 1.06 \[ \frac{1}{4} (-10 x-11 \log (1-2 x)+5) \]

Antiderivative was successfully verified.

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

[Out]

(5 - 10*x - 11*Log[1 - 2*x])/4

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Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{5\,x}{2}}-{\frac{11\,\ln \left ( -1+2\,x \right ) }{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)/(1-2*x),x)

[Out]

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

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Maxima [A]  time = 1.34362, size = 16, normalized size = 1. \[ -\frac{5}{2} \, x - \frac{11}{4} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/2*x - 11/4*log(2*x - 1)

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Fricas [A]  time = 0.212593, size = 16, normalized size = 1. \[ -\frac{5}{2} \, x - \frac{11}{4} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/2*x - 11/4*log(2*x - 1)

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Sympy [A]  time = 0.145218, size = 15, normalized size = 0.94 \[ - \frac{5 x}{2} - \frac{11 \log{\left (2 x - 1 \right )}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)/(1-2*x),x)

[Out]

-5*x/2 - 11*log(2*x - 1)/4

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GIAC/XCAS [A]  time = 0.209935, size = 18, normalized size = 1.12 \[ -\frac{5}{2} \, x - \frac{11}{4} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/2*x - 11/4*ln(abs(2*x - 1))