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

Optimal. Leaf size=10 \[ x-2 \log (2 x+3) \]

[Out]

x - 2*Log[3 + 2*x]

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Rubi [A]  time = 0.0145224, antiderivative size = 10, 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 \[ x-2 \log (2 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(-1 + 2*x)/(3 + 2*x),x]

[Out]

x - 2*Log[3 + 2*x]

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Rubi in Sympy [A]  time = 1.65684, size = 8, normalized size = 0.8 \[ x - 2 \log{\left (2 x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - 2*log(2*x + 3)

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Mathematica [A]  time = 0.00293552, size = 10, normalized size = 1. \[ x-2 \log (2 x+3) \]

Antiderivative was successfully verified.

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

[Out]

x - 2*Log[3 + 2*x]

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Maple [A]  time = 0.003, size = 11, normalized size = 1.1 \[ x-2\,\ln \left ( 3+2\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2*x-1)/(3+2*x),x)

[Out]

x-2*ln(3+2*x)

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Maxima [A]  time = 1.33747, size = 14, normalized size = 1.4 \[ x - 2 \, \log \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - 2*log(2*x + 3)

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Fricas [A]  time = 0.211592, size = 14, normalized size = 1.4 \[ x - 2 \, \log \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - 2*log(2*x + 3)

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Sympy [A]  time = 0.058728, size = 8, normalized size = 0.8 \[ x - 2 \log{\left (2 x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x-1)/(3+2*x),x)

[Out]

x - 2*log(2*x + 3)

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GIAC/XCAS [A]  time = 0.202613, size = 15, normalized size = 1.5 \[ x - 2 \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - 2*ln(abs(2*x + 3))