Optimal. Leaf size=21 \[ \frac{1}{2} \log (1-2 x)-\frac{1}{2} \log (2 x+1) \]
[Out]
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Rubi [A] time = 0.012799, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{1}{2} \log (1-2 x)-\frac{1}{2} \log (2 x+1) \]
Antiderivative was successfully verified.
[In] Int[(-1 + 2*x)^(-1) - (1 + 2*x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.93035, size = 15, normalized size = 0.71 \[ \frac{\log{\left (- 2 x + 1 \right )}}{2} - \frac{\log{\left (2 x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-1+2*x)-1/(1+2*x),x)
[Out]
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Mathematica [A] time = 0.00370188, size = 23, normalized size = 1.1 \[ 2 \left (\frac{1}{4} \log (1-2 x)-\frac{1}{4} \log (2 x+1)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + 2*x)^(-1) - (1 + 2*x)^(-1),x]
[Out]
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Maple [A] time = 0.002, size = 18, normalized size = 0.9 \[{\frac{\ln \left ( 2\,x-1 \right ) }{2}}-{\frac{\ln \left ( 1+2\,x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2*x-1)-1/(1+2*x),x)
[Out]
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Maxima [A] time = 0.84113, size = 23, normalized size = 1.1 \[ -\frac{1}{2} \, \log \left (2 \, x + 1\right ) + \frac{1}{2} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(2*x + 1) + 1/(2*x - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269485, size = 23, normalized size = 1.1 \[ -\frac{1}{2} \, \log \left (2 \, x + 1\right ) + \frac{1}{2} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(2*x + 1) + 1/(2*x - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.177171, size = 15, normalized size = 0.71 \[ \frac{\log{\left (x - \frac{1}{2} \right )}}{2} - \frac{\log{\left (x + \frac{1}{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-1+2*x)-1/(1+2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.263533, size = 26, normalized size = 1.24 \[ -\frac{1}{2} \,{\rm ln}\left ({\left | 2 \, x + 1 \right |}\right ) + \frac{1}{2} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(2*x + 1) + 1/(2*x - 1),x, algorithm="giac")
[Out]