Optimal. Leaf size=21 \[ \frac {1}{2} \log (1-2 x)-\frac {1}{2} \log (2 x+1) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \frac {1}{2} \log (1-2 x)-\frac {1}{2} \log (2 x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {align*} \int \left (\frac {1}{-1+2 x}-\frac {1}{1+2 x}\right ) \, dx &=\frac {1}{2} \log (1-2 x)-\frac {1}{2} \log (1+2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 23, normalized size = 1.10 \[ 2 \left (\frac {1}{4} \log (1-2 x)-\frac {1}{4} \log (2 x+1)\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 17, normalized size = 0.81 \[ -\frac {1}{2} \, \log \left (2 \, x + 1\right ) + \frac {1}{2} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.42, size = 19, normalized size = 0.90 \[ -\frac {1}{2} \, \log \left ({\left | 2 \, x + 1 \right |}\right ) + \frac {1}{2} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ \frac {\ln \left (2 x -1\right )}{2}-\frac {\ln \left (2 x +1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.94, size = 17, normalized size = 0.81 \[ -\frac {1}{2} \, \log \left (2 \, x + 1\right ) + \frac {1}{2} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.15, size = 6, normalized size = 0.29 \[ -\mathrm {atanh}\left (2\,x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, 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]
[Out]
________________________________________________________________________________________