Optimal. Leaf size=2 \[ \text {arctanh}(x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {212}
\begin {gather*} \text {arctanh}(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 212
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\text {arctanh}(x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(19\) vs. \(2(2)=4\).
time = 0.00, size = 19, normalized size = 9.50 \begin {gather*} -\frac {1}{2} \log (1-x)+\frac {1}{2} \log (1+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 3, normalized size = 1.50
method | result | size |
default | \(\arctanh \left (x \right )\) | \(3\) |
meijerg | \(\arctanh \left (x \right )\) | \(3\) |
norman | \(-\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (1+x \right )}{2}\) | \(14\) |
risch | \(-\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (1+x \right )}{2}\) | \(14\) |
parallelrisch | \(-\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (1+x \right )}{2}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 13 vs.
\(2 (2) = 4\).
time = 0.32, size = 13, normalized size = 6.50 \begin {gather*} \frac {1}{2} \, \log \left (x + 1\right ) - \frac {1}{2} \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 13 vs.
\(2 (2) = 4\).
time = 0.56, size = 13, normalized size = 6.50 \begin {gather*} \frac {1}{2} \, \log \left (x + 1\right ) - \frac {1}{2} \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 12 vs.
\(2 (2) = 4\).
time = 0.03, size = 12, normalized size = 6.00 \begin {gather*} - \frac {\log {\left (x - 1 \right )}}{2} + \frac {\log {\left (x + 1 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 15 vs.
\(2 (2) = 4\).
time = 0.46, size = 15, normalized size = 7.50 \begin {gather*} \frac {1}{2} \, \log \left ({\left | x + 1 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.07, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {atanh}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________