Optimal. Leaf size=11 \[ \frac {1}{3} \sin ^{-1}\left (\frac {3 \log (x)}{2}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {222}
\begin {gather*} \frac {1}{3} \text {ArcSin}\left (\frac {3 \log (x)}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 222
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt {4-9 \log ^2(x)}} \, dx &=\text {Subst}\left (\int \frac {1}{\sqrt {4-9 x^2}} \, dx,x,\log (x)\right )\\ &=\frac {1}{3} \sin ^{-1}\left (\frac {3 \log (x)}{2}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] Result contains complex when optimal does not.
time = 0.01, size = 26, normalized size = 2.36 \begin {gather*} \frac {1}{3} i \log \left (-3 i \log (x)+\sqrt {4-9 \log ^2(x)}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 8, normalized size = 0.73
method | result | size |
derivativedivides | \(\frac {\arcsin \left (\frac {3 \ln \left (x \right )}{2}\right )}{3}\) | \(8\) |
default | \(\frac {\arcsin \left (\frac {3 \ln \left (x \right )}{2}\right )}{3}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.49, size = 7, normalized size = 0.64 \begin {gather*} \frac {1}{3} \, \arcsin \left (\frac {3}{2} \, \log \left (x\right )\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. 21 vs.
\(2 (7) = 14\).
time = 0.38, size = 21, normalized size = 1.91 \begin {gather*} -\frac {2}{3} \, \arctan \left (\frac {\sqrt {-9 \, \log \left (x\right )^{2} + 4} - 2}{3 \, \log \left (x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \sqrt {- \left (3 \log {\left (x \right )} - 2\right ) \left (3 \log {\left (x \right )} + 2\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.55, size = 7, normalized size = 0.64 \begin {gather*} \frac {1}{3} \, \arcsin \left (\frac {3}{2} \, \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.40, size = 7, normalized size = 0.64 \begin {gather*} \frac {\mathrm {asin}\left (\frac {3\,\ln \left (x\right )}{2}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________