Optimal. Leaf size=27 \[ e^{\frac {1}{4}+\log ^2\left (e^{\frac {1}{3} (-5-5 \log (2 x))} x\right )}+x \]
________________________________________________________________________________________
Rubi [A] time = 0.44, antiderivative size = 30, normalized size of antiderivative = 1.11, number of steps used = 4, number of rules used = 3, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {12, 14, 6706} \begin {gather*} e^{\log ^2\left (\frac {1}{2\ 2^{2/3} e^{5/3} x^{2/3}}\right )+\frac {1}{4}}+x \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
Rule 12
Rule 14
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {3 x-4 \exp \left (\frac {1}{4} \left (1+4 \log ^2\left (e^{\frac {1}{3} (-5-5 \log (2 x))} x\right )\right )\right ) \log \left (e^{\frac {1}{3} (-5-5 \log (2 x))} x\right )}{x} \, dx\\ &=\frac {1}{3} \int \left (3-\frac {4 e^{\frac {1}{4}+\log ^2\left (e^{-\frac {5}{3} (1+\log (2 x))} x\right )} \log \left (e^{-\frac {5}{3} (1+\log (2 x))} x\right )}{x}\right ) \, dx\\ &=x-\frac {4}{3} \int \frac {e^{\frac {1}{4}+\log ^2\left (e^{-\frac {5}{3} (1+\log (2 x))} x\right )} \log \left (e^{-\frac {5}{3} (1+\log (2 x))} x\right )}{x} \, dx\\ &=e^{\frac {1}{4}+\log ^2\left (\frac {1}{2\ 2^{2/3} e^{5/3} x^{2/3}}\right )}+x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.14, size = 25, normalized size = 0.93 \begin {gather*} e^{\frac {1}{4}+\log ^2\left (e^{-\frac {5}{3} (1+\log (2 x))} x\right )}+x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.58, size = 18, normalized size = 0.67 \begin {gather*} x + e^{\left (\log \left (\frac {2^{\frac {1}{3}} e^{\left (-\frac {5}{3}\right )}}{4 \, x^{\frac {2}{3}}}\right )^{2} + \frac {1}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.16, size = 31, normalized size = 1.15 \begin {gather*} x + e^{\left (\frac {25}{9} \, \log \relax (2)^{2} + \frac {20}{9} \, \log \relax (2) \log \relax (x) + \frac {4}{9} \, \log \relax (x)^{2} + \frac {50}{9} \, \log \relax (2) + \frac {20}{9} \, \log \relax (x) + \frac {109}{36}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 22, normalized size = 0.81
method | result | size |
default | \(x +{\mathrm e}^{\ln \left (x \,{\mathrm e}^{-\frac {5 \ln \left (2 x \right )}{3}-\frac {5}{3}}\right )^{2}+\frac {1}{4}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 18, normalized size = 0.67 \begin {gather*} x + e^{\left (\log \left (\frac {2^{\frac {1}{3}} e^{\left (-\frac {5}{3}\right )}}{4 \, x^{\frac {2}{3}}}\right )^{2} + \frac {1}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.62, size = 35, normalized size = 1.30 \begin {gather*} x+32\,2^{5/9}\,x^{20/9}\,{\left ({\mathrm {e}}^{{\ln \relax (2)}^2}\right )}^{25/9}\,{\mathrm {e}}^{{\ln \left (\frac {1}{x^{2/3}}\right )}^2}\,{\mathrm {e}}^{109/36}\,{\mathrm {e}}^{-\frac {10\,\ln \left (\frac {1}{x^{2/3}}\right )\,\ln \relax (2)}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________