Optimal. Leaf size=28 \[ \frac {1}{2} \left (-1-e^{e^{\frac {2 e^{-x^4}}{\log (5)}}}-x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.36, antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps
used = 7, number of rules used = 5, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.082, Rules used = {12, 6874, 6847,
2320, 2225} \begin {gather*} -\frac {1}{2} e^{e^{\frac {2 e^{-x^4}}{\log (5)}}}-\frac {x}{2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2225
Rule 2320
Rule 6847
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int e^{-x^4} \left (8 e^{e^{\frac {2 e^{-x^4}}{\log (5)}}+\frac {2 e^{-x^4}}{\log (5)}} x^3-e^{x^4} \log (5)\right ) \, dx}{2 \log (5)}\\ &=\frac {\int \left (8 e^{e^{\frac {2 e^{-x^4}}{\log (5)}}-x^4+\frac {2 e^{-x^4}}{\log (5)}} x^3-\log (5)\right ) \, dx}{2 \log (5)}\\ &=-\frac {x}{2}+\frac {4 \int e^{e^{\frac {2 e^{-x^4}}{\log (5)}}-x^4+\frac {2 e^{-x^4}}{\log (5)}} x^3 \, dx}{\log (5)}\\ &=-\frac {x}{2}+\frac {\text {Subst}\left (\int e^{e^{\frac {2 e^{-x}}{\log (5)}}-x+\frac {2 e^{-x}}{\log (5)}} \, dx,x,x^4\right )}{\log (5)}\\ &=-\frac {x}{2}-\frac {\text {Subst}\left (\int e^{e^{\frac {2 x}{\log (5)}}+\frac {2 x}{\log (5)}} \, dx,x,e^{-x^4}\right )}{\log (5)}\\ &=-\frac {x}{2}-\frac {1}{2} \text {Subst}\left (\int e^x \, dx,x,e^{\frac {2 e^{-x^4}}{\log (5)}}\right )\\ &=-\frac {1}{2} e^{e^{\frac {2 e^{-x^4}}{\log (5)}}}-\frac {x}{2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.15, size = 32, normalized size = 1.14 \begin {gather*} \frac {-e^{e^{\frac {2 e^{-x^4}}{\log (5)}}} \log (5)-x \log (5)}{\log (25)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.39, size = 32, normalized size = 1.14
method | result | size |
risch | \(-\frac {x}{2}-\frac {{\mathrm e}^{{\mathrm e}^{\frac {2 \,{\mathrm e}^{-x^{4}}}{\ln \left (5\right )}}}}{2}\) | \(21\) |
default | \(\frac {-{\mathrm e}^{{\mathrm e}^{\frac {2 \,{\mathrm e}^{-x^{4}}}{\ln \left (5\right )}}} \ln \left (5\right )-x \ln \left (5\right )}{2 \ln \left (5\right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.49, size = 28, normalized size = 1.00 \begin {gather*} -\frac {x \log \left (5\right ) + e^{\left (e^{\left (\frac {2 \, e^{\left (-x^{4}\right )}}{\log \left (5\right )}\right )}\right )} \log \left (5\right )}{2 \, \log \left (5\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. 65 vs.
\(2 (21) = 42\).
time = 0.38, size = 65, normalized size = 2.32 \begin {gather*} -\frac {1}{2} \, {\left (x e^{\left (\frac {2 \, e^{\left (-x^{4}\right )}}{\log \left (5\right )}\right )} + e^{\left (\frac {{\left (e^{\left (x^{4} + \frac {2 \, e^{\left (-x^{4}\right )}}{\log \left (5\right )}\right )} \log \left (5\right ) + 2\right )} e^{\left (-x^{4}\right )}}{\log \left (5\right )}\right )}\right )} e^{\left (-\frac {2 \, e^{\left (-x^{4}\right )}}{\log \left (5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.16, size = 19, normalized size = 0.68 \begin {gather*} - \frac {x}{2} - \frac {e^{e^{\frac {2 e^{- x^{4}}}{\log {\left (5 \right )}}}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.98, size = 20, normalized size = 0.71 \begin {gather*} -\frac {x}{2}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{-x^4}}{\ln \left (5\right )}}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________