Optimal. Leaf size=29 \[ \frac {1}{5 x}+\frac {e^{e^{x^3-\frac {4}{x \log (2)}}}}{x} \]
________________________________________________________________________________________
Rubi [F] time = 1.21, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-x \log (2)+e^{e^{\frac {-4+x^4 \log (2)}{x \log (2)}}} \left (-5 x \log (2)+e^{\frac {-4+x^4 \log (2)}{x \log (2)}} \left (20+15 x^4 \log (2)\right )\right )}{5 x^3 \log (2)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-x \log (2)+e^{e^{\frac {-4+x^4 \log (2)}{x \log (2)}}} \left (-5 x \log (2)+e^{\frac {-4+x^4 \log (2)}{x \log (2)}} \left (20+15 x^4 \log (2)\right )\right )}{x^3} \, dx}{5 \log (2)}\\ &=\frac {\int \left (-\frac {\left (1+5 e^{e^{x^3-\frac {4}{x \log (2)}}}\right ) \log (2)}{x^2}+\frac {5 e^{e^{x^3-\frac {4}{x \log (2)}}+x^3-\frac {4}{x \log (2)}} \left (4+x^4 \log (8)\right )}{x^3}\right ) \, dx}{5 \log (2)}\\ &=-\left (\frac {1}{5} \int \frac {1+5 e^{e^{x^3-\frac {4}{x \log (2)}}}}{x^2} \, dx\right )+\frac {\int \frac {e^{e^{x^3-\frac {4}{x \log (2)}}+x^3-\frac {4}{x \log (2)}} \left (4+x^4 \log (8)\right )}{x^3} \, dx}{\log (2)}\\ &=-\left (\frac {1}{5} \int \left (\frac {1}{x^2}+\frac {5 e^{e^{\frac {x^4-\frac {4}{\log (2)}}{x}}}}{x^2}\right ) \, dx\right )+\frac {\int \left (\frac {4 e^{e^{x^3-\frac {4}{x \log (2)}}+x^3-\frac {4}{x \log (2)}}}{x^3}+e^{e^{x^3-\frac {4}{x \log (2)}}+x^3-\frac {4}{x \log (2)}} x \log (8)\right ) \, dx}{\log (2)}\\ &=\frac {1}{5 x}+\frac {4 \int \frac {e^{e^{x^3-\frac {4}{x \log (2)}}+x^3-\frac {4}{x \log (2)}}}{x^3} \, dx}{\log (2)}+\frac {\log (8) \int e^{e^{x^3-\frac {4}{x \log (2)}}+x^3-\frac {4}{x \log (2)}} x \, dx}{\log (2)}-\int \frac {e^{e^{\frac {x^4-\frac {4}{\log (2)}}{x}}}}{x^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F] time = 1.43, size = 75, normalized size = 2.59 \begin {gather*} \frac {\int \frac {-x \log (2)+e^{e^{\frac {-4+x^4 \log (2)}{x \log (2)}}} \left (-5 x \log (2)+e^{\frac {-4+x^4 \log (2)}{x \log (2)}} \left (20+15 x^4 \log (2)\right )\right )}{x^3} \, dx}{5 \log (2)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.61, size = 27, normalized size = 0.93 \begin {gather*} \frac {5 \, e^{\left (e^{\left (\frac {x^{4} \log \relax (2) - 4}{x \log \relax (2)}\right )}\right )} + 1}{5 \, x} \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.14, size = 29, normalized size = 1.00
method | result | size |
norman | \(\frac {x \,{\mathrm e}^{{\mathrm e}^{\frac {x^{4} \ln \relax (2)-4}{x \ln \relax (2)}}}+\frac {x}{5}}{x^{2}}\) | \(29\) |
risch | \(\frac {1}{5 x}+\frac {{\mathrm e}^{{\mathrm e}^{\frac {x^{4} \ln \relax (2)-4}{x \ln \relax (2)}}}}{x}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {-\mathit {undef} + \frac {\log \relax (2)}{x}}{5 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.47, size = 22, normalized size = 0.76 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{-\frac {4}{x\,\ln \relax (2)}}}+\frac {1}{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.32, size = 22, normalized size = 0.76 \begin {gather*} \frac {e^{e^{\frac {x^{4} \log {\relax (2 )} - 4}{x \log {\relax (2 )}}}}}{x} + \frac {1}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________