Optimal. Leaf size=24 \[ 2+\frac {1}{8} e^{e^{\frac {1}{x^2 \log ^2(2+\log (4))}}+x} x \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.12, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps
used = 2, number of rules used = 2, integrand size = 65, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12, 2326}
\begin {gather*} \frac {1}{8} x e^{e^{\frac {1}{x^2 \log ^2(2+\log (4))}}+x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{e^{\frac {1}{x^2 \log ^2(2+\log (4))}}} \left (-2 e^{x+\frac {1}{x^2 \log ^2(2+\log (4))}}+e^x \left (x^2+x^3\right ) \log ^2(2+\log (4))\right )}{x^2} \, dx}{8 \log ^2(2+\log (4))}\\ &=\frac {1}{8} e^{e^{\frac {1}{x^2 \log ^2(2+\log (4))}}+x} x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.10, size = 22, normalized size = 0.92 \begin {gather*} \frac {1}{8} e^{e^{\frac {1}{x^2 \log ^2(2+\log (4))}}+x} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.38, size = 22, normalized size = 0.92
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{{\mathrm e}^{\frac {1}{x^{2} \left (\ln \left (2\right )+\ln \left (1+\ln \left (2\right )\right )\right )^{2}}}+x}}{8}\) | \(22\) |
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. 64 vs.
\(2 (22) = 44\).
time = 0.59, size = 64, normalized size = 2.67 \begin {gather*} \frac {{\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (\log \left (2\right ) + 1\right ) + \log \left (\log \left (2\right ) + 1\right )^{2}\right )} x e^{\left (x + e^{\left (\frac {1}{{\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (\log \left (2\right ) + 1\right ) + \log \left (\log \left (2\right ) + 1\right )^{2}\right )} x^{2}}\right )}\right )}}{8 \, \log \left (2 \, \log \left (2\right ) + 2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 39, normalized size = 1.62 \begin {gather*} \frac {1}{8} \, x e^{\left (x + e^{\left (-x + \frac {x^{3} \log \left (2 \, \log \left (2\right ) + 2\right )^{2} + 1}{x^{2} \log \left (2 \, \log \left (2\right ) + 2\right )^{2}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: GeneratorsError} \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 = 3.42, size = 18, normalized size = 0.75 \begin {gather*} \frac {x\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {1}{x^2\,{\ln \left (\ln \left (4\right )+2\right )}^2}}}\,{\mathrm {e}}^x}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________