Optimal. Leaf size=22 \[ e^{\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 3.81, 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 {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) \left (-8+4 x+(32-32 x) \log \left (x^2\right )\right )}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4 \exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) (-2+x)}{x^3}-\frac {32 \exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) (-1+x) \log \left (x^2\right )}{x^3}\right ) \, dx\\ &=4 \int \frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) (-2+x)}{x^3} \, dx-32 \int \frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) (-1+x) \log \left (x^2\right )}{x^3} \, dx\\ &=4 \int \left (-\frac {2 \exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right )}{x^3}+\frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right )}{x^2}\right ) \, dx-32 \int \left (-\frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^3}+\frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2}\right ) \, dx\\ &=4 \int \frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right )}{x^2} \, dx-8 \int \frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right )}{x^3} \, dx+32 \int \frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^3} \, dx-32 \int \frac {\exp \left (\frac {4 e^{2 \log ^2\left (x^2\right )} (1-x)}{x^2}+2 \log ^2\left (x^2\right )\right ) \log \left (x^2\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.40, size = 20, normalized size = 0.91 \begin {gather*} e^{-\frac {4 e^{2 \log ^2\left (x^2\right )} (-1+x)}{x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.35, size = 19, normalized size = 0.86
method | result | size |
risch | \({\mathrm e}^{-\frac {4 \left (x -1\right ) {\mathrm e}^{2 \ln \left (x^{2}\right )^{2}}}{x^{2}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.40, size = 26, normalized size = 1.18 \begin {gather*} e^{\left (-\frac {4 \, e^{\left (8 \, \log \left (x\right )^{2}\right )}}{x} + \frac {4 \, e^{\left (8 \, \log \left (x\right )^{2}\right )}}{x^{2}}\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. 40 vs.
\(2 (18) = 36\).
time = 0.38, size = 40, normalized size = 1.82 \begin {gather*} e^{\left (-2 \, \log \left (x^{2}\right )^{2} + \frac {2 \, {\left (x^{2} \log \left (x^{2}\right )^{2} - 2 \, {\left (x - 1\right )} e^{\left (2 \, \log \left (x^{2}\right )^{2}\right )}\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.25, size = 19, normalized size = 0.86 \begin {gather*} e^{\frac {4 \cdot \left (1 - x\right ) e^{2 \log {\left (x^{2} \right )}^{2}}}{x^{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 = 5.63, size = 31, normalized size = 1.41 \begin {gather*} {\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,{\ln \left (x^2\right )}^2}}{x}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{2\,{\ln \left (x^2\right )}^2}}{x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________