Optimal. Leaf size=28 \[ e^{-4+x \left (x+\left (\log (2)+x \left (2 x-\log \left (-25+\log \left (x^2\right )\right )\right )\right )^2\right )} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 17.95, 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 (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\exp \left (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) \left (8 x^3+500 x^4+50 x \left (1+\frac {2 \log (2)}{25}\right )+300 x^2 \log (2)+25 \log ^2(2)-2 x \log \left (x^2\right )-20 x^4 \log \left (x^2\right )-12 x^2 \log (2) \log \left (x^2\right )-\log ^2(2) \log \left (x^2\right )\right )}{25-\log \left (x^2\right )}-\frac {4 \exp \left (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) x \left (-x-100 x^2-25 \log (2)+4 x^2 \log \left (x^2\right )+\log (2) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )}{-25+\log \left (x^2\right )}+3 \exp \left (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) x^2 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) \, dx\\ &=3 \int \exp \left (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) x^2 \log ^2\left (-25+\log \left (x^2\right )\right ) \, dx-4 \int \frac {\exp \left (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) x \left (-x-100 x^2-25 \log (2)+4 x^2 \log \left (x^2\right )+\log (2) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )}{-25+\log \left (x^2\right )} \, dx+\int \frac {\exp \left (-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )\right ) \left (8 x^3+500 x^4+50 x \left (1+\frac {2 \log (2)}{25}\right )+300 x^2 \log (2)+25 \log ^2(2)-2 x \log \left (x^2\right )-20 x^4 \log \left (x^2\right )-12 x^2 \log (2) \log \left (x^2\right )-\log ^2(2) \log \left (x^2\right )\right )}{25-\log \left (x^2\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F]
time = 0.67, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.58, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (3 x^{2} \ln \left (x^{2}\right )-75 x^{2}\right ) \ln \left (\ln \left (x^{2}\right )-25\right )^{2}+\left (\left (-4 x \ln \left (2\right )-16 x^{3}\right ) \ln \left (x^{2}\right )+100 x \ln \left (2\right )+400 x^{3}+4 x^{2}\right ) \ln \left (\ln \left (x^{2}\right )-25\right )+\left (\ln \left (2\right )^{2}+12 x^{2} \ln \left (2\right )+20 x^{4}+2 x \right ) \ln \left (x^{2}\right )-25 \ln \left (2\right )^{2}+\left (-300 x^{2}-4 x \right ) \ln \left (2\right )-500 x^{4}-8 x^{3}-50 x \right ) {\mathrm e}^{x^{3} \ln \left (\ln \left (x^{2}\right )-25\right )^{2}+\left (-2 x^{2} \ln \left (2\right )-4 x^{4}\right ) \ln \left (\ln \left (x^{2}\right )-25\right )+x \ln \left (2\right )^{2}+4 x^{3} \ln \left (2\right )+4 x^{5}+x^{2}-4}}{\ln \left (x^{2}\right )-25}\, dx\]
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. 63 vs.
\(2 (27) = 54\).
time = 0.63, size = 63, normalized size = 2.25 \begin {gather*} e^{\left (4 \, x^{5} - 4 \, x^{4} \log \left (2 \, \log \left (x\right ) - 25\right ) + x^{3} \log \left (2 \, \log \left (x\right ) - 25\right )^{2} + 4 \, x^{3} \log \left (2\right ) - 2 \, x^{2} \log \left (2\right ) \log \left (2 \, \log \left (x\right ) - 25\right ) + x \log \left (2\right )^{2} + x^{2} - 4\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. 58 vs.
\(2 (27) = 54\).
time = 0.37, size = 58, normalized size = 2.07 \begin {gather*} e^{\left (4 \, x^{5} + x^{3} \log \left (\log \left (x^{2}\right ) - 25\right )^{2} + 4 \, x^{3} \log \left (2\right ) + x \log \left (2\right )^{2} + x^{2} - 2 \, {\left (2 \, x^{4} + x^{2} \log \left (2\right )\right )} \log \left (\log \left (x^{2}\right ) - 25\right ) - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 63 vs.
\(2 (24) = 48\).
time = 0.82, size = 63, normalized size = 2.25 \begin {gather*} e^{4 x^{5} + x^{3} \log {\left (\log {\left (x^{2} \right )} - 25 \right )}^{2} + 4 x^{3} \log {\left (2 \right )} + x^{2} + x \log {\left (2 \right )}^{2} + \left (- 4 x^{4} - 2 x^{2} \log {\left (2 \right )}\right ) \log {\left (\log {\left (x^{2} \right )} - 25 \right )} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 63 vs.
\(2 (27) = 54\).
time = 2.57, size = 63, normalized size = 2.25 \begin {gather*} e^{\left (4 \, x^{5} - 4 \, x^{4} \log \left (\log \left (x^{2}\right ) - 25\right ) + x^{3} \log \left (\log \left (x^{2}\right ) - 25\right )^{2} + 4 \, x^{3} \log \left (2\right ) - 2 \, x^{2} \log \left (2\right ) \log \left (\log \left (x^{2}\right ) - 25\right ) + x \log \left (2\right )^{2} + x^{2} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.53, size = 61, normalized size = 2.18 \begin {gather*} \frac {{16}^{x^3}\,{\mathrm {e}}^{x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{x^3\,{\ln \left (\ln \left (x^2\right )-25\right )}^2}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{4\,x^5}}{{\left (\ln \left (x^2\right )-25\right )}^{4\,x^4+2\,\ln \left (2\right )\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________