Optimal. Leaf size=30 \[ e^{\frac {\left (5-x-x^2\right ) (-5+x+4 (3+x))}{\log (\log (5))}}-x \]
________________________________________________________________________________________
Rubi [A] time = 0.11, antiderivative size = 27, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 6706} \begin {gather*} e^{\frac {-5 x^3-12 x^2+18 x+35}{\log (\log (5))}}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e^{\frac {35+18 x-12 x^2-5 x^3}{\log (\log (5))}} \left (18-24 x-15 x^2\right )-\log (\log (5))\right ) \, dx}{\log (\log (5))}\\ &=-x+\frac {\int e^{\frac {35+18 x-12 x^2-5 x^3}{\log (\log (5))}} \left (18-24 x-15 x^2\right ) \, dx}{\log (\log (5))}\\ &=e^{\frac {35+18 x-12 x^2-5 x^3}{\log (\log (5))}}-x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 27, normalized size = 0.90 \begin {gather*} e^{\frac {35+18 x-12 x^2-5 x^3}{\log (\log (5))}}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.61, size = 27, normalized size = 0.90 \begin {gather*} -x + e^{\left (-\frac {5 \, x^{3} + 12 \, x^{2} - 18 \, x - 35}{\log \left (\log \relax (5)\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 3.00, size = 55, normalized size = 1.83 \begin {gather*} -\frac {x \log \left (\log \relax (5)\right ) - e^{\left (-\frac {5 \, x^{3}}{\log \left (\log \relax (5)\right )} - \frac {12 \, x^{2}}{\log \left (\log \relax (5)\right )} + \frac {18 \, x}{\log \left (\log \relax (5)\right )} + \frac {35}{\log \left (\log \relax (5)\right )}\right )} \log \left (\log \relax (5)\right )}{\log \left (\log \relax (5)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 24, normalized size = 0.80
method | result | size |
risch | \(-x +{\mathrm e}^{-\frac {\left (5 x +7\right ) \left (x^{2}+x -5\right )}{\ln \left (\ln \relax (5)\right )}}\) | \(24\) |
norman | \(-x +{\mathrm e}^{\frac {-5 x^{3}-12 x^{2}+18 x +35}{\ln \left (\ln \relax (5)\right )}}\) | \(27\) |
default | \(\frac {\ln \left (\ln \relax (5)\right ) {\mathrm e}^{\frac {-5 x^{3}-12 x^{2}+18 x +35}{\ln \left (\ln \relax (5)\right )}}-x \ln \left (\ln \relax (5)\right )}{\ln \left (\ln \relax (5)\right )}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.51, size = 55, normalized size = 1.83 \begin {gather*} -\frac {x \log \left (\log \relax (5)\right ) - e^{\left (-\frac {5 \, x^{3}}{\log \left (\log \relax (5)\right )} - \frac {12 \, x^{2}}{\log \left (\log \relax (5)\right )} + \frac {18 \, x}{\log \left (\log \relax (5)\right )} + \frac {35}{\log \left (\log \relax (5)\right )}\right )} \log \left (\log \relax (5)\right )}{\log \left (\log \relax (5)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.19, size = 44, normalized size = 1.47 \begin {gather*} {\mathrm {e}}^{\frac {18\,x}{\ln \left (\ln \relax (5)\right )}}\,{\mathrm {e}}^{-\frac {5\,x^3}{\ln \left (\ln \relax (5)\right )}}\,{\mathrm {e}}^{-\frac {12\,x^2}{\ln \left (\ln \relax (5)\right )}}\,{\mathrm {e}}^{\frac {35}{\ln \left (\ln \relax (5)\right )}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 22, normalized size = 0.73 \begin {gather*} - x + e^{\frac {- 5 x^{3} - 12 x^{2} + 18 x + 35}{\log {\left (\log {\relax (5 )} \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________