Optimal. Leaf size=29 \[ \frac {7}{10 \left (e^{3-e^2-e^{x+\log ^2(3)} x}+\log (3)\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.77, antiderivative size = 36, normalized size of antiderivative = 1.24, number of steps
used = 3, number of rules used = 3, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6820, 12, 6818}
\begin {gather*} -\frac {7 e^3}{10 \log (3) \left (\log (3) e^{x e^{x+\log ^2(3)}+e^2}+e^3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {7 \exp \left (x+e^{x+\log ^2(3)} x+3 \left (1+\frac {1}{3} \left (e^2+\log ^2(3)\right )\right )\right ) (1+x)}{10 \left (e^3+e^{e^2+e^{x+\log ^2(3)} x} \log (3)\right )^2} \, dx\\ &=\frac {7}{10} \int \frac {\exp \left (x+e^{x+\log ^2(3)} x+3 \left (1+\frac {1}{3} \left (e^2+\log ^2(3)\right )\right )\right ) (1+x)}{\left (e^3+e^{e^2+e^{x+\log ^2(3)} x} \log (3)\right )^2} \, dx\\ &=-\frac {7 e^3}{10 \log (3) \left (e^3+e^{e^2+e^{x+\log ^2(3)} x} \log (3)\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.14, size = 36, normalized size = 1.24 \begin {gather*} -\frac {7 e^3}{10 \log (3) \left (e^3+e^{e^2+e^{x+\log ^2(3)} x} \log (3)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.34, size = 25, normalized size = 0.86
method | result | size |
norman | \(\frac {7}{10 \left (\ln \left (3\right )+{\mathrm e}^{-x \,{\mathrm e}^{\ln \left (3\right )^{2}+x}-{\mathrm e}^{2}+3}\right )}\) | \(25\) |
risch | \(\frac {7}{10 \left (\ln \left (3\right )+{\mathrm e}^{-x \,{\mathrm e}^{\ln \left (3\right )^{2}+x}-{\mathrm e}^{2}+3}\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.56, size = 30, normalized size = 1.03 \begin {gather*} -\frac {7 \, e^{3}}{10 \, {\left (e^{\left (x e^{\left (\log \left (3\right )^{2} + x\right )} + e^{2}\right )} \log \left (3\right )^{2} + e^{3} \log \left (3\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 44, normalized size = 1.52 \begin {gather*} \frac {7 \, e^{\left (\log \left (3\right )^{2} + x\right )}}{10 \, {\left (e^{\left (\log \left (3\right )^{2} + x\right )} \log \left (3\right ) + e^{\left (-x e^{\left (\log \left (3\right )^{2} + x\right )} + \log \left (3\right )^{2} + x - e^{2} + 3\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 24, normalized size = 0.83 \begin {gather*} \frac {7}{10 e^{- x e^{x + \log {\left (3 \right )}^{2}} - e^{2} + 3} + 10 \log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 29, normalized size = 1.00 \begin {gather*} -\frac {7 \, e^{3}}{10 \, {\left (e^{\left (x e^{\left (\log \left (3\right )^{2} + x\right )} + e^{2}\right )} \log \left (3\right ) + e^{3}\right )} \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.17, size = 29, normalized size = 1.00 \begin {gather*} \frac {7}{10\,\left (\ln \left (3\right )+{\mathrm {e}}^{-{\mathrm {e}}^2}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{{\ln \left (3\right )}^2}\,{\mathrm {e}}^x}\,{\mathrm {e}}^3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________