Optimal. Leaf size=20 \[ e^{\log ^2\left (\frac {19}{4}+e^x+x+e^{-x} x\right )} \]
________________________________________________________________________________________
Rubi [A] time = 8.07, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 4, integrand size = 104, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6688, 12, 6742, 6706} \begin {gather*} e^{\log ^2\left (e^{-x} x+x+e^x+\frac {19}{4}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6688
Rule 6706
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 e^{\log ^2\left (\frac {19}{4}+e^x+x+e^{-x} x\right )} \left (1+e^x+e^{2 x}-x\right ) \log \left (\frac {19}{4}+e^x+x+e^{-x} x\right )}{4 e^{2 x}+4 x+e^x (19+4 x)} \, dx\\ &=8 \int \frac {e^{\log ^2\left (\frac {19}{4}+e^x+x+e^{-x} x\right )} \left (1+e^x+e^{2 x}-x\right ) \log \left (\frac {19}{4}+e^x+x+e^{-x} x\right )}{4 e^{2 x}+4 x+e^x (19+4 x)} \, dx\\ &=e^{\log ^2\left (\frac {19}{4}+e^x+x+e^{-x} x\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 1.86, size = 20, normalized size = 1.00 \begin {gather*} e^{\log ^2\left (\frac {19}{4}+e^x+x+e^{-x} x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.58, size = 28, normalized size = 1.40 \begin {gather*} e^{\left (\log \left (\frac {1}{4} \, {\left ({\left (4 \, x + 19\right )} e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )}\right )} e^{\left (-x\right )}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.32, size = 85, normalized size = 4.25 \begin {gather*} e^{\left (x^{2} + 4 \, x \log \relax (2) + 4 \, \log \relax (2)^{2} - 2 \, x \log \left (4 \, x e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )} + 19 \, e^{x}\right ) - 4 \, \log \relax (2) \log \left (4 \, x e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )} + 19 \, e^{x}\right ) + \log \left (4 \, x e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )} + 19 \, e^{x}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.20, size = 198, normalized size = 9.90
method | result | size |
risch | \({\mathrm e}^{\frac {\left (i \pi \mathrm {csgn}\left (i {\mathrm e}^{-x} \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right )^{3}-i \pi \mathrm {csgn}\left (i {\mathrm e}^{-x} \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )-i \pi \mathrm {csgn}\left (i {\mathrm e}^{-x} \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right )^{2} \mathrm {csgn}\left (i \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right )+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-x} \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right )+2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \left (x \left ({\mathrm e}^{x}+1\right )+{\mathrm e}^{2 x}+\frac {19 \,{\mathrm e}^{x}}{4}\right )\right )^{2}}{4}}\) | \(198\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.68, size = 82, normalized size = 4.10 \begin {gather*} e^{\left (x^{2} + 4 \, x \log \relax (2) + 4 \, \log \relax (2)^{2} - 2 \, x \log \left ({\left (4 \, x + 19\right )} e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )}\right ) - 4 \, \log \relax (2) \log \left ({\left (4 \, x + 19\right )} e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )}\right ) + \log \left ({\left (4 \, x + 19\right )} e^{x} + 4 \, x + 4 \, e^{\left (2 \, x\right )}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.01, size = 15, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{{\ln \left (x+{\mathrm {e}}^x+x\,{\mathrm {e}}^{-x}+\frac {19}{4}\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________