Optimal. Leaf size=21 \[ 2 \left (2 \left (4-e+e^{e^x}\right )-\log (9)\right )^2 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps
used = 5, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2320, 2225}
\begin {gather*} 8 e^{2 e^x}+8 e^{e^x} (8-2 e-\log (9)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2225
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=16 \int e^{2 e^x+x} \, dx+(8 (8-2 e-\log (9))) \int e^{e^x+x} \, dx\\ &=16 \text {Subst}\left (\int e^{2 x} \, dx,x,e^x\right )+(8 (8-2 e-\log (9))) \text {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=8 e^{2 e^x}+8 e^{e^x} (8-2 e-\log (9))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 21, normalized size = 1.00 \begin {gather*} 8 e^{e^x} \left (8-2 e+e^{e^x}-\log (9)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 28, normalized size = 1.33
method | result | size |
norman | \(\left (-16 \ln \left (3\right )-16 \,{\mathrm e}+64\right ) {\mathrm e}^{{\mathrm e}^{x}}+8 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}\) | \(23\) |
derivativedivides | \(-16 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}-16 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (3\right )+64 \,{\mathrm e}^{{\mathrm e}^{x}}+8 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}\) | \(28\) |
default | \(-16 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}-16 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (3\right )+64 \,{\mathrm e}^{{\mathrm e}^{x}}+8 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}\) | \(28\) |
risch | \(-16 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}-16 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (3\right )+64 \,{\mathrm e}^{{\mathrm e}^{x}}+8 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 19, normalized size = 0.90 \begin {gather*} -16 \, {\left (e + \log \left (3\right ) - 4\right )} e^{\left (e^{x}\right )} + 8 \, e^{\left (2 \, e^{x}\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. 33 vs.
\(2 (15) = 30\).
time = 0.33, size = 33, normalized size = 1.57 \begin {gather*} -8 \, {\left (2 \, {\left (e + \log \left (3\right ) - 4\right )} e^{\left (2 \, x + e^{x}\right )} - e^{\left (2 \, x + 2 \, e^{x}\right )}\right )} e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 24, normalized size = 1.14 \begin {gather*} 8 e^{2 e^{x}} + \left (- 16 e - 16 \log {\left (3 \right )} + 64\right ) e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 19, normalized size = 0.90 \begin {gather*} -16 \, {\left (e + \log \left (3\right ) - 4\right )} e^{\left (e^{x}\right )} + 8 \, e^{\left (2 \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.18, size = 18, normalized size = 0.86 \begin {gather*} 8\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\left ({\mathrm {e}}^{{\mathrm {e}}^x}-2\,\mathrm {e}-2\,\ln \left (3\right )+8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________