Optimal. Leaf size=20 \[ \log \left (5 \left (e^{2 e^{e^x}}-64 (4-10 x)\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps
used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6816}
\begin {gather*} \log \left (-640 x-e^{2 e^{e^x}}+256\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (256-e^{2 e^{e^x}}-640 x\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.06, size = 17, normalized size = 0.85 \begin {gather*} \log \left (256-e^{2 e^{e^x}}-640 x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.18, size = 13, normalized size = 0.65
method | result | size |
derivativedivides | \(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+640 x -256\right )\) | \(13\) |
norman | \(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+640 x -256\right )\) | \(13\) |
risch | \(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+640 x -256\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 12, normalized size = 0.60 \begin {gather*} \log \left (640 \, x + e^{\left (2 \, e^{\left (e^{x}\right )}\right )} - 256\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. 32 vs.
\(2 (14) = 28\).
time = 0.43, size = 32, normalized size = 1.60 \begin {gather*} -x - e^{x} + \log \left (128 \, {\left (5 \, x - 2\right )} e^{\left (x + e^{x}\right )} + e^{\left (x + e^{x} + 2 \, e^{\left (e^{x}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.10, size = 14, normalized size = 0.70 \begin {gather*} \log {\left (640 x + e^{2 e^{e^{x}}} - 256 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.14, size = 12, normalized size = 0.60 \begin {gather*} \ln \left (640\,x+{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}-256\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________