Optimal. Leaf size=22 \[ \frac {16}{\log \left (4+\log \left (5 \left (5-\frac {e^x}{4}+2 x\right )\right )\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.09, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 64, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6818}
\begin {gather*} \frac {16}{\log \left (\log \left (\frac {5}{4} \left (8 x-e^x+20\right )\right )+4\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {16}{\log \left (4+\log \left (\frac {5}{4} \left (20-e^x+8 x\right )\right )\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 20, normalized size = 0.91 \begin {gather*} \frac {16}{\log \left (4+\log \left (25-\frac {5 e^x}{4}+10 x\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.04, size = 18, normalized size = 0.82
method | result | size |
risch | \(\frac {16}{\ln \left (\ln \left (-\frac {5 \,{\mathrm e}^{x}}{4}+10 x +25\right )+4\right )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [C] Result contains complex when optimal does not.
time = 0.53, size = 24, normalized size = 1.09 \begin {gather*} \frac {16}{\log \left (i \, \pi + \log \left (5\right ) - 2 \, \log \left (2\right ) + \log \left (-8 \, x + e^{x} - 20\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 17, normalized size = 0.77 \begin {gather*} \frac {16}{\log \left (\log \left (10 \, x - \frac {5}{4} \, e^{x} + 25\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.83, size = 17, normalized size = 0.77 \begin {gather*} \frac {16}{\log {\left (\log {\left (10 x - \frac {5 e^{x}}{4} + 25 \right )} + 4 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 74 vs.
\(2 (17) = 34\).
time = 0.47, size = 74, normalized size = 3.36 \begin {gather*} -\frac {16 \, {\left (\log \left (10 \, x - \frac {5}{4} \, e^{x} + 25\right ) + 4\right )}}{2 \, \log \left (2\right ) \log \left (\log \left (10 \, x - \frac {5}{4} \, e^{x} + 25\right ) + 4\right ) - \log \left (40 \, x - 5 \, e^{x} + 100\right ) \log \left (\log \left (10 \, x - \frac {5}{4} \, e^{x} + 25\right ) + 4\right ) - 4 \, \log \left (\log \left (10 \, x - \frac {5}{4} \, e^{x} + 25\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.67, size = 17, normalized size = 0.77 \begin {gather*} \frac {16}{\ln \left (\ln \left (10\,x-\frac {5\,{\mathrm {e}}^x}{4}+25\right )+4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________