Optimal. Leaf size=19 \[ \log \left (\left (-4+e^{\frac {1}{-5+\frac {x}{e^5}}}-x\right ) x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.53, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 127, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6873, 12,
6817} \begin {gather*} \log \left (x \left (x-e^{\frac {1}{\frac {x}{e^5}-5}}+4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6817
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{10} \left (100+50 x-\frac {(-4-2 x) x^2}{e^{10}}-\frac {x (40+20 x)}{e^5}-e^{\frac {1}{-5+\frac {x}{e^5}}} \left (25-\frac {11 x}{e^5}+\frac {x^2}{e^{10}}\right )\right )}{\left (5 e^5-x\right )^2 x \left (4-e^{\frac {1}{-5+\frac {x}{e^5}}}+x\right )} \, dx\\ &=e^{10} \int \frac {100+50 x-\frac {(-4-2 x) x^2}{e^{10}}-\frac {x (40+20 x)}{e^5}-e^{\frac {1}{-5+\frac {x}{e^5}}} \left (25-\frac {11 x}{e^5}+\frac {x^2}{e^{10}}\right )}{\left (5 e^5-x\right )^2 x \left (4-e^{\frac {1}{-5+\frac {x}{e^5}}}+x\right )} \, dx\\ &=\log \left (x \left (4-e^{\frac {1}{-5+\frac {x}{e^5}}}+x\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.07, size = 24, normalized size = 1.26 \begin {gather*} \log (x)+\log \left (4-e^{\frac {e^5}{-5 e^5+x}}+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.56, size = 19, normalized size = 1.00
method | result | size |
norman | \(\ln \left (x \right )+\ln \left (x -{\mathrm e}^{\frac {1}{x \,{\mathrm e}^{-5}-5}}+4\right )\) | \(19\) |
risch | \(\ln \left (-x \right )+\ln \left (-x +{\mathrm e}^{\frac {1}{x \,{\mathrm e}^{-5}-5}}-4\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 21, normalized size = 1.11 \begin {gather*} \log \left (x\right ) + \log \left (-x + e^{\left (\frac {e^{5}}{x - 5 \, e^{5}}\right )} - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 21, normalized size = 1.11 \begin {gather*} \log \left (x\right ) + \log \left (-x + e^{\left (\frac {e^{5}}{x - 5 \, e^{5}}\right )} - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.21, size = 17, normalized size = 0.89 \begin {gather*} \log {\left (x \right )} + \log {\left (- x + e^{\frac {1}{\frac {x}{e^{5}} - 5}} - 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. 93 vs.
\(2 (19) = 38\).
time = 0.60, size = 93, normalized size = 4.89 \begin {gather*} {\left (e^{5} \log \left (\frac {5 \, e^{10}}{x - 5 \, e^{5}} + \frac {4 \, e^{5}}{x - 5 \, e^{5}} - \frac {e^{\left (\frac {e^{5}}{x - 5 \, e^{5}} + 5\right )}}{x - 5 \, e^{5}} + e^{5}\right ) + e^{5} \log \left (\frac {5 \, e^{5}}{x - 5 \, e^{5}} + 1\right ) - 2 \, e^{5} \log \left (\frac {e^{5}}{x - 5 \, e^{5}}\right )\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.40, size = 18, normalized size = 0.95 \begin {gather*} \ln \left (x-{\mathrm {e}}^{\frac {1}{x\,{\mathrm {e}}^{-5}-5}}+4\right )+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________