Optimal. Leaf size=29 \[ -5-x+\frac {1}{2} \left (1-\frac {e^5-x^2}{4 x}\right ) \log (5) \]
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Rubi [A]
time = 0.01, antiderivative size = 24, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 14}
\begin {gather*} -\frac {1}{8} x (8-\log (5))-\frac {e^5 \log (5)}{8 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \frac {-8 x^2+\left (e^5+x^2\right ) \log (5)}{x^2} \, dx\\ &=\frac {1}{8} \int \left (-8 \left (1-\frac {\log (5)}{8}\right )+\frac {e^5 \log (5)}{x^2}\right ) \, dx\\ &=-\frac {1}{8} x (8-\log (5))-\frac {e^5 \log (5)}{8 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 0.76 \begin {gather*} \frac {1}{8} \left (-8 x-\frac {e^5 \log (5)}{x}+x \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 19, normalized size = 0.66
method | result | size |
default | \(\frac {x \ln \left (5\right )}{8}-x -\frac {{\mathrm e}^{5} \ln \left (5\right )}{8 x}\) | \(19\) |
risch | \(\frac {x \ln \left (5\right )}{8}-x -\frac {{\mathrm e}^{5} \ln \left (5\right )}{8 x}\) | \(19\) |
norman | \(\frac {\left (-1+\frac {\ln \left (5\right )}{8}\right ) x^{2}-\frac {{\mathrm e}^{5} \ln \left (5\right )}{8}}{x}\) | \(22\) |
gosper | \(-\frac {-x^{2} \ln \left (5\right )+{\mathrm e}^{5} \ln \left (5\right )+8 x^{2}}{8 x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 17, normalized size = 0.59 \begin {gather*} \frac {1}{8} \, x {\left (\log \left (5\right ) - 8\right )} - \frac {e^{5} \log \left (5\right )}{8 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 23, normalized size = 0.79 \begin {gather*} -\frac {8 \, x^{2} - {\left (x^{2} - e^{5}\right )} \log \left (5\right )}{8 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 0.66 \begin {gather*} - \frac {x \left (8 - \log {\left (5 \right )}\right )}{8} - \frac {e^{5} \log {\left (5 \right )}}{8 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 18, normalized size = 0.62 \begin {gather*} \frac {1}{8} \, x \log \left (5\right ) - x - \frac {e^{5} \log \left (5\right )}{8 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.16, size = 18, normalized size = 0.62 \begin {gather*} x\,\left (\frac {\ln \left (5\right )}{8}-1\right )-\frac {{\mathrm {e}}^5\,\ln \left (5\right )}{8\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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