Optimal. Leaf size=18 \[ \log \left (4+\frac {25 x^2}{16}+e^5 \log \left (\frac {5}{4}\right )\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps
used = 2, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 266}
\begin {gather*} \log \left (25 x^2+16 \left (4+e^5 \log \left (\frac {5}{4}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 266
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (50 \int \frac {x}{-64-25 x^2-16 e^5 \log \left (\frac {5}{4}\right )} \, dx\right )\\ &=\log \left (25 x^2+16 \left (4+e^5 \log \left (\frac {5}{4}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} \log \left (64+25 x^2+16 e^5 \log \left (\frac {5}{4}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 15, normalized size = 0.83
method | result | size |
derivativedivides | \(\ln \left (16 \,{\mathrm e}^{5} \ln \left (\frac {4}{5}\right )-25 x^{2}-64\right )\) | \(15\) |
default | \(\ln \left (16 \,{\mathrm e}^{5} \ln \left (\frac {4}{5}\right )-25 x^{2}-64\right )\) | \(15\) |
norman | \(\ln \left (16 \,{\mathrm e}^{5} \ln \left (\frac {4}{5}\right )-25 x^{2}-64\right )\) | \(15\) |
meijerg | \(\ln \left (1-\frac {25 x^{2}}{16 \,{\mathrm e}^{5} \ln \left (\frac {4}{5}\right )-64}\right )\) | \(19\) |
risch | \(\ln \left (16 \,{\mathrm e}^{5} \ln \left (5\right )-32 \,{\mathrm e}^{5} \ln \left (2\right )+25 x^{2}+64\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.78 \begin {gather*} \log \left (25 \, x^{2} - 16 \, e^{5} \log \left (\frac {4}{5}\right ) + 64\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 14, normalized size = 0.78 \begin {gather*} \log \left (25 \, x^{2} - 16 \, e^{5} \log \left (\frac {4}{5}\right ) + 64\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 24, normalized size = 1.33 \begin {gather*} \log {\left (25 x^{2} - 32 e^{5} \log {\left (2 \right )} + 64 + 16 e^{5} \log {\left (5 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 14, normalized size = 0.78 \begin {gather*} \log \left (25 \, x^{2} - 16 \, e^{5} \log \left (\frac {4}{5}\right ) + 64\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 14, normalized size = 0.78 \begin {gather*} \ln \left (25\,x^2-16\,{\mathrm {e}}^5\,\ln \left (\frac {4}{5}\right )+64\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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