Optimal. Leaf size=15 \[ \frac {1}{2 x+6 (2+x)-\log (16)} \]
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Rubi [A]
time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps
used = 4, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2006, 27,
32} \begin {gather*} \frac {1}{8 x+12-\log (16)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rule 2006
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (8 \int \frac {1}{144+192 x+64 x^2+(-24-16 x) \log (16)+\log ^2(16)} \, dx\right )\\ &=-\left (8 \int \frac {1}{64 x^2+16 x (12-\log (16))+(-12+\log (16))^2} \, dx\right )\\ &=-\left (8 \int \frac {1}{(12+8 x-\log (16))^2} \, dx\right )\\ &=\frac {1}{12+8 x-\log (16)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.73 \begin {gather*} -\frac {1}{-12-8 x+\log (16)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 14, normalized size = 0.93
method | result | size |
gosper | \(-\frac {1}{4 \left (\ln \left (2\right )-2 x -3\right )}\) | \(12\) |
norman | \(-\frac {1}{4 \left (\ln \left (2\right )-2 x -3\right )}\) | \(12\) |
risch | \(-\frac {1}{4 \left (\ln \left (2\right )-2 x -3\right )}\) | \(12\) |
default | \(\frac {1}{8 x +12-4 \ln \left (2\right )}\) | \(14\) |
meijerg | \(-\frac {x}{4 \left (-\frac {\ln \left (2\right )}{2}+\frac {3}{2}\right ) \left (-\ln \left (2\right )+3\right ) \left (1+\frac {2 x}{-\ln \left (2\right )+3}\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{4 \, {\left (2 \, x - \log \left (2\right ) + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{4 \, {\left (2 \, x - \log \left (2\right ) + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{8 x - 4 \log {\left (2 \right )} + 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{4 \, {\left (2 \, x - \log \left (2\right ) + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.58, size = 51, normalized size = 3.40 \begin {gather*} \frac {2\,\mathrm {atanh}\left (\frac {16\,x-\ln \left (256\right )+24}{\sqrt {\ln \left (256\right )-8\,\ln \left (2\right )}\,\sqrt {8\,\ln \left (2\right )+\ln \left (256\right )-48}}\right )}{\sqrt {\ln \left (256\right )-8\,\ln \left (2\right )}\,\sqrt {8\,\ln \left (2\right )+\ln \left (256\right )-48}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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