Optimal. Leaf size=21 \[ \frac {-2+x-\frac {-1+2 x}{\log (4)}}{2 x} \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 30} \begin {gather*} \frac {1-\log (16)}{2 x \log (4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {(-1+2 \log (4)) \int \frac {1}{x^2} \, dx}{2 \log (4)}\\ &=\frac {1-\log (16)}{2 x \log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.62 \begin {gather*} -\frac {-1+\log (16)}{x \log (16)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 15, normalized size = 0.71 \begin {gather*} -\frac {4 \, \log \relax (2) - 1}{4 \, x \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 15, normalized size = 0.71 \begin {gather*} -\frac {4 \, \log \relax (2) - 1}{4 \, x \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 16, normalized size = 0.76
method | result | size |
gosper | \(-\frac {4 \ln \relax (2)-1}{4 x \ln \relax (2)}\) | \(16\) |
default | \(-\frac {4 \ln \relax (2)-1}{4 x \ln \relax (2)}\) | \(16\) |
norman | \(-\frac {4 \ln \relax (2)-1}{4 x \ln \relax (2)}\) | \(16\) |
risch | \(-\frac {1}{x}+\frac {1}{4 x \ln \relax (2)}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 15, normalized size = 0.71 \begin {gather*} -\frac {4 \, \log \relax (2) - 1}{4 \, x \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.62 \begin {gather*} -\frac {\ln \left (16\right )-1}{4\,x\,\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 14, normalized size = 0.67 \begin {gather*} - \frac {-1 + 4 \log {\relax (2 )}}{4 x \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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