Optimal. Leaf size=19 \[ \log (2) \left (\frac {5}{4} \left (16-\frac {23}{x}\right )-\log (4)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.47, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 30}
\begin {gather*} -\frac {115 \log (2)}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} (115 \log (2)) \int \frac {1}{x^2} \, dx\\ &=-\frac {115 \log (2)}{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.47 \begin {gather*} -\frac {115 \log (2)}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 8, normalized size = 0.42
method | result | size |
gosper | \(-\frac {115 \ln \left (2\right )}{4 x}\) | \(8\) |
default | \(-\frac {115 \ln \left (2\right )}{4 x}\) | \(8\) |
norman | \(-\frac {115 \ln \left (2\right )}{4 x}\) | \(8\) |
risch | \(-\frac {115 \ln \left (2\right )}{4 x}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115 \, \log \left (2\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115 \, \log \left (2\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.42 \begin {gather*} - \frac {115 \log {\left (2 \right )}}{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115 \, \log \left (2\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 7, normalized size = 0.37 \begin {gather*} -\frac {115\,\ln \left (2\right )}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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