Optimal. Leaf size=19 \[ -\frac {19}{12}-\frac {\left (x+\frac {\log (2)}{2}\right )^2}{x} \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps
used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 14}
\begin {gather*} -x-\frac {\log ^2(2)}{4 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}{4} \int \frac {-4 x^2+\log ^2(2)}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-4+\frac {\log ^2(2)}{x^2}\right ) \, dx\\ &=-x-\frac {\log ^2(2)}{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} -x-\frac {\log ^2(2)}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.40, size = 14, normalized size = 0.74
method | result | size |
default | \(-x -\frac {\ln \left (2\right )^{2}}{4 x}\) | \(14\) |
risch | \(-x -\frac {\ln \left (2\right )^{2}}{4 x}\) | \(14\) |
gosper | \(-\frac {\ln \left (2\right )^{2}+4 x^{2}}{4 x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.68 \begin {gather*} -x - \frac {\log \left (2\right )^{2}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 15, normalized size = 0.79 \begin {gather*} -\frac {4 \, x^{2} + \log \left (2\right )^{2}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.53 \begin {gather*} - x - \frac {\log {\left (2 \right )}^{2}}{4 x} \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 = 0.68 \begin {gather*} -x - \frac {\log \left (2\right )^{2}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} -x-\frac {{\ln \left (2\right )}^2}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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