Optimal. Leaf size=14 \[ 3+x-x^2+\log (5)+\log ^2(x) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {14, 2301} \begin {gather*} -x^2+x+\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-2 x+\frac {2 \log (x)}{x}\right ) \, dx\\ &=x-x^2+2 \int \frac {\log (x)}{x} \, dx\\ &=x-x^2+\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} x-x^2+\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 11, normalized size = 0.79 \begin {gather*} -x^{2} + \log \relax (x)^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 11, normalized size = 0.79 \begin {gather*} -x^{2} + \log \relax (x)^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 12, normalized size = 0.86
method | result | size |
default | \(\ln \relax (x )^{2}-x^{2}+x\) | \(12\) |
norman | \(\ln \relax (x )^{2}-x^{2}+x\) | \(12\) |
risch | \(\ln \relax (x )^{2}-x^{2}+x\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 11, normalized size = 0.79 \begin {gather*} -x^{2} + \log \relax (x)^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.16, size = 11, normalized size = 0.79 \begin {gather*} -x^2+x+{\ln \relax (x)}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.57 \begin {gather*} - x^{2} + x + \log {\relax (x )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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