Optimal. Leaf size=19 \[ -x^2+4 \left (-\frac {323}{81}+5 x\right )^2+\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.68, 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*} 99 x^2-\frac {12920 x}{81}+\log (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}{81} \int \frac {81-12920 x+16038 x^2}{x} \, dx\\ &=\frac {1}{81} \int \left (-12920+\frac {81}{x}+16038 x\right ) \, dx\\ &=-\frac {12920 x}{81}+99 x^2+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.68 \begin {gather*} -\frac {12920 x}{81}+99 x^2+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 11, normalized size = 0.58 \begin {gather*} 99 \, x^{2} - \frac {12920}{81} \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 12, normalized size = 0.63 \begin {gather*} 99 \, x^{2} - \frac {12920}{81} \, x + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 0.63
method | result | size |
default | \(99 x^{2}-\frac {12920 x}{81}+\ln \relax (x )\) | \(12\) |
norman | \(99 x^{2}-\frac {12920 x}{81}+\ln \relax (x )\) | \(12\) |
risch | \(99 x^{2}-\frac {12920 x}{81}+\ln \relax (x )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 11, normalized size = 0.58 \begin {gather*} 99 \, x^{2} - \frac {12920}{81} \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.58 \begin {gather*} \ln \relax (x)-\frac {12920\,x}{81}+99\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 12, normalized size = 0.63 \begin {gather*} 99 x^{2} - \frac {12920 x}{81} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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