Optimal. Leaf size=20 \[ -\frac {4}{15} x^2 \left (\frac {81}{x}+\frac {16 \log (x)}{x^2}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.60, number of steps
used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 45}
\begin {gather*} -\frac {108 x}{5}-\frac {64 \log (x)}{15} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{15} \int \frac {-64-324 x}{x} \, dx\\ &=\frac {1}{15} \int \left (-324-\frac {64}{x}\right ) \, dx\\ &=-\frac {108 x}{5}-\frac {64 \log (x)}{15}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 0.60 \begin {gather*} -\frac {4}{15} (81 x+16 \log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 9, normalized size = 0.45
method | result | size |
default | \(-\frac {108 x}{5}-\frac {64 \ln \left (x \right )}{15}\) | \(9\) |
norman | \(-\frac {108 x}{5}-\frac {64 \ln \left (x \right )}{15}\) | \(9\) |
risch | \(-\frac {108 x}{5}-\frac {64 \ln \left (x \right )}{15}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 8, normalized size = 0.40 \begin {gather*} -\frac {108}{5} \, x - \frac {64}{15} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 8, normalized size = 0.40 \begin {gather*} -\frac {108}{5} \, x - \frac {64}{15} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.60 \begin {gather*} - \frac {108 x}{5} - \frac {64 \log {\left (x \right )}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 9, normalized size = 0.45 \begin {gather*} -\frac {108}{5} \, x - \frac {64}{15} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.43, size = 8, normalized size = 0.40 \begin {gather*} -\frac {108\,x}{5}-\frac {64\,\ln \left (x\right )}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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