Optimal. Leaf size=13 \[ \frac {(6-x)^2 \log (x)}{x} \]
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Rubi [A]
time = 0.04, antiderivative size = 16, normalized size of antiderivative = 1.23, number of steps
used = 6, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {14, 45, 2372}
\begin {gather*} x \log (x)+\frac {36 \log (x)}{x}-12 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 45
Rule 2372
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {(-6+x)^2}{x^2}+\frac {\left (-36+x^2\right ) \log (x)}{x^2}\right ) \, dx\\ &=\int \frac {(-6+x)^2}{x^2} \, dx+\int \frac {\left (-36+x^2\right ) \log (x)}{x^2} \, dx\\ &=\left (\frac {36}{x}+x\right ) \log (x)-\int \left (1+\frac {36}{x^2}\right ) \, dx+\int \left (1+\frac {36}{x^2}-\frac {12}{x}\right ) \, dx\\ &=-12 \log (x)+\left (\frac {36}{x}+x\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 1.23 \begin {gather*} -12 \log (x)+\frac {36 \log (x)}{x}+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 17, normalized size = 1.31
method | result | size |
default | \(x \ln \left (x \right )+\frac {36 \ln \left (x \right )}{x}-12 \ln \left (x \right )\) | \(17\) |
risch | \(\frac {\left (x^{2}+36\right ) \ln \left (x \right )}{x}-12 \ln \left (x \right )\) | \(17\) |
norman | \(\frac {x^{2} \ln \left (x \right )-12 x \ln \left (x \right )+36 \ln \left (x \right )}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 16, normalized size = 1.23 \begin {gather*} x \log \left (x\right ) + \frac {36 \, \log \left (x\right )}{x} - 12 \, \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 = 14, normalized size = 1.08 \begin {gather*} \frac {{\left (x^{2} - 12 \, x + 36\right )} \log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 1.08 \begin {gather*} - 12 \log {\left (x \right )} + \frac {\left (x^{2} + 36\right ) \log {\left (x \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 15, normalized size = 1.15 \begin {gather*} {\left (x + \frac {36}{x}\right )} \log \left (x\right ) - 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.90, size = 11, normalized size = 0.85 \begin {gather*} \frac {\ln \left (x\right )\,{\left (x-6\right )}^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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