Optimal. Leaf size=15 \[ (-5 x-\log (105)) (4+2 \log (x)) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {14, 43, 2295} \begin {gather*} -20 x-10 x \log (x)-2 \log (105) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 (15 x+\log (105))}{x}-10 \log (x)\right ) \, dx\\ &=-\left (2 \int \frac {15 x+\log (105)}{x} \, dx\right )-10 \int \log (x) \, dx\\ &=10 x-10 x \log (x)-2 \int \left (15+\frac {\log (105)}{x}\right ) \, dx\\ &=-20 x-10 x \log (x)-2 \log (105) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -20 x-10 x \log (x)-2 \log (105) \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 14, normalized size = 0.93 \begin {gather*} -2 \, {\left (5 \, x + \log \left (105\right )\right )} \log \relax (x) - 20 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 15, normalized size = 1.00 \begin {gather*} -10 \, x \log \relax (x) - 2 \, \log \left (105\right ) \log \relax (x) - 20 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 1.07
method | result | size |
default | \(-10 x \ln \relax (x )-20 x -2 \ln \left (105\right ) \ln \relax (x )\) | \(16\) |
norman | \(-10 x \ln \relax (x )-20 x -2 \ln \left (105\right ) \ln \relax (x )\) | \(16\) |
risch | \(-10 x \ln \relax (x )-2 \ln \relax (5) \ln \relax (x )-2 \ln \relax (x ) \ln \relax (7)-2 \ln \relax (3) \ln \relax (x )-20 x\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 15, normalized size = 1.00 \begin {gather*} -10 \, x \log \relax (x) - 2 \, \log \left (105\right ) \log \relax (x) - 20 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.85, size = 15, normalized size = 1.00 \begin {gather*} -20\,x-2\,\ln \left (105\right )\,\ln \relax (x)-10\,x\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 19, normalized size = 1.27 \begin {gather*} - 10 x \log {\relax (x )} - 20 x - 2 \log {\left (105 \right )} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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