Optimal. Leaf size=23 \[ -35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2296, 2295} \[ -35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x) \]
Antiderivative was successfully verified.
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Rule 2295
Rule 2296
Rubi steps
\begin {align*} \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx &=-x+3 \int \log ^3(x) \, dx-8 \int \log ^2(x) \, dx\\ &=-x-8 x \log ^2(x)+3 x \log ^3(x)-9 \int \log ^2(x) \, dx+16 \int \log (x) \, dx\\ &=-17 x+16 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x)+18 \int \log (x) \, dx\\ &=-35 x+34 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 23, normalized size = 1.00 \[ -35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.80, size = 23, normalized size = 1.00 \[ 3 \, x \log \relax (x)^{3} - 17 \, x \log \relax (x)^{2} + 34 \, x \log \relax (x) - 35 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.58, size = 23, normalized size = 1.00 \[ 3 \, x \log \relax (x)^{3} - 17 \, x \log \relax (x)^{2} + 34 \, x \log \relax (x) - 35 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 24, normalized size = 1.04
method | result | size |
default | \(-35 x +34 x \ln \relax (x )-17 x \ln \relax (x )^{2}+3 x \ln \relax (x )^{3}\) | \(24\) |
norman | \(-35 x +34 x \ln \relax (x )-17 x \ln \relax (x )^{2}+3 x \ln \relax (x )^{3}\) | \(24\) |
risch | \(-35 x +34 x \ln \relax (x )-17 x \ln \relax (x )^{2}+3 x \ln \relax (x )^{3}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 36, normalized size = 1.57 \[ 3 \, {\left (\log \relax (x)^{3} - 3 \, \log \relax (x)^{2} + 6 \, \log \relax (x) - 6\right )} x - 8 \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x - x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.29, size = 20, normalized size = 0.87 \[ x\,\left (3\,{\ln \relax (x)}^3-17\,{\ln \relax (x)}^2+34\,\ln \relax (x)-35\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 26, normalized size = 1.13 \[ 3 x \log {\relax (x )}^{3} - 17 x \log {\relax (x )}^{2} + 34 x \log {\relax (x )} - 35 x \]
Verification of antiderivative is not currently implemented for this CAS.
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