Optimal. Leaf size=23 \[ -35 x+34 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x) \]
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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 = {2333, 2332}
\begin {gather*} -35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2332
Rule 2333
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 \begin {gather*} -35 x+34 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 24, normalized size = 1.04
method | result | size |
default | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
norman | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
risch | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.50, size = 36, normalized size = 1.57 \begin {gather*} 3 \, {\left (\log \left (x\right )^{3} - 3 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) - 6\right )} x - 8 \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.86, size = 23, normalized size = 1.00 \begin {gather*} 3 \, x \log \left (x\right )^{3} - 17 \, x \log \left (x\right )^{2} + 34 \, x \log \left (x\right ) - 35 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 26, normalized size = 1.13 \begin {gather*} 3 x \log {\left (x \right )}^{3} - 17 x \log {\left (x \right )}^{2} + 34 x \log {\left (x \right )} - 35 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.75, size = 23, normalized size = 1.00 \begin {gather*} 3 \, x \log \left (x\right )^{3} - 17 \, x \log \left (x\right )^{2} + 34 \, x \log \left (x\right ) - 35 \, x \end {gather*}
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 \begin {gather*} x\,\left (3\,{\ln \left (x\right )}^3-17\,{\ln \left (x\right )}^2+34\,\ln \left (x\right )-35\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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