Optimal. Leaf size=20 \[ 5 x-x^2 \log ^2(x (3-\log (x))) \]
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Rubi [F]
time = 0.25, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-15+5 \log (x)+(4 x-2 x \log (x)) \log (3 x-x \log (x))+(6 x-2 x \log (x)) \log ^2(3 x-x \log (x))}{-3+\log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5+\frac {2 x (-2+\log (x)) \log (3 x-x \log (x))}{3-\log (x)}-2 x \log ^2(3 x-x \log (x))\right ) \, dx\\ &=5 x+2 \int \frac {x (-2+\log (x)) \log (3 x-x \log (x))}{3-\log (x)} \, dx-2 \int x \log ^2(3 x-x \log (x)) \, dx\\ &=5 x-2 \int x \log ^2(3 x-x \log (x)) \, dx+2 \int \left (\frac {2 x \log (3 x-x \log (x))}{-3+\log (x)}+\frac {x \log (x) \log (3 x-x \log (x))}{3-\log (x)}\right ) \, dx\\ &=5 x+2 \int \frac {x \log (x) \log (3 x-x \log (x))}{3-\log (x)} \, dx-2 \int x \log ^2(3 x-x \log (x)) \, dx+4 \int \frac {x \log (3 x-x \log (x))}{-3+\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.21, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-15+5 \log (x)+(4 x-2 x \log (x)) \log (3 x-x \log (x))+(6 x-2 x \log (x)) \log ^2(3 x-x \log (x))}{-3+\log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 3.25, size = 22, normalized size = 1.10
method | result | size |
norman | \(5 x -x^{2} \ln \left (-x \ln \left (x \right )+3 x \right )^{2}\) | \(22\) |
risch | \(\text {Expression too large to display}\) | \(765\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.43, size = 76, normalized size = 3.80 \begin {gather*} -x^{2} \log \left (x\right )^{2} - 2 \, x^{2} \log \left (x\right ) \log \left (-\log \left (x\right ) + 3\right ) - x^{2} \log \left (-\log \left (x\right ) + 3\right )^{2} - 5 \, e^{3} E_{1}\left (-\log \left (x\right ) + 3\right ) \log \left (x\right ) + 5 \, e^{3} E_{2}\left (-\log \left (x\right ) + 3\right ) + 15 \, e^{3} E_{1}\left (-\log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 21, normalized size = 1.05 \begin {gather*} -x^{2} \log \left (-x \log \left (x\right ) + 3 \, x\right )^{2} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 17, normalized size = 0.85 \begin {gather*} - x^{2} \log {\left (- x \log {\left (x \right )} + 3 x \right )}^{2} + 5 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 41 vs.
\(2 (19) = 38\).
time = 0.41, size = 41, normalized size = 2.05 \begin {gather*} -x^{2} \log \left (x\right )^{2} - 2 \, x^{2} \log \left (x\right ) \log \left (-\log \left (x\right ) + 3\right ) - x^{2} \log \left (-\log \left (x\right ) + 3\right )^{2} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.37, size = 21, normalized size = 1.05 \begin {gather*} 5\,x-x^2\,{\ln \left (3\,x-x\,\ln \left (x\right )\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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