Optimal. Leaf size=30 \[ 1-\frac {1}{(-3+e-x) x \left (-3-\frac {3}{x}+2 x\right )}+\log (\log (x)) \]
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Rubi [A]
time = 0.45, antiderivative size = 26, normalized size of antiderivative = 0.87, number of steps
used = 5, number of rules used = 4, integrand size = 199, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6820, 1604,
2339, 29} \begin {gather*} \log (\log (x))-\frac {1}{(x-e+3) \left (-2 x^2+3 x+3\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 1604
Rule 2339
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {3 (4-e)-2 (3-2 e) x-6 x^2}{(3-e+x)^2 \left (3+3 x-2 x^2\right )^2}+\frac {1}{x \log (x)}\right ) \, dx\\ &=\int \frac {3 (4-e)-2 (3-2 e) x-6 x^2}{(3-e+x)^2 \left (3+3 x-2 x^2\right )^2} \, dx+\int \frac {1}{x \log (x)} \, dx\\ &=-\frac {1}{(3-e+x) \left (3+3 x-2 x^2\right )}+\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-\frac {1}{(3-e+x) \left (3+3 x-2 x^2\right )}+\log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 26, normalized size = 0.87 \begin {gather*} -\frac {1}{(-3+e-x) \left (-3-3 x+2 x^2\right )}+\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.78, size = 28, normalized size = 0.93
method | result | size |
default | \(\ln \left (\ln \left (x \right )\right )-\frac {1}{\left (2 x^{2}-3 x -3\right ) \left ({\mathrm e}-3-x \right )}\) | \(28\) |
norman | \(\ln \left (\ln \left (x \right )\right )-\frac {1}{\left (2 x^{2}-3 x -3\right ) \left ({\mathrm e}-3-x \right )}\) | \(28\) |
risch | \(-\frac {1}{2 x^{2} {\mathrm e}-2 x^{3}-3 x \,{\mathrm e}-3 x^{2}-3 \,{\mathrm e}+12 x +9}+\ln \left (\ln \left (x \right )\right )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 35, normalized size = 1.17 \begin {gather*} \frac {1}{2 \, x^{3} - x^{2} {\left (2 \, e - 3\right )} + 3 \, x {\left (e - 4\right )} + 3 \, e - 9} + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 67 vs.
\(2 (30) = 60\).
time = 0.38, size = 67, normalized size = 2.23 \begin {gather*} \frac {{\left (2 \, x^{3} + 3 \, x^{2} - {\left (2 \, x^{2} - 3 \, x - 3\right )} e - 12 \, x - 9\right )} \log \left (\log \left (x\right )\right ) + 1}{2 \, x^{3} + 3 \, x^{2} - {\left (2 \, x^{2} - 3 \, x - 3\right )} e - 12 \, x - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.99, size = 36, normalized size = 1.20 \begin {gather*} \log {\left (\log {\left (x \right )} \right )} + \frac {1}{2 x^{3} + x^{2} \cdot \left (3 - 2 e\right ) + x \left (-12 + 3 e\right ) - 9 + 3 e} \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. 88 vs.
\(2 (30) = 60\).
time = 0.57, size = 88, normalized size = 2.93 \begin {gather*} \frac {2 \, x^{3} \log \left (\log \left (x\right )\right ) - 2 \, x^{2} e \log \left (\log \left (x\right )\right ) + 3 \, x^{2} \log \left (\log \left (x\right )\right ) + 3 \, x e \log \left (\log \left (x\right )\right ) - 12 \, x \log \left (\log \left (x\right )\right ) + 3 \, e \log \left (\log \left (x\right )\right ) - 9 \, \log \left (\log \left (x\right )\right ) + 2}{2 \, x^{3} - 2 \, x^{2} e + 3 \, x^{2} + 3 \, x e - 12 \, x + 3 \, e - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.03, size = 36, normalized size = 1.20 \begin {gather*} \ln \left (\ln \left (x\right )\right )+\frac {1}{2\,x^3+\left (3-2\,\mathrm {e}\right )\,x^2+\left (3\,\mathrm {e}-12\right )\,x+3\,\mathrm {e}-9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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