Optimal. Leaf size=26 \[ 1+\left (-x+e \log \left (-x (-16+3 x)+\log \left (e^2 x\right )\right )\right )^2 \]
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Rubi [A]
time = 0.18, antiderivative size = 20, normalized size of antiderivative = 0.77, number of steps
used = 3, number of rules used = 3, integrand size = 115, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6820, 12,
6818} \begin {gather*} \left (x-e \log \left (-3 x^2+16 x+\log (x)+2\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (x \left (2+16 x-3 x^2\right )+e \left (-1-16 x+6 x^2\right )+x \log (x)\right ) \left (x-e \log \left (2+16 x-3 x^2+\log (x)\right )\right )}{x \left (2+16 x-3 x^2+\log (x)\right )} \, dx\\ &=2 \int \frac {\left (x \left (2+16 x-3 x^2\right )+e \left (-1-16 x+6 x^2\right )+x \log (x)\right ) \left (x-e \log \left (2+16 x-3 x^2+\log (x)\right )\right )}{x \left (2+16 x-3 x^2+\log (x)\right )} \, dx\\ &=\left (x-e \log \left (2+16 x-3 x^2+\log (x)\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 21, normalized size = 0.81 \begin {gather*} \left (-x+e \log \left (2+16 x-3 x^2+\log (x)\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 42.44, size = 45, normalized size = 1.73
method | result | size |
risch | \({\mathrm e}^{2} \ln \left (\ln \left ({\mathrm e}^{2} x \right )-3 x^{2}+16 x \right )^{2}-2 \,{\mathrm e} \ln \left (\ln \left ({\mathrm e}^{2} x \right )-3 x^{2}+16 x \right ) x +x^{2}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.42, size = 40, normalized size = 1.54 \begin {gather*} -2 \, x e \log \left (-3 \, x^{2} + 16 \, x + \log \left (x\right ) + 2\right ) + e^{2} \log \left (-3 \, x^{2} + 16 \, x + \log \left (x\right ) + 2\right )^{2} + x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 44, normalized size = 1.69 \begin {gather*} -2 \, x e \log \left (-3 \, x^{2} + 16 \, x + \log \left (x e^{2}\right )\right ) + e^{2} \log \left (-3 \, x^{2} + 16 \, x + \log \left (x e^{2}\right )\right )^{2} + x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (22) = 44\).
time = 0.21, size = 48, normalized size = 1.85 \begin {gather*} x^{2} - 2 e x \log {\left (- 3 x^{2} + 16 x + \log {\left (x e^{2} \right )} \right )} + e^{2} \log {\left (- 3 x^{2} + 16 x + \log {\left (x e^{2} \right )} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 40, normalized size = 1.54 \begin {gather*} -2 \, x e \log \left (-3 \, x^{2} + 16 \, x + \log \left (x\right ) + 2\right ) + e^{2} \log \left (-3 \, x^{2} + 16 \, x + \log \left (x\right ) + 2\right )^{2} + x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.00, size = 21, normalized size = 0.81 \begin {gather*} {\left (x-\mathrm {e}\,\ln \left (16\,x+\ln \left (x\right )-3\,x^2+2\right )\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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