Optimal. Leaf size=26 \[ 9 e^2-\log \left (4+\left (1+\frac {x}{3-e^2}\right )^2\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {1587} \begin {gather*} -\log \left (x^2+6 x-2 e^2 (x+15)+5 \left (9+e^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (5 \left (9+e^4\right )+6 x+x^2-2 e^2 (15+x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 0.92 \begin {gather*} -\log \left (45+5 e^4+6 x+x^2-2 e^2 (15+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 22, normalized size = 0.85 \begin {gather*} -\log \left (x^{2} - 2 \, {\left (x + 15\right )} e^{2} + 6 \, x + 5 \, e^{4} + 45\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 24, normalized size = 0.92 \begin {gather*} -\log \left (x^{2} - 2 \, x e^{2} + 6 \, x + 5 \, e^{4} - 30 \, e^{2} + 45\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.92, size = 25, normalized size = 0.96
method | result | size |
risch | \(-\ln \left (x^{2}+\left (-2 \,{\mathrm e}^{2}+6\right ) x +5 \,{\mathrm e}^{4}-30 \,{\mathrm e}^{2}+45\right )\) | \(25\) |
default | \(-\ln \left (5 \,{\mathrm e}^{4}-2 \,{\mathrm e}^{2} x +x^{2}-30 \,{\mathrm e}^{2}+6 x +45\right )\) | \(27\) |
norman | \(-\ln \left (5 \,{\mathrm e}^{4}-2 \,{\mathrm e}^{2} x +x^{2}-30 \,{\mathrm e}^{2}+6 x +45\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 22, normalized size = 0.85 \begin {gather*} -\log \left (x^{2} - 2 \, {\left (x + 15\right )} e^{2} + 6 \, x + 5 \, e^{4} + 45\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 24, normalized size = 0.92 \begin {gather*} -\ln \left (x^2+\left (6-2\,{\mathrm {e}}^2\right )\,x+5\,{\left ({\mathrm {e}}^2-3\right )}^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 26, normalized size = 1.00 \begin {gather*} - \log {\left (x^{2} + x \left (6 - 2 e^{2}\right ) - 30 e^{2} + 45 + 5 e^{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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