Optimal. Leaf size=18 \[ \log \left (x+\log ^2\left (e^3+2 (3-x)+x\right )\right ) \]
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Rubi [A]
time = 0.15, antiderivative size = 14, normalized size of antiderivative = 0.78, number of steps
used = 3, number of rules used = 3, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {6, 6873, 6816}
\begin {gather*} \log \left (x+\log ^2\left (-x+e^3+6\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 6816
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6+e^3-x-2 \log \left (6+e^3-x\right )}{\left (6+e^3\right ) x-x^2+\left (6+e^3-x\right ) \log ^2\left (6+e^3-x\right )} \, dx\\ &=\int \frac {6 \left (1+\frac {e^3}{6}\right )-x-2 \log \left (6+e^3-x\right )}{\left (6+e^3-x\right ) \left (x+\log ^2\left (6+e^3-x\right )\right )} \, dx\\ &=\log \left (x+\log ^2\left (6+e^3-x\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 14, normalized size = 0.78 \begin {gather*} \log \left (x+\log ^2\left (6+e^3-x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 18, normalized size = 1.00
method | result | size |
norman | \(\ln \left (\ln \left ({\mathrm e}^{3}-x +6\right )^{2}+x \right )\) | \(14\) |
risch | \(\ln \left (\ln \left ({\mathrm e}^{3}-x +6\right )^{2}+x \right )\) | \(14\) |
default | \(\ln \left (-\ln \left ({\mathrm e}^{3}-x +6\right )^{2}-x \right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.72 \begin {gather*} \log \left (\log \left (-x + e^{3} + 6\right )^{2} + x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 13, normalized size = 0.72 \begin {gather*} \log \left (\log \left (-x + e^{3} + 6\right )^{2} + x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 12, normalized size = 0.67 \begin {gather*} \log {\left (x + \log {\left (- x + 6 + e^{3} \right )}^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.94 \begin {gather*} \log \left (-\log \left (-x + e^{3} + 6\right )^{2} - x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.18, size = 13, normalized size = 0.72 \begin {gather*} \ln \left ({\ln \left ({\mathrm {e}}^3-x+6\right )}^2+x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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