Optimal. Leaf size=15 \[ x \left (6-x-\frac {x}{e}+\log (x)\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.80, number of steps
used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 2332}
\begin {gather*} -\frac {x^2}{e}-\frac {1}{4} (7-2 x)^2-x+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int (e (7-2 x)-2 x+e \log (x)) \, dx}{e}\\ &=-\frac {1}{4} (7-2 x)^2-\frac {x^2}{e}+\int \log (x) \, dx\\ &=-\frac {1}{4} (7-2 x)^2-x-\frac {x^2}{e}+x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.27 \begin {gather*} 6 x-\frac {(1+e) x^2}{e}+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(34\) vs.
\(2(16)=32\).
time = 0.06, size = 35, normalized size = 2.33
method | result | size |
risch | \(-x^{2}+x \ln \left (x \right )+6 x -x^{2} {\mathrm e}^{-1}\) | \(21\) |
norman | \(x \ln \left (x \right )+6 x -\left (1+{\mathrm e}\right ) {\mathrm e}^{-1} x^{2}\) | \(22\) |
default | \({\mathrm e}^{-1} \left ({\mathrm e} \left (-x^{2}+7 x \right )+x \,{\mathrm e} \ln \left (x \right )-x \,{\mathrm e}-x^{2}\right )\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 30 vs.
\(2 (14) = 28\).
time = 0.27, size = 30, normalized size = 2.00 \begin {gather*} -{\left (x^{2} + {\left (x^{2} - 7 \, x\right )} e - {\left (x \log \left (x\right ) - x\right )} e\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 26, normalized size = 1.73 \begin {gather*} {\left (x e \log \left (x\right ) - x^{2} - {\left (x^{2} - 6 \, x\right )} e\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 20, normalized size = 1.33 \begin {gather*} \frac {x^{2} \left (- e - 1\right )}{e} + x \log {\left (x \right )} + 6 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. 30 vs.
\(2 (14) = 28\).
time = 0.42, size = 30, normalized size = 2.00 \begin {gather*} -{\left (x^{2} + {\left (x^{2} - 7 \, x\right )} e - {\left (x \log \left (x\right ) - x\right )} e\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.53, size = 14, normalized size = 0.93 \begin {gather*} -x\,\left (x-\ln \left (x\right )+x\,{\mathrm {e}}^{-1}-6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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