Optimal. Leaf size=19 \[ 8 \left (e^{e^6}+4 x^2\right ) \log (-e+x) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(42\) vs. \(2(19)=38\).
time = 0.10, antiderivative size = 42, normalized size of antiderivative = 2.21, number of steps
used = 7, number of rules used = 4, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {6874, 711,
2442, 45} \begin {gather*} 32 x^2 \log (x-e)+8 \left (4 e^2+e^{e^6}\right ) \log (e-x)-32 e^2 \log (e-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 711
Rule 2442
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {8 \left (e^{e^6}+4 x^2\right )}{e-x}+64 x \log (-e+x)\right ) \, dx\\ &=-\left (8 \int \frac {e^{e^6}+4 x^2}{e-x} \, dx\right )+64 \int x \log (-e+x) \, dx\\ &=32 x^2 \log (-e+x)-8 \int \left (-4 e+\frac {4 e^2+e^{e^6}}{e-x}-4 x\right ) \, dx-32 \int \frac {x^2}{-e+x} \, dx\\ &=32 e x+16 x^2+8 \left (4 e^2+e^{e^6}\right ) \log (e-x)+32 x^2 \log (-e+x)-32 \int \left (e-\frac {e^2}{e-x}+x\right ) \, dx\\ &=-32 e^2 \log (e-x)+8 \left (4 e^2+e^{e^6}\right ) \log (e-x)+32 x^2 \log (-e+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 27, normalized size = 1.42 \begin {gather*} -8 \left (-e^{e^6} \log (e-x)-4 x^2 \log (-e+x)\right ) \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. \(79\) vs.
\(2(20)=40\).
time = 1.11, size = 80, normalized size = 4.21
method | result | size |
risch | \(32 \ln \left (x -{\mathrm e}\right ) x^{2}+8 \,{\mathrm e}^{{\mathrm e}^{6}} \ln \left (x -{\mathrm e}\right )\) | \(26\) |
norman | \(32 \ln \left (x -{\mathrm e}\right ) x^{2}+8 \,{\mathrm e}^{{\mathrm e}^{6}} \ln \left (x -{\mathrm e}\right )\) | \(28\) |
derivativedivides | \(64 \,{\mathrm e} \left (\left (x -{\mathrm e}\right ) \ln \left (x -{\mathrm e}\right )-x +{\mathrm e}\right )+32 \ln \left (x -{\mathrm e}\right ) \left (x -{\mathrm e}\right )^{2}+32 \,{\mathrm e}^{2} \ln \left (x -{\mathrm e}\right )+64 \,{\mathrm e} \left (x -{\mathrm e}\right )+8 \,{\mathrm e}^{{\mathrm e}^{6}} \ln \left (x -{\mathrm e}\right )\) | \(80\) |
default | \(64 \,{\mathrm e} \left (\left (x -{\mathrm e}\right ) \ln \left (x -{\mathrm e}\right )-x +{\mathrm e}\right )+32 \ln \left (x -{\mathrm e}\right ) \left (x -{\mathrm e}\right )^{2}+32 \,{\mathrm e}^{2} \ln \left (x -{\mathrm e}\right )+64 \,{\mathrm e} \left (x -{\mathrm e}\right )+8 \,{\mathrm e}^{{\mathrm e}^{6}} \ln \left (x -{\mathrm e}\right )\) | \(80\) |
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. 125 vs.
\(2 (18) = 36\).
time = 0.28, size = 125, normalized size = 6.58 \begin {gather*} -64 \, {\left (e \log \left (x - e\right ) + x\right )} e \log \left (x - e\right ) - 32 \, e^{2} \log \left (x - e\right )^{2} + 32 \, {\left (e \log \left (x - e\right )^{2} + 2 \, e \log \left (x - e\right ) + 2 \, x\right )} e - 64 \, x e + 32 \, {\left (x^{2} + 2 \, x e + 2 \, e^{2} \log \left (x - e\right )\right )} \log \left (x - e\right ) - 64 \, e^{2} \log \left (x - e\right ) + 8 \, e^{\left (e^{6}\right )} \log \left (x - e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 18, normalized size = 0.95 \begin {gather*} 8 \, {\left (4 \, x^{2} + e^{\left (e^{6}\right )}\right )} \log \left (x - e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 1.26 \begin {gather*} 32 x^{2} \log {\left (x - e \right )} + 8 e^{e^{6}} \log {\left (x - e \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 25, normalized size = 1.32 \begin {gather*} 32 \, x^{2} \log \left (x - e\right ) + 8 \, e^{\left (e^{6}\right )} \log \left (x - e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.40, size = 18, normalized size = 0.95 \begin {gather*} 8\,\ln \left (x-\mathrm {e}\right )\,\left (4\,x^2+{\mathrm {e}}^{{\mathrm {e}}^6}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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