Optimal. Leaf size=27 \[ e^x+8 x \left (e^3+x+x \left (-5+\frac {2+x}{x}\right )\right )-\log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 21, normalized size of antiderivative = 0.78, number of steps
used = 6, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {6, 14, 2225}
\begin {gather*} -24 x^2+8 \left (2+e^3\right ) x+e^x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 14
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+e^x x+\left (16+8 e^3\right ) x-48 x^2}{x} \, dx\\ &=\int \left (e^x+\frac {-1+8 \left (2+e^3\right ) x-48 x^2}{x}\right ) \, dx\\ &=\int e^x \, dx+\int \frac {-1+8 \left (2+e^3\right ) x-48 x^2}{x} \, dx\\ &=e^x+\int \left (8 \left (2+e^3\right )-\frac {1}{x}-48 x\right ) \, dx\\ &=e^x+8 \left (2+e^3\right ) x-24 x^2-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.81 \begin {gather*} e^x+16 x+8 e^3 x-24 x^2-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 21, normalized size = 0.78
method | result | size |
default | \(-24 x^{2}+16 x -\ln \left (x \right )+8 x \,{\mathrm e}^{3}+{\mathrm e}^{x}\) | \(21\) |
norman | \(\left (8 \,{\mathrm e}^{3}+16\right ) x -24 x^{2}+{\mathrm e}^{x}-\ln \left (x \right )\) | \(21\) |
risch | \(-24 x^{2}+16 x -\ln \left (x \right )+8 x \,{\mathrm e}^{3}+{\mathrm e}^{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 20, normalized size = 0.74 \begin {gather*} -24 \, x^{2} + 8 \, x e^{3} + 16 \, x + e^{x} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 20, normalized size = 0.74 \begin {gather*} -24 \, x^{2} + 8 \, x e^{3} + 16 \, x + e^{x} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 20, normalized size = 0.74 \begin {gather*} - 24 x^{2} - x \left (- 8 e^{3} - 16\right ) + e^{x} - \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 20, normalized size = 0.74 \begin {gather*} -24 \, x^{2} + 8 \, x e^{3} + 16 \, x + e^{x} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 20, normalized size = 0.74 \begin {gather*} {\mathrm {e}}^x-\ln \left (x\right )-24\,x^2+x\,\left (8\,{\mathrm {e}}^3+16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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