Optimal. Leaf size=19 \[ 2+x+e^8 \log \left ((3+x) \left (-e^x+x\right )\right ) \]
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Rubi [F] time = 0.48, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^8 (-3-2 x)-3 x-x^2+e^x \left (3+x+e^8 (4+x)\right )}{-3 x-x^2+e^x (3+x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^8 (-3-2 x)-3 x-x^2+e^x \left (3+x+e^8 (4+x)\right )}{\left (e^x-x\right ) (3+x)} \, dx\\ &=\int \left (\frac {e^8 (-1+x)}{e^x-x}+\frac {3+4 e^8+\left (1+e^8\right ) x}{3+x}\right ) \, dx\\ &=e^8 \int \frac {-1+x}{e^x-x} \, dx+\int \frac {3+4 e^8+\left (1+e^8\right ) x}{3+x} \, dx\\ &=e^8 \int \left (-\frac {1}{e^x-x}+\frac {x}{e^x-x}\right ) \, dx+\int \left (1+e^8+\frac {e^8}{3+x}\right ) \, dx\\ &=\left (1+e^8\right ) x+e^8 \log (3+x)-e^8 \int \frac {1}{e^x-x} \, dx+e^8 \int \frac {x}{e^x-x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 22, normalized size = 1.16 \begin {gather*} x+e^8 \log \left (e^x-x\right )+e^8 \log (3+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 19, normalized size = 1.00 \begin {gather*} e^{8} \log \left (x + 3\right ) + e^{8} \log \left (-x + e^{x}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 19, normalized size = 1.00 \begin {gather*} e^{8} \log \left (x + 3\right ) + e^{8} \log \left (-x + e^{x}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 1.05
method | result | size |
norman | \(x +{\mathrm e}^{8} \ln \left (3+x \right )+{\mathrm e}^{8} \ln \left (x -{\mathrm e}^{x}\right )\) | \(20\) |
risch | \(x +{\mathrm e}^{8} \ln \left (3+x \right )+{\mathrm e}^{8} \ln \left ({\mathrm e}^{x}-x \right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 19, normalized size = 1.00 \begin {gather*} e^{8} \log \left (x + 3\right ) + e^{8} \log \left (-x + e^{x}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 19, normalized size = 1.00 \begin {gather*} x+\ln \left (x+3\right )\,{\mathrm {e}}^8+{\mathrm {e}}^8\,\ln \left (x-{\mathrm {e}}^x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 19, normalized size = 1.00 \begin {gather*} x + e^{8} \log {\left (- x + e^{x} \right )} + e^{8} \log {\left (x + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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