Optimal. Leaf size=16 \[ 14+e^x+x (\log (2)+\log (8-x)) \]
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Rubi [A]
time = 0.06, antiderivative size = 29, normalized size of antiderivative = 1.81, number of steps
used = 7, number of rules used = 5, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.161, Rules used = {6820, 2225, 45,
2436, 2332} \begin {gather*} e^x+x \log (2)-(8-x) \log (8-x)+8 \log (8-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 2225
Rule 2332
Rule 2436
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x+\frac {x}{-8+x}+\log (2)+\log (8-x)\right ) \, dx\\ &=x \log (2)+\int e^x \, dx+\int \frac {x}{-8+x} \, dx+\int \log (8-x) \, dx\\ &=e^x+x \log (2)+\int \left (1+\frac {8}{-8+x}\right ) \, dx-\text {Subst}(\int \log (x) \, dx,x,8-x)\\ &=e^x+x \log (2)+8 \log (8-x)-(8-x) \log (8-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 27, normalized size = 1.69 \begin {gather*} e^x+x \log (2)-(8-x) \log (8-x)+8 \log (-8+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.93, size = 28, normalized size = 1.75
method | result | size |
norman | \(x \ln \left (2\right )+\ln \left (8-x \right ) x +{\mathrm e}^{x}\) | \(16\) |
risch | \(x \ln \left (2\right )+\ln \left (8-x \right ) x +{\mathrm e}^{x}\) | \(16\) |
default | \(x \ln \left (2\right )+8 \ln \left (-8+x \right )+{\mathrm e}^{x}-\ln \left (8-x \right ) \left (8-x \right )+8\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 15, normalized size = 0.94 \begin {gather*} x \log \left (2\right ) + x \log \left (-x + 8\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 14, normalized size = 0.88 \begin {gather*} x \log {\left (8 - x \right )} + x \log {\left (2 \right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 0.94 \begin {gather*} x \log \left (2\right ) + x \log \left (-x + 8\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.13, size = 11, normalized size = 0.69 \begin {gather*} {\mathrm {e}}^x+x\,\ln \left (16-2\,x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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