Optimal. Leaf size=20 \[ 10-x-(3+x)^2+\log \left (e^{8/3}+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {1850} \begin {gather*} -x^2-7 x+\log \left (x+e^{8/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-7-2 x+\frac {1}{e^{8/3}+x}\right ) \, dx\\ &=-7 x-x^2+\log \left (e^{8/3}+x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 27, normalized size = 1.35 \begin {gather*} -7 e^{8/3}+e^{16/3}-x (7+x)+\log \left (e^{8/3}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 14, normalized size = 0.70 \begin {gather*} -x^{2} - 7 \, x + \log \left (x + e^{\frac {8}{3}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} - 7 \, x + \log \left ({\left | x + e^{\frac {8}{3}} \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.38, size = 15, normalized size = 0.75
method | result | size |
default | \(-x^{2}-7 x +\ln \left ({\mathrm e}^{\frac {8}{3}}+x \right )\) | \(15\) |
norman | \(-x^{2}-7 x +\ln \left ({\mathrm e}^{\frac {8}{3}}+x \right )\) | \(15\) |
risch | \(-x^{2}-7 x +\ln \left ({\mathrm e}^{\frac {8}{3}}+x \right )\) | \(15\) |
meijerg | \(-7 \,{\mathrm e}^{\frac {8}{3}} \ln \left (1+x \,{\mathrm e}^{-\frac {8}{3}}\right )-2 \,{\mathrm e}^{\frac {16}{3}} \left (-\frac {x \,{\mathrm e}^{-\frac {8}{3}} \left (-3 x \,{\mathrm e}^{-\frac {8}{3}}+6\right )}{6}+\ln \left (1+x \,{\mathrm e}^{-\frac {8}{3}}\right )\right )+{\mathrm e}^{\frac {8}{3}} \left (-2 \,{\mathrm e}^{\frac {8}{3}}-7\right ) \left (x \,{\mathrm e}^{-\frac {8}{3}}-\ln \left (1+x \,{\mathrm e}^{-\frac {8}{3}}\right )\right )+\ln \left (1+x \,{\mathrm e}^{-\frac {8}{3}}\right )\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 14, normalized size = 0.70 \begin {gather*} -x^{2} - 7 \, x + \log \left (x + e^{\frac {8}{3}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 14, normalized size = 0.70 \begin {gather*} \ln \left (x+{\mathrm {e}}^{8/3}\right )-7\,x-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.70 \begin {gather*} - x^{2} - 7 x + \log {\left (x + e^{\frac {8}{3}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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