Optimal. Leaf size=17 \[ -1+e^x-\left (2-x+x^2\right ) \log (5) \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2225}
\begin {gather*} e^x-\frac {1}{4} (1-2 x)^2 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{4} (1-2 x)^2 \log (5)+\int e^x \, dx\\ &=e^x-\frac {1}{4} (1-2 x)^2 \log (5)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.88 \begin {gather*} e^x+x \log (5)-x^2 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 15, normalized size = 0.88
method | result | size |
default | \(-x^{2} \ln \left (5\right )+x \ln \left (5\right )+{\mathrm e}^{x}\) | \(15\) |
norman | \(-x^{2} \ln \left (5\right )+x \ln \left (5\right )+{\mathrm e}^{x}\) | \(15\) |
risch | \(-x^{2} \ln \left (5\right )+x \ln \left (5\right )+{\mathrm e}^{x}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.82 \begin {gather*} -{\left (x^{2} - x\right )} \log \left (5\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} -{\left (x^{2} - x\right )} \log \left (5\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.82 \begin {gather*} - x^{2} \log {\left (5 \right )} + x \log {\left (5 \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 = 14, normalized size = 0.82 \begin {gather*} -{\left (x^{2} - x\right )} \log \left (5\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 14, normalized size = 0.82 \begin {gather*} {\mathrm {e}}^x+x\,\ln \left (5\right )-x^2\,\ln \left (5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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