Optimal. Leaf size=23 \[ -1+x+\frac {1}{4} \left (5+x^2\right )-\frac {1}{2} x \log \left (5 e^x\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps
used = 4, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {12, 2188, 30}
\begin {gather*} x-\frac {1}{4} \log ^2\left (5 e^x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2188
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (2-\log \left (5 e^x\right )\right ) \, dx\\ &=x-\frac {1}{2} \int \log \left (5 e^x\right ) \, dx\\ &=x-\frac {1}{2} \text {Subst}\left (\int x \, dx,x,\log \left (5 e^x\right )\right )\\ &=x-\frac {1}{4} \log ^2\left (5 e^x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.61 \begin {gather*} x-\frac {1}{4} \log ^2\left (5 e^x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.09, size = 12, normalized size = 0.52
method | result | size |
default | \(x -\frac {\ln \left (5 \,{\mathrm e}^{x}\right )^{2}}{4}\) | \(12\) |
derivativedivides | \(\ln \left (5 \,{\mathrm e}^{x}\right )-\frac {\ln \left (5 \,{\mathrm e}^{x}\right )^{2}}{4}\) | \(16\) |
norman | \(\ln \left (5 \,{\mathrm e}^{x}\right )-\frac {\ln \left (5 \,{\mathrm e}^{x}\right )^{2}}{4}\) | \(16\) |
risch | \(-\frac {x \ln \left ({\mathrm e}^{x}\right )}{2}+\frac {x \left (x -2 \ln \left (5\right )\right )}{4}+x\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 11, normalized size = 0.48 \begin {gather*} -\frac {1}{4} \, \log \left (5 \, e^{x}\right )^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 12, normalized size = 0.52 \begin {gather*} -\frac {1}{4} \, x^{2} - \frac {1}{2} \, x \log \left (5\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.52 \begin {gather*} - \frac {x^{2}}{4} + x \left (1 - \frac {\log {\left (5 \right )}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 12, normalized size = 0.52 \begin {gather*} -\frac {1}{4} \, x^{2} - \frac {1}{2} \, x \log \left (5\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.44, size = 8, normalized size = 0.35 \begin {gather*} -\frac {x\,\left (x+\ln \left (25\right )-4\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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