Optimal. Leaf size=34 \[ e^{e^3}-x+\frac {1}{2} \left (x-\log \left (\frac {4}{e^2-x+5 x^2}\right )\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 23, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1657, 628} \begin {gather*} \frac {1}{2} \log \left (5 x^2-x+e^2\right )-\frac {x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rule 1657
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{2}-\frac {1-10 x}{2 e^2-2 x+10 x^2}\right ) \, dx\\ &=-\frac {x}{2}-\int \frac {1-10 x}{2 e^2-2 x+10 x^2} \, dx\\ &=-\frac {x}{2}+\frac {1}{2} \log \left (e^2-x+5 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.62 \begin {gather*} \frac {1}{2} \left (-x+\log \left (e^2-x+5 x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 18, normalized size = 0.53 \begin {gather*} -\frac {1}{2} \, x + \frac {1}{2} \, \log \left (5 \, x^{2} - x + e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 18, normalized size = 0.53 \begin {gather*} -\frac {1}{2} \, x + \frac {1}{2} \, \log \left (5 \, x^{2} - x + e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.52, size = 19, normalized size = 0.56
method | result | size |
default | \(-\frac {x}{2}+\frac {\ln \left (5 x^{2}-x +{\mathrm e}^{2}\right )}{2}\) | \(19\) |
risch | \(-\frac {x}{2}+\frac {\ln \left (5 x^{2}-x +{\mathrm e}^{2}\right )}{2}\) | \(19\) |
norman | \(-\frac {x}{2}+\frac {\ln \left (2 \,{\mathrm e}^{2}+10 x^{2}-2 x \right )}{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 18, normalized size = 0.53 \begin {gather*} -\frac {1}{2} \, x + \frac {1}{2} \, \log \left (5 \, x^{2} - x + e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.61, size = 18, normalized size = 0.53 \begin {gather*} \frac {\ln \left (5\,x^2-x+{\mathrm {e}}^2\right )}{2}-\frac {x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.44 \begin {gather*} - \frac {x}{2} + \frac {\log {\left (5 x^{2} - x + e^{2} \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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