Optimal. Leaf size=25 \[ \frac {1+e^3-e^5-\frac {x+x^3}{x}}{\log (2)} \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.36, number of steps
used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30}
\begin {gather*} -\frac {x^2}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {2 \int x \, dx}{\log (2)}\\ &=-\frac {x^2}{\log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^2}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 10, normalized size = 0.40
method | result | size |
gosper | \(-\frac {x^{2}}{\ln \left (2\right )}\) | \(10\) |
default | \(-\frac {x^{2}}{\ln \left (2\right )}\) | \(10\) |
norman | \(-\frac {x^{2}}{\ln \left (2\right )}\) | \(10\) |
risch | \(-\frac {x^{2}}{\ln \left (2\right )}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^{2}}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^{2}}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 7, normalized size = 0.28 \begin {gather*} - \frac {x^{2}}{\log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^{2}}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^2}{\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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