Optimal. Leaf size=20 \[ \frac {e^4}{5-x+x^2+\log \left (2 x^2\right )} \]
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Rubi [A]
time = 0.11, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {12, 6820, 6818}
\begin {gather*} \frac {e^4}{x^2+\log \left (2 x^2\right )-x+5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^4 \int \frac {-2+x-2 x^2}{25 x-10 x^2+11 x^3-2 x^4+x^5+\left (10 x-2 x^2+2 x^3\right ) \log \left (2 x^2\right )+x \log ^2\left (2 x^2\right )} \, dx\\ &=e^4 \int \frac {-2+x-2 x^2}{x \left (5-x+x^2+\log \left (2 x^2\right )\right )^2} \, dx\\ &=\frac {e^4}{5-x+x^2+\log \left (2 x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {e^4}{5-x+x^2+\log \left (2 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.82, size = 20, normalized size = 1.00
method | result | size |
norman | \(\frac {{\mathrm e}^{4}}{x^{2}-x +5+\ln \left (2 x^{2}\right )}\) | \(20\) |
risch | \(\frac {{\mathrm e}^{4}}{x^{2}-x +5+\ln \left (2 x^{2}\right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.49, size = 19, normalized size = 0.95 \begin {gather*} \frac {e^{4}}{x^{2} - x + \log \left (2\right ) + 2 \, \log \left (x\right ) + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 19, normalized size = 0.95 \begin {gather*} \frac {e^{4}}{x^{2} - x + \log \left (2 \, x^{2}\right ) + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.75 \begin {gather*} \frac {e^{4}}{x^{2} - x + \log {\left (2 x^{2} \right )} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 19, normalized size = 0.95 \begin {gather*} \frac {e^{4}}{x^{2} - x + \log \left (2 \, x^{2}\right ) + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.34, size = 54, normalized size = 2.70 \begin {gather*} -\frac {x^2\,\left (\frac {{\mathrm {e}}^4\,\ln \left (2\,x^2\right )}{5}-\frac {{\mathrm {e}}^4\,\left (\ln \left (2\,x^2\right )+5\right )}{5}\right )}{5\,x^2-x^3+x^4+x^2\,\ln \left (2\,x^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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