Optimal. Leaf size=16 \[ x+\log \left (\frac {e^4}{144}+e^{2 x}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {2282, 72} \begin {gather*} x+\log \left (144 e^{2 x}+e^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 72
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {e^4+432 x}{x \left (e^4+144 x\right )} \, dx,x,e^{2 x}\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {1}{x}+\frac {288}{e^4+144 x}\right ) \, dx,x,e^{2 x}\right )\\ &=x+\log \left (e^4+144 e^{2 x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.88 \begin {gather*} x+\log \left (e^4+144 e^{2 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 12, normalized size = 0.75 \begin {gather*} x + \log \left (e^{4} + 144 \, e^{\left (2 \, x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 12, normalized size = 0.75 \begin {gather*} x + \log \left (e^{4} + 144 \, e^{\left (2 \, x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 0.81
method | result | size |
risch | \(x +\ln \left (\frac {{\mathrm e}^{4}}{144}+{\mathrm e}^{2 x}\right )\) | \(13\) |
norman | \(x +\ln \left (144 \,{\mathrm e}^{2 x}+{\mathrm e}^{4}\right )\) | \(15\) |
derivativedivides | \(\ln \left (144 \,{\mathrm e}^{2 x}+{\mathrm e}^{4}\right )+\frac {\ln \left ({\mathrm e}^{2 x}\right )}{2}\) | \(19\) |
default | \(\ln \left (144 \,{\mathrm e}^{2 x}+{\mathrm e}^{4}\right )+\frac {\ln \left ({\mathrm e}^{2 x}\right )}{2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 12, normalized size = 0.75 \begin {gather*} x + \log \left (e^{4} + 144 \, e^{\left (2 \, x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.54, size = 12, normalized size = 0.75 \begin {gather*} x+\ln \left (144\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.75 \begin {gather*} x + \log {\left (e^{2 x} + \frac {e^{4}}{144} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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