Optimal. Leaf size=15 \[ -5+2 x+\frac {3 x^2 \log (9)}{e^4} \]
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Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.47, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {9}
\begin {gather*} \frac {\left (3 x \log (9)+e^4\right )^2}{3 e^4 \log (9)} \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\left (e^4+3 x \log (9)\right )^2}{3 e^4 \log (9)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} 2 x+\frac {3 x^2 \log (9)}{e^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 21, normalized size = 1.40
method | result | size |
risch | \(6 \ln \left (3\right ) x^{2} {\mathrm e}^{-4}+2 x\) | \(14\) |
gosper | \(2 x \left ({\mathrm e}^{4}+3 x \ln \left (3\right )\right ) {\mathrm e}^{-4}\) | \(18\) |
default | \({\mathrm e}^{-4} \left (6 x^{2} \ln \left (3\right )+2 x \,{\mathrm e}^{4}\right )\) | \(21\) |
norman | \(\left (2 \,{\mathrm e}^{2} x +6 \,{\mathrm e}^{-2} \ln \left (3\right ) x^{2}\right ) {\mathrm e}^{-2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 16, normalized size = 1.07 \begin {gather*} 2 \, {\left (3 \, x^{2} \log \left (3\right ) + x e^{4}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 1.07 \begin {gather*} 2 \, {\left (3 \, x^{2} \log \left (3\right ) + x e^{4}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 14, normalized size = 0.93 \begin {gather*} \frac {6 x^{2} \log {\left (3 \right )}}{e^{4}} + 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 16, normalized size = 1.07 \begin {gather*} 2 \, {\left (3 \, x^{2} \log \left (3\right ) + x e^{4}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 18, normalized size = 1.20 \begin {gather*} \frac {{\mathrm {e}}^{-4}\,{\left ({\mathrm {e}}^4+6\,x\,\ln \left (3\right )\right )}^2}{6\,\ln \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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