Optimal. Leaf size=12 \[ 4 \left (-\frac {18}{e^3}+e^2\right ) x \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} -\frac {4 \left (18-e^5\right ) x}{e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {4 \left (18-e^5\right ) x}{e^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.08 \begin {gather*} -\frac {72 x}{e^3}+4 e^2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 12, normalized size = 1.00 \begin {gather*} 4 \, {\left (x e^{5} - 18 \, x\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 9, normalized size = 0.75 \begin {gather*} 4 \, x {\left (e^{5} - 18\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 1.17
method | result | size |
risch | \(4 \,{\mathrm e}^{-3} x \,{\mathrm e}^{5}-72 \,{\mathrm e}^{-3} x\) | \(14\) |
default | \(\left (4 \,{\mathrm e}^{2} {\mathrm e}^{3}-72\right ) {\mathrm e}^{-3} x\) | \(15\) |
norman | \(4 \left ({\mathrm e}^{2} {\mathrm e}^{3}-18\right ) {\mathrm e}^{-3} x\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 9, normalized size = 0.75 \begin {gather*} 4 \, x {\left (e^{5} - 18\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} x\,{\mathrm {e}}^{-3}\,\left (4\,{\mathrm {e}}^5-72\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.04, size = 10, normalized size = 0.83 \begin {gather*} \frac {x \left (-72 + 4 e^{5}\right )}{e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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