Optimal. Leaf size=16 \[ 8-\frac {11 x}{5}-5 \left (-3+\frac {x}{e^2}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {8} \begin {gather*} -\frac {\left (25+11 e^2\right ) x}{5 e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\left (25+11 e^2\right ) x}{5 e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.75 \begin {gather*} -\frac {11 x}{5}-\frac {5 x}{e^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 13, normalized size = 0.81 \begin {gather*} -\frac {1}{5} \, {\left (11 \, x e^{2} + 25 \, x\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 11, normalized size = 0.69 \begin {gather*} -\frac {1}{5} \, x {\left (11 \, e^{2} + 25\right )} e^{\left (-2\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 = 0.88
method | result | size |
default | \(\frac {\left (-11 \,{\mathrm e}^{2}-25\right ) {\mathrm e}^{-2} x}{5}\) | \(14\) |
norman | \(-\frac {{\mathrm e}^{-2} \left (11 \,{\mathrm e}^{2}+25\right ) x}{5}\) | \(14\) |
risch | \(-\frac {11 \,{\mathrm e}^{-2} x \,{\mathrm e}^{2}}{5}-5 \,{\mathrm e}^{-2} x\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.89, size = 11, normalized size = 0.69 \begin {gather*} -\frac {1}{5} \, x {\left (11 \, e^{2} + 25\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 11, normalized size = 0.69 \begin {gather*} -x\,{\mathrm {e}}^{-2}\,\left (\frac {11\,{\mathrm {e}}^2}{5}+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.04, size = 14, normalized size = 0.88 \begin {gather*} \frac {x \left (- \frac {11 e^{2}}{5} - 5\right )}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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