Optimal. Leaf size=19 \[ \frac {2 (3-x) x \left (7+\frac {1}{e^8}+x\right )}{-3+x} \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12}
\begin {gather*} -\frac {1}{2} (2 x+7)^2-\frac {2 x}{e^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-2+e^8 (-14-4 x)\right ) \, dx}{e^8}\\ &=-\frac {2 x}{e^8}-\frac {1}{2} (7+2 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} -14 x-\frac {2 x}{e^8}-2 x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 26, normalized size = 1.37
method | result | size |
risch | \(-2 x^{2}-14 x -2 \,{\mathrm e}^{-8} x\) | \(15\) |
gosper | \(-2 x \left (x \,{\mathrm e}^{8}+7 \,{\mathrm e}^{8}+1\right ) {\mathrm e}^{-8}\) | \(22\) |
default | \({\mathrm e}^{-8} \left (-2 x^{2} {\mathrm e}^{8}-14 x \,{\mathrm e}^{8}-2 x \right )\) | \(26\) |
norman | \(\left (-2 x^{2} {\mathrm e}^{4}-2 \left (7 \,{\mathrm e}^{8}+1\right ) {\mathrm e}^{-4} x \right ) {\mathrm e}^{-4}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 16, normalized size = 0.84 \begin {gather*} -2 \, {\left ({\left (x^{2} + 7 \, x\right )} e^{8} + x\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 16, normalized size = 0.84 \begin {gather*} -2 \, {\left ({\left (x^{2} + 7 \, x\right )} e^{8} + x\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 0.89 \begin {gather*} - 2 x^{2} + \frac {x \left (- 14 e^{8} - 2\right )}{e^{8}} \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 = 0.84 \begin {gather*} -2 \, {\left ({\left (x^{2} + 7 \, x\right )} e^{8} + x\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.49, size = 16, normalized size = 0.84 \begin {gather*} -\frac {{\mathrm {e}}^{-16}\,{\left ({\mathrm {e}}^8\,\left (4\,x+14\right )+2\right )}^2}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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