Optimal. Leaf size=14 \[ 17-\left (\frac {3}{e^2}+\frac {1}{x^2}\right ) x \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14} \begin {gather*} -\frac {3 x}{e^2}-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^2-3 x^2}{x^2} \, dx}{e^2}\\ &=\frac {\int \left (-3+\frac {e^2}{x^2}\right ) \, dx}{e^2}\\ &=-\frac {1}{x}-\frac {3 x}{e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{x}-\frac {3 x}{e^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 15, normalized size = 1.07 \begin {gather*} -\frac {{\left (3 \, x^{2} + e^{2}\right )} e^{\left (-2\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 1.00 \begin {gather*} -{\left (3 \, x + \frac {e^{2}}{x}\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 = 12, normalized size = 0.86
method | result | size |
risch | \(-3 x \,{\mathrm e}^{-2}-\frac {1}{x}\) | \(12\) |
norman | \(\frac {-1-3 x^{2} {\mathrm e}^{-2}}{x}\) | \(16\) |
default | \({\mathrm e}^{-2} \left (-3 x -\frac {{\mathrm e}^{2}}{x}\right )\) | \(17\) |
gosper | \(-\frac {\left (3 x^{2}+{\mathrm e}^{2}\right ) {\mathrm e}^{-2}}{x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 14, normalized size = 1.00 \begin {gather*} -{\left (3 \, x + \frac {e^{2}}{x}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 0.79 \begin {gather*} -3\,x\,{\mathrm {e}}^{-2}-\frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 0.86 \begin {gather*} \frac {- 3 x - \frac {e^{2}}{x}}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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