Optimal. Leaf size=17 \[ -2-\frac {3 \left (e^3-x\right )}{e x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.24, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 37} \begin {gather*} -\frac {3 \left (2 e^3-x\right )^2}{4 e^4 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 37
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {6 e^3-3 x}{x^3} \, dx}{e}\\ &=-\frac {3 \left (2 e^3-x\right )^2}{4 e^4 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.06 \begin {gather*} \frac {-\frac {3 e^3}{x^2}+\frac {3}{x}}{e} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 13, normalized size = 0.76 \begin {gather*} \frac {3 \, {\left (x - e^{3}\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 13, normalized size = 0.76 \begin {gather*} \frac {3 \, {\left (x - e^{3}\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 15, normalized size = 0.88
method | result | size |
risch | \(\frac {{\mathrm e}^{-1} \left (-3 \,{\mathrm e}^{3}+3 x \right )}{x^{2}}\) | \(15\) |
gosper | \(-\frac {3 \left (-x +{\mathrm e}^{3}\right ) {\mathrm e}^{-1}}{x^{2}}\) | \(16\) |
default | \(3 \,{\mathrm e}^{-1} \left (\frac {1}{x}-\frac {{\mathrm e}^{3}}{x^{2}}\right )\) | \(18\) |
norman | \(\frac {3 \,{\mathrm e}^{-1} x -3 \,{\mathrm e}^{-1} {\mathrm e}^{3}}{x^{2}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 13, normalized size = 0.76 \begin {gather*} \frac {3 \, {\left (x - e^{3}\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.46, size = 14, normalized size = 0.82 \begin {gather*} \frac {{\mathrm {e}}^{-1}\,\left (3\,x-3\,{\mathrm {e}}^3\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.88 \begin {gather*} - \frac {- 3 x + 3 e^{3}}{e x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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