Optimal. Leaf size=10 \[ \frac {2 \left (e^3+x\right )}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} \frac {2 e^3}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 e^3\right ) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {2 e^3}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 0.80 \begin {gather*} \frac {2 e^3}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 7, normalized size = 0.70 \begin {gather*} \frac {2 \, e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 7, normalized size = 0.70 \begin {gather*} \frac {2 \, e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 0.80
method | result | size |
gosper | \(\frac {2 \,{\mathrm e}^{3}}{x}\) | \(8\) |
default | \(\frac {2 \,{\mathrm e}^{3}}{x}\) | \(8\) |
norman | \(\frac {2 \,{\mathrm e}^{3}}{x}\) | \(8\) |
risch | \(\frac {2 \,{\mathrm e}^{3}}{x}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 7, normalized size = 0.70 \begin {gather*} \frac {2 \, e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 7, normalized size = 0.70 \begin {gather*} \frac {2\,{\mathrm {e}}^3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 5, normalized size = 0.50 \begin {gather*} \frac {2 e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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