Optimal. Leaf size=9 \[ \frac {-4+e^3}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.33, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 30} \begin {gather*} -\frac {4-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 (4-e^3\right ) \int \frac {1}{x^2} \, dx\\ &=-\frac {4-e^3}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.33 \begin {gather*} -\frac {4-e^3}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{3} - 4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{3} - 4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 9, normalized size = 1.00
method | result | size |
gosper | \(\frac {{\mathrm e}^{3}-4}{x}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{3}-4}{x}\) | \(9\) |
default | \(-\frac {4-{\mathrm e}^{3}}{x}\) | \(12\) |
risch | \(-\frac {4}{x}+\frac {{\mathrm e}^{3}}{x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{3} - 4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.38, size = 8, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^3-4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 7, normalized size = 0.78 \begin {gather*} - \frac {4 - e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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