Optimal. Leaf size=10 \[ -\frac {e^{-x}}{x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2228}
\begin {gather*} -\frac {e^{-x}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2228
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=-\frac {e^{-x}}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 10, normalized size = 1.00 \begin {gather*} -\frac {e^{-x}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 10, normalized size = 1.00
method | result | size |
gosper | \(-\frac {{\mathrm e}^{-x}}{x^{2}}\) | \(10\) |
derivativedivides | \(-\frac {{\mathrm e}^{-x}}{x^{2}}\) | \(10\) |
default | \(-\frac {{\mathrm e}^{-x}}{x^{2}}\) | \(10\) |
norman | \(-\frac {{\mathrm e}^{-x}}{x^{2}}\) | \(10\) |
risch | \(-\frac {{\mathrm e}^{-x}}{x^{2}}\) | \(10\) |
parallelrisch | \(-\frac {{\mathrm e}^{-x}}{x^{2}}\) | \(10\) |
meijerg | \(-\frac {1}{x^{2}}+\frac {1}{x}-\frac {1}{2}+\frac {9 x^{2}-12 x +6}{6 x^{2}}-\frac {\left (3-3 x \right ) {\mathrm e}^{-x}}{3 x^{2}}+\frac {-2 x +2}{2 x}-\frac {{\mathrm e}^{-x}}{x}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.35, size = 11, normalized size = 1.10 \begin {gather*} -\Gamma \left (-1, x\right ) - 2 \, \Gamma \left (-2, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.55, size = 9, normalized size = 0.90 \begin {gather*} -\frac {e^{\left (-x\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.80 \begin {gather*} - \frac {e^{- x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.48, size = 9, normalized size = 0.90 \begin {gather*} -\frac {e^{\left (-x\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 9, normalized size = 0.90 \begin {gather*} -\frac {{\mathrm {e}}^{-x}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 10, normalized size = 1.00 \begin {gather*} -\frac {{\mathrm e}^{x} \left (x +4\right )}{x^{2}} \end {gather*}
Warning: Unable to verify antiderivative.
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