Optimal. Leaf size=15 \[ -2-\frac {e^5}{x}-x^2 \]
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Rubi [A]
time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14}
\begin {gather*} -x^2-\frac {e^5}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^5}{x^2}-2 x\right ) \, dx\\ &=-\frac {e^5}{x}-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} -\frac {e^5}{x}-x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 14, normalized size = 0.93
method | result | size |
gosper | \(-\frac {{\mathrm e}^{5}+x^{3}}{x}\) | \(12\) |
default | \(-x^{2}-\frac {{\mathrm e}^{5}}{x}\) | \(14\) |
risch | \(-x^{2}-\frac {{\mathrm e}^{5}}{x}\) | \(14\) |
norman | \(\frac {-x^{3}-{\mathrm e}^{5}}{x}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.87 \begin {gather*} -x^{2} - \frac {e^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 11, normalized size = 0.73 \begin {gather*} -\frac {x^{3} + e^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.53 \begin {gather*} - x^{2} - \frac {e^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 13, normalized size = 0.87 \begin {gather*} -x^{2} - \frac {e^{5}}{x} \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 = 0.73 \begin {gather*} -\frac {x^3+{\mathrm {e}}^5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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