Optimal. Leaf size=23 \[ e^2+\frac {4}{5} \left (2-e^5-\frac {2}{x}-x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps
used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14}
\begin {gather*} -\frac {4 x}{5}-\frac {8}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {8-4 x^2}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-4+\frac {8}{x^2}\right ) \, dx\\ &=-\frac {8}{5 x}-\frac {4 x}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 0.57 \begin {gather*} -\frac {8}{5 x}-\frac {4 x}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 10, normalized size = 0.43
method | result | size |
default | \(-\frac {4 x}{5}-\frac {8}{5 x}\) | \(10\) |
risch | \(-\frac {4 x}{5}-\frac {8}{5 x}\) | \(10\) |
gosper | \(-\frac {4 \left (x^{2}+2\right )}{5 x}\) | \(11\) |
norman | \(\frac {-\frac {8}{5}-\frac {4 x^{2}}{5}}{x}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 9, normalized size = 0.39 \begin {gather*} -\frac {4}{5} \, x - \frac {8}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 10, normalized size = 0.43 \begin {gather*} -\frac {4 \, {\left (x^{2} + 2\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.43 \begin {gather*} - \frac {4 x}{5} - \frac {8}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 9, normalized size = 0.39 \begin {gather*} -\frac {4}{5} \, x - \frac {8}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 10, normalized size = 0.43 \begin {gather*} -\frac {4\,\left (x^2+2\right )}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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