Optimal. Leaf size=18 \[ -2+\frac {2}{x}+\frac {1}{2} \left (1+\frac {x}{e^{22}}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.78, number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 14} \begin {gather*} \frac {x}{2 e^{22}}+\frac {2}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-4 e^{22}+x^2}{x^2} \, dx}{2 e^{22}}\\ &=\frac {\int \left (1-\frac {4 e^{22}}{x^2}\right ) \, dx}{2 e^{22}}\\ &=\frac {2}{x}+\frac {x}{2 e^{22}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{x}+\frac {x}{2 e^{22}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 15, normalized size = 0.83 \begin {gather*} \frac {{\left (x^{2} + 4 \, e^{22}\right )} e^{\left (-22\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 13, normalized size = 0.72 \begin {gather*} \frac {1}{2} \, {\left (x + \frac {4 \, e^{22}}{x}\right )} e^{\left (-22\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 12, normalized size = 0.67
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{-22}}{2}+\frac {2}{x}\) | \(12\) |
default | \(\frac {{\mathrm e}^{-22} \left (x +\frac {4 \,{\mathrm e}^{22}}{x}\right )}{2}\) | \(16\) |
norman | \(\frac {2+\frac {{\mathrm e}^{-22} x^{2}}{2}}{x}\) | \(16\) |
gosper | \(\frac {\left (x^{2}+4 \,{\mathrm e}^{22}\right ) {\mathrm e}^{-22}}{2 x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 13, normalized size = 0.72 \begin {gather*} \frac {1}{2} \, {\left (x + \frac {4 \, e^{22}}{x}\right )} e^{\left (-22\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.40, size = 11, normalized size = 0.61 \begin {gather*} \frac {x\,{\mathrm {e}}^{-22}}{2}+\frac {2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 0.67 \begin {gather*} \frac {x + \frac {4 e^{22}}{x}}{2 e^{22}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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