Optimal. Leaf size=17 \[ -3+e^2-\frac {-1+x^{-1+x}}{x} \]
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Rubi [F]
time = 0.06, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-1+x^{-1+x} (2-x-x \log (x))}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x^2}-x^{-3+x} (-2+x+x \log (x))\right ) \, dx\\ &=\frac {1}{x}-\int x^{-3+x} (-2+x+x \log (x)) \, dx\\ &=\frac {1}{x}-\int \left (-2 x^{-3+x}+x^{-2+x}+x^{-2+x} \log (x)\right ) \, dx\\ &=\frac {1}{x}+2 \int x^{-3+x} \, dx-\int x^{-2+x} \, dx-\int x^{-2+x} \log (x) \, dx\\ &=\frac {1}{x}+2 \int x^{-3+x} \, dx-\log (x) \int x^{-2+x} \, dx-\int x^{-2+x} \, dx+\int \frac {\int x^{-2+x} \, dx}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} -\frac {-x+x^x}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 17, normalized size = 1.00
method | result | size |
risch | \(-\frac {x^{x -1}}{x}+\frac {1}{x}\) | \(15\) |
norman | \(\frac {1-{\mathrm e}^{\left (x -1\right ) \ln \left (x \right )}}{x}\) | \(16\) |
default | \(-\frac {{\mathrm e}^{\left (x -1\right ) \ln \left (x \right )}}{x}+\frac {1}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 12, normalized size = 0.71 \begin {gather*} \frac {1}{x} - \frac {x^{x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 12, normalized size = 0.71 \begin {gather*} -\frac {x^{x - 1} - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 12, normalized size = 0.71 \begin {gather*} - \frac {e^{\left (x - 1\right ) \log {\left (x \right )}}}{x} + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 12, normalized size = 0.71 \begin {gather*} \frac {1}{x} - \frac {x^{x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.40, size = 11, normalized size = 0.65 \begin {gather*} \frac {x-x^x}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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