Optimal. Leaf size=17 \[ \left (e^{\frac {1}{x}}-\frac {1}{5 x}\right ) x^2 \]
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Rubi [A]
time = 0.03, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps
used = 9, number of rules used = 5, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.294, Rules used = {12, 2258, 2237,
2241, 2245} \begin {gather*} e^{\frac {1}{x}} x^2-\frac {x}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2237
Rule 2241
Rule 2245
Rule 2258
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (-1+e^{\frac {1}{x}} (-5+10 x)\right ) \, dx\\ &=-\frac {x}{5}+\frac {1}{5} \int e^{\frac {1}{x}} (-5+10 x) \, dx\\ &=-\frac {x}{5}+\frac {1}{5} \int \left (-5 e^{\frac {1}{x}}+10 e^{\frac {1}{x}} x\right ) \, dx\\ &=-\frac {x}{5}+2 \int e^{\frac {1}{x}} x \, dx-\int e^{\frac {1}{x}} \, dx\\ &=-\frac {x}{5}-e^{\frac {1}{x}} x+e^{\frac {1}{x}} x^2+\int e^{\frac {1}{x}} \, dx-\int \frac {e^{\frac {1}{x}}}{x} \, dx\\ &=-\frac {x}{5}+e^{\frac {1}{x}} x^2+\text {Ei}\left (\frac {1}{x}\right )+\int \frac {e^{\frac {1}{x}}}{x} \, dx\\ &=-\frac {x}{5}+e^{\frac {1}{x}} x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 0.88 \begin {gather*} -\frac {x}{5}+e^{\frac {1}{x}} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 13, normalized size = 0.76
method | result | size |
derivativedivides | \(-\frac {x}{5}+x^{2} {\mathrm e}^{\frac {1}{x}}\) | \(13\) |
default | \(-\frac {x}{5}+x^{2} {\mathrm e}^{\frac {1}{x}}\) | \(13\) |
norman | \(-\frac {x}{5}+x^{2} {\mathrm e}^{\frac {1}{x}}\) | \(13\) |
risch | \(-\frac {x}{5}+x^{2} {\mathrm e}^{\frac {1}{x}}\) | \(13\) |
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 = 0.29, size = 20, normalized size = 1.18 \begin {gather*} -\frac {1}{5} \, x + \Gamma \left (-1, -\frac {1}{x}\right ) + 2 \, \Gamma \left (-2, -\frac {1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.71 \begin {gather*} x^{2} e^{\frac {1}{x}} - \frac {1}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.59 \begin {gather*} x^{2} e^{\frac {1}{x}} - \frac {x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 12, normalized size = 0.71 \begin {gather*} x^{2} e^{\frac {1}{x}} - \frac {1}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 12, normalized size = 0.71 \begin {gather*} x^2\,{\mathrm {e}}^{1/x}-\frac {x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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