Optimal. Leaf size=18 \[ \frac {-2+e^{25}+e^x-x}{5 x} \]
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Rubi [A]
time = 0.04, antiderivative size = 25, normalized size of antiderivative = 1.39, number of steps
used = 4, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14, 2228}
\begin {gather*} \frac {e^x}{5 x}-\frac {2-e^{25}}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2228
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {2-e^{25}+e^x (-1+x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {2-e^{25}}{x^2}+\frac {e^x (-1+x)}{x^2}\right ) \, dx\\ &=-\frac {2-e^{25}}{5 x}+\frac {1}{5} \int \frac {e^x (-1+x)}{x^2} \, dx\\ &=\frac {e^x}{5 x}-\frac {2-e^{25}}{5 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 15, normalized size = 0.83 \begin {gather*} \frac {-2+e^{25}+e^x}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 21, normalized size = 1.17
method | result | size |
norman | \(\frac {\frac {{\mathrm e}^{x}}{5}+\frac {{\mathrm e}^{25}}{5}-\frac {2}{5}}{x}\) | \(15\) |
default | \(-\frac {2}{5 x}+\frac {{\mathrm e}^{25}}{5 x}+\frac {{\mathrm e}^{x}}{5 x}\) | \(21\) |
risch | \(-\frac {2}{5 x}+\frac {{\mathrm e}^{25}}{5 x}+\frac {{\mathrm e}^{x}}{5 x}\) | \(21\) |
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 = 0.33, size = 24, normalized size = 1.33 \begin {gather*} \frac {e^{25}}{5 \, x} - \frac {2}{5 \, x} + \frac {1}{5} \, {\rm Ei}\left (x\right ) - \frac {1}{5} \, \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 11, normalized size = 0.61 \begin {gather*} \frac {e^{25} + e^{x} - 2}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.83 \begin {gather*} \frac {e^{x}}{5 x} - \frac {\frac {2}{5} - \frac {e^{25}}{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 11, normalized size = 0.61 \begin {gather*} \frac {e^{25} + e^{x} - 2}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.22, size = 11, normalized size = 0.61 \begin {gather*} \frac {{\mathrm {e}}^{25}+{\mathrm {e}}^x-2}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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