Optimal. Leaf size=19 \[ 4 x+\frac {9-e+e^x+3 x}{x} \]
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Rubi [A]
time = 0.03, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps
used = 5, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {14, 2228}
\begin {gather*} 4 x+\frac {e^x}{x}+\frac {9-e}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2228
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^x (-1+x)}{x^2}+\frac {-9+e+4 x^2}{x^2}\right ) \, dx\\ &=\int \frac {e^x (-1+x)}{x^2} \, dx+\int \frac {-9+e+4 x^2}{x^2} \, dx\\ &=\frac {e^x}{x}+\int \left (4+\frac {-9+e}{x^2}\right ) \, dx\\ &=\frac {9-e}{x}+\frac {e^x}{x}+4 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 17, normalized size = 0.89 \begin {gather*} \frac {9-e+e^x+4 x^2}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 23, normalized size = 1.21
method | result | size |
norman | \(\frac {4 x^{2}-{\mathrm e}+9+{\mathrm e}^{x}}{x}\) | \(18\) |
default | \(-\frac {{\mathrm e}}{x}+4 x +\frac {9}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(23\) |
risch | \(-\frac {{\mathrm e}}{x}+4 x +\frac {9}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(23\) |
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 = 25, normalized size = 1.32 \begin {gather*} 4 \, x - \frac {e}{x} + \frac {9}{x} + {\rm Ei}\left (x\right ) - \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 17, normalized size = 0.89 \begin {gather*} \frac {4 \, x^{2} - e + e^{x} + 9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} 4 x + \frac {e^{x}}{x} + \frac {9 - e}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 17, normalized size = 0.89 \begin {gather*} \frac {4 \, x^{2} - e + e^{x} + 9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.67, size = 16, normalized size = 0.84 \begin {gather*} 4\,x+\frac {{\mathrm {e}}^x-\mathrm {e}+9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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