Optimal. Leaf size=21 \[ \frac {1}{2} \left (e^{\frac {9 e^{x/2}}{x}}+\log (2)\right ) \]
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Rubi [F]
time = 0.53, 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 {e^{\frac {9 e^{x/2}}{x}+\frac {x}{2}} (-18+9 x)}{4 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {e^{\frac {9 e^{x/2}}{x}+\frac {x}{2}} (-18+9 x)}{x^2} \, dx\\ &=\frac {1}{4} \int \frac {e^{\frac {18 e^{x/2}+x^2}{2 x}} (-18+9 x)}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-\frac {18 e^{\frac {18 e^{x/2}+x^2}{2 x}}}{x^2}+\frac {9 e^{\frac {18 e^{x/2}+x^2}{2 x}}}{x}\right ) \, dx\\ &=\frac {9}{4} \int \frac {e^{\frac {18 e^{x/2}+x^2}{2 x}}}{x} \, dx-\frac {9}{2} \int \frac {e^{\frac {18 e^{x/2}+x^2}{2 x}}}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 18, normalized size = 0.86 \begin {gather*} \frac {1}{2} e^{\frac {9 e^{x/2}}{x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 13, normalized size = 0.62
method | result | size |
norman | \(\frac {{\mathrm e}^{\frac {9 \,{\mathrm e}^{\frac {x}{2}}}{x}}}{2}\) | \(13\) |
risch | \(\frac {{\mathrm e}^{\frac {9 \,{\mathrm e}^{\frac {x}{2}}}{x}}}{2}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 12, normalized size = 0.57 \begin {gather*} \frac {1}{2} \, e^{\left (\frac {9 \, e^{\left (\frac {1}{2} \, x\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 22, normalized size = 1.05 \begin {gather*} \frac {1}{2} \, e^{\left (-\frac {1}{2} \, x + \frac {x^{2} + 18 \, e^{\left (\frac {1}{2} \, x\right )}}{2 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 10, normalized size = 0.48 \begin {gather*} \frac {e^{\frac {9 e^{\frac {x}{2}}}{x}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 22, normalized size = 1.05 \begin {gather*} \frac {1}{2} \, e^{\left (-\frac {1}{2} \, x + \frac {x^{2} + 18 \, e^{\left (\frac {1}{2} \, x\right )}}{2 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.61, size = 12, normalized size = 0.57 \begin {gather*} \frac {{\mathrm {e}}^{\frac {9\,{\mathrm {e}}^{x/2}}{x}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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