Optimal. Leaf size=21 \[ \frac {-e^{27+x}+\frac {1}{x}-x}{9 x} \]
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Rubi [A] time = 0.04, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2197} \begin {gather*} \frac {1}{9 x^2}-\frac {e^{x+27}}{9 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {-2+e^{27+x} \left (x-x^2\right )}{x^3} \, dx\\ &=\frac {1}{9} \int \left (-\frac {2}{x^3}-\frac {e^{27+x} (-1+x)}{x^2}\right ) \, dx\\ &=\frac {1}{9 x^2}-\frac {1}{9} \int \frac {e^{27+x} (-1+x)}{x^2} \, dx\\ &=\frac {1}{9 x^2}-\frac {e^{27+x}}{9 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 0.86 \begin {gather*} \frac {1}{9} \left (\frac {1}{x^2}-\frac {e^{27+x}}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.07, size = 13, normalized size = 0.62 \begin {gather*} -\frac {x e^{\left (x + 27\right )} - 1}{9 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 13, normalized size = 0.62 \begin {gather*} -\frac {x e^{\left (x + 27\right )} - 1}{9 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.67
method | result | size |
norman | \(\frac {\frac {1}{9}-\frac {{\mathrm e}^{x +27} x}{9}}{x^{2}}\) | \(14\) |
derivativedivides | \(\frac {1}{9 x^{2}}-\frac {{\mathrm e}^{x +27}}{9 x}\) | \(16\) |
default | \(\frac {1}{9 x^{2}}-\frac {{\mathrm e}^{x +27}}{9 x}\) | \(16\) |
risch | \(\frac {1}{9 x^{2}}-\frac {{\mathrm e}^{x +27}}{9 x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 21, normalized size = 1.00 \begin {gather*} -\frac {1}{9} \, {\rm Ei}\relax (x) e^{27} + \frac {1}{9} \, e^{27} \Gamma \left (-1, -x\right ) + \frac {1}{9 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 13, normalized size = 0.62 \begin {gather*} -\frac {x\,{\mathrm {e}}^{x+27}-1}{9\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.67 \begin {gather*} - \frac {e^{x + 27}}{9 x} + \frac {1}{9 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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