Optimal. Leaf size=22 \[ 14+x-e^{5+\frac {(-2+x) (1+x)^2}{x^2}} x \]
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Rubi [A] time = 0.10, antiderivative size = 44, normalized size of antiderivative = 2.00, number of steps used = 3, number of rules used = 2, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.047, Rules used = {14, 2288} \begin {gather*} x-\frac {e^{-\frac {2}{x^2}+x-\frac {3}{x}+5} \left (x^3+3 x+4\right )}{\left (\frac {4}{x^3}+\frac {3}{x^2}+1\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {e^{5-\frac {2}{x^2}-\frac {3}{x}+x} \left (4+3 x+x^2+x^3\right )}{x^2}\right ) \, dx\\ &=x-\int \frac {e^{5-\frac {2}{x^2}-\frac {3}{x}+x} \left (4+3 x+x^2+x^3\right )}{x^2} \, dx\\ &=x-\frac {e^{5-\frac {2}{x^2}-\frac {3}{x}+x} \left (4+3 x+x^3\right )}{\left (1+\frac {4}{x^3}+\frac {3}{x^2}\right ) x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 20, normalized size = 0.91 \begin {gather*} x-e^{5-\frac {2}{x^2}-\frac {3}{x}+x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 23, normalized size = 1.05 \begin {gather*} -x e^{\left (\frac {x^{3} + 5 \, x^{2} - 3 \, x - 2}{x^{2}}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 23, normalized size = 1.05 \begin {gather*} -x e^{\left (\frac {x^{3} + 5 \, x^{2} - 3 \, x - 2}{x^{2}}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 24, normalized size = 1.09
method | result | size |
risch | \(-{\mathrm e}^{\frac {x^{3}+5 x^{2}-3 x -2}{x^{2}}} x +x\) | \(24\) |
norman | \(\frac {x^{2}-{\mathrm e}^{\frac {x^{3}+5 x^{2}-3 x -2}{x^{2}}} x^{2}}{x}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 19, normalized size = 0.86 \begin {gather*} -x e^{\left (x - \frac {3}{x} - \frac {2}{x^{2}} + 5\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.35, size = 21, normalized size = 0.95 \begin {gather*} x-x\,{\mathrm {e}}^5\,{\mathrm {e}}^{-\frac {3}{x}}\,{\mathrm {e}}^{-\frac {2}{x^2}}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 20, normalized size = 0.91 \begin {gather*} - x e^{\frac {x^{3} + 5 x^{2} - 3 x - 2}{x^{2}}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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