Optimal. Leaf size=17 \[ \frac {e^{1-x (10+x)} x}{2+x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(35\) vs. \(2(17)=34\).
time = 0.05, antiderivative size = 35, normalized size of antiderivative = 2.06, number of steps
used = 2, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {27, 2326}
\begin {gather*} \frac {e^{-x^2-10 x+1} \left (x^3+7 x^2+10 x\right )}{(x+2)^2 (x+5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{1-10 x-x^2} \left (2-20 x-14 x^2-2 x^3\right )}{(2+x)^2} \, dx\\ &=\frac {e^{1-10 x-x^2} \left (10 x+7 x^2+x^3\right )}{(2+x)^2 (5+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.75, size = 22, normalized size = 1.29 \begin {gather*} \frac {2 e^{1-10 x-x^2} x}{4+2 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.32, size = 19, normalized size = 1.12
method | result | size |
gosper | \(\frac {x \,{\mathrm e}^{-x^{2}-10 x +1}}{2+x}\) | \(19\) |
norman | \(\frac {x \,{\mathrm e}^{-x^{2}-10 x +1}}{2+x}\) | \(19\) |
risch | \(\frac {x \,{\mathrm e}^{-x^{2}-10 x +1}}{2+x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 18, normalized size = 1.06 \begin {gather*} \frac {x e^{\left (-x^{2} - 10 \, x + 1\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 18, normalized size = 1.06 \begin {gather*} \frac {x e^{\left (-x^{2} - 10 \, x + 1\right )}}{x + 2} \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 = 0.82 \begin {gather*} \frac {x e^{- x^{2} - 10 x + 1}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 18, normalized size = 1.06 \begin {gather*} \frac {x e^{\left (-x^{2} - 10 \, x + 1\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 19, normalized size = 1.12 \begin {gather*} \frac {x\,{\mathrm {e}}^{-10\,x}\,\mathrm {e}\,{\mathrm {e}}^{-x^2}}{x+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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