Optimal. Leaf size=11 \[ 4+e^{2+x} x^2 \]
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Rubi [A]
time = 0.04, antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps
used = 8, number of rules used = 4, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.308, Rules used = {1607, 2227,
2207, 2225} \begin {gather*} e^{x+2} x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2+x} x (2+x) \, dx\\ &=\int \left (2 e^{2+x} x+e^{2+x} x^2\right ) \, dx\\ &=2 \int e^{2+x} x \, dx+\int e^{2+x} x^2 \, dx\\ &=2 e^{2+x} x+e^{2+x} x^2-2 \int e^{2+x} \, dx-2 \int e^{2+x} x \, dx\\ &=-2 e^{2+x}+e^{2+x} x^2+2 \int e^{2+x} \, dx\\ &=e^{2+x} x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 0.82 \begin {gather*} e^{2+x} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 9, normalized size = 0.82
method | result | size |
gosper | \(x^{2} {\mathrm e}^{2+x}\) | \(9\) |
default | \(x^{2} {\mathrm e}^{2} {\mathrm e}^{x}\) | \(9\) |
norman | \(x^{2} {\mathrm e}^{2} {\mathrm e}^{x}\) | \(9\) |
risch | \(x^{2} {\mathrm e}^{2+x}\) | \(9\) |
meijerg | \(-{\mathrm e}^{2} \left (2-\frac {\left (3 x^{2}-6 x +6\right ) {\mathrm e}^{x}}{3}\right )+2 \,{\mathrm e}^{2} \left (1-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}\right )\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (10) = 20\).
time = 0.28, size = 33, normalized size = 3.00 \begin {gather*} {\left (x^{2} e^{2} - 2 \, x e^{2} + 2 \, e^{2}\right )} e^{x} + 2 \, {\left (x e^{2} - e^{2}\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 8, normalized size = 0.73 \begin {gather*} x^{2} e^{\left (x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.73 \begin {gather*} x^{2} e^{2} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 8, normalized size = 0.73 \begin {gather*} x^{2} e^{\left (x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.65, size = 8, normalized size = 0.73 \begin {gather*} x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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