Optimal. Leaf size=27 \[ \frac {2 \left (4+\left (e^{x \left (2+\frac {3}{x}+x\right )}+\frac {2}{x}\right ) x\right )}{x} \]
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Rubi [A] time = 0.03, antiderivative size = 18, normalized size of antiderivative = 0.67, number of steps used = 3, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14, 2236} \begin {gather*} 2 e^{x^2+2 x+3}+\frac {12}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2236
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {12}{x^2}+4 e^{3+2 x+x^2} (1+x)\right ) \, dx\\ &=\frac {12}{x}+4 \int e^{3+2 x+x^2} (1+x) \, dx\\ &=2 e^{3+2 x+x^2}+\frac {12}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 18, normalized size = 0.67 \begin {gather*} 2 e^{3+2 x+x^2}+\frac {12}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 18, normalized size = 0.67 \begin {gather*} \frac {2 \, {\left (x e^{\left (x^{2} + 2 \, x + 3\right )} + 6\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 18, normalized size = 0.67 \begin {gather*} \frac {2 \, {\left (x e^{\left (x^{2} + 2 \, x + 3\right )} + 6\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 18, normalized size = 0.67
method | result | size |
default | \(\frac {12}{x}+2 \,{\mathrm e}^{x^{2}+2 x +3}\) | \(18\) |
risch | \(\frac {12}{x}+2 \,{\mathrm e}^{x^{2}+2 x +3}\) | \(18\) |
norman | \(\frac {12+2 x \,{\mathrm e}^{x^{2}+2 x +3}}{x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.66, size = 60, normalized size = 2.22 \begin {gather*} -2 i \, \sqrt {\pi } \operatorname {erf}\left (i \, x + i\right ) e^{2} - 2 \, {\left (\frac {\sqrt {\pi } {\left (x + 1\right )} {\left (\operatorname {erf}\left (\sqrt {-{\left (x + 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (x + 1\right )}^{2}}} - e^{\left ({\left (x + 1\right )}^{2}\right )}\right )} e^{2} + \frac {12}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 18, normalized size = 0.67 \begin {gather*} \frac {12}{x}+2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^3 \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 = 0.52 \begin {gather*} 2 e^{x^{2} + 2 x + 3} + \frac {12}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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