Optimal. Leaf size=19 \[ e^{\frac {1}{3} (3-7 x)^2}+\frac {9}{x} \]
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Rubi [A] time = 0.03, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {12, 14, 2209} \begin {gather*} e^{\frac {1}{3} (3-7 x)^2}+\frac {9}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-27+e^{\frac {1}{3} \left (9-42 x+49 x^2\right )} \left (-42 x^2+98 x^3\right )}{x^2} \, dx\\ &=\frac {1}{3} \int \left (-\frac {27}{x^2}+14 e^{\frac {1}{3} (3-7 x)^2} (-3+7 x)\right ) \, dx\\ &=\frac {9}{x}+\frac {14}{3} \int e^{\frac {1}{3} (3-7 x)^2} (-3+7 x) \, dx\\ &=e^{\frac {1}{3} (3-7 x)^2}+\frac {9}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {1}{3} (3-7 x)^2}+\frac {9}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 19, normalized size = 1.00 \begin {gather*} \frac {x e^{\left (\frac {49}{3} \, x^{2} - 14 \, x + 3\right )} + 9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 19, normalized size = 1.00 \begin {gather*} \frac {x e^{\left (\frac {49}{3} \, x^{2} - 14 \, x + 3\right )} + 9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.89
method | result | size |
risch | \(\frac {9}{x}+{\mathrm e}^{\frac {\left (7 x -3\right )^{2}}{3}}\) | \(17\) |
default | \(\frac {9}{x}+{\mathrm e}^{\frac {49}{3} x^{2}-14 x +3}\) | \(18\) |
norman | \(\frac {9+x \,{\mathrm e}^{\frac {49}{3} x^{2}-14 x +3}}{x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.56, size = 92, normalized size = 4.84 \begin {gather*} i \, \sqrt {3} \sqrt {\pi } \operatorname {erf}\left (\frac {7}{3} i \, \sqrt {3} x - i \, \sqrt {3}\right ) + \frac {1}{3} \, \sqrt {3} {\left (\frac {3 \, \sqrt {3} \sqrt {\frac {1}{3}} \sqrt {\pi } {\left (7 \, x - 3\right )} {\left (\operatorname {erf}\left (\sqrt {\frac {1}{3}} \sqrt {-{\left (7 \, x - 3\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (7 \, x - 3\right )}^{2}}} + \sqrt {3} e^{\left (\frac {1}{3} \, {\left (7 \, x - 3\right )}^{2}\right )}\right )} + \frac {9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 17, normalized size = 0.89 \begin {gather*} {\mathrm {e}}^{\frac {49\,x^2}{3}-14\,x+3}+\frac {9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.79 \begin {gather*} e^{\frac {49 x^{2}}{3} - 14 x + 3} + \frac {9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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