Optimal. Leaf size=20 \[ 15+e^4 x \left (-e^{\frac {4}{x^2}}+2 x\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps used = 3, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14, 2288} \begin {gather*} 2 e^4 x^2-e^{\frac {4}{x^2}+4} x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4 e^4 x-\frac {e^{4+\frac {4}{x^2}} \left (-8+x^2\right )}{x^2}\right ) \, dx\\ &=2 e^4 x^2-\int \frac {e^{4+\frac {4}{x^2}} \left (-8+x^2\right )}{x^2} \, dx\\ &=-e^{4+\frac {4}{x^2}} x+2 e^4 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 1.00 \begin {gather*} e^4 \left (-e^{\frac {4}{x^2}} x+2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 22, normalized size = 1.10 \begin {gather*} 2 \, x^{2} e^{4} - x e^{\left (\frac {4 \, {\left (x^{2} + 1\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 22, normalized size = 1.10 \begin {gather*} 2 \, x^{2} e^{4} - x e^{\left (\frac {4 \, {\left (x^{2} + 1\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 20, normalized size = 1.00
method | result | size |
derivativedivides | \(2 x^{2} {\mathrm e}^{4}-x \,{\mathrm e}^{4} {\mathrm e}^{\frac {4}{x^{2}}}\) | \(20\) |
default | \(2 x^{2} {\mathrm e}^{4}-x \,{\mathrm e}^{4} {\mathrm e}^{\frac {4}{x^{2}}}\) | \(20\) |
risch | \(2 x^{2} {\mathrm e}^{4}-x \,{\mathrm e}^{\frac {4 x^{2}+4}{x^{2}}}\) | \(23\) |
norman | \(\frac {2 x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4} {\mathrm e}^{\frac {4}{x^{2}}}}{x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.40, size = 56, normalized size = 2.80 \begin {gather*} -x \sqrt {-\frac {1}{x^{2}}} e^{4} \Gamma \left (-\frac {1}{2}, -\frac {4}{x^{2}}\right ) + 2 \, x^{2} e^{4} - \frac {2 \, \sqrt {\pi } {\left (\operatorname {erf}\left (2 \, \sqrt {-\frac {1}{x^{2}}}\right ) - 1\right )} e^{4}}{x \sqrt {-\frac {1}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.50, size = 16, normalized size = 0.80 \begin {gather*} x\,{\mathrm {e}}^4\,\left (2\,x-{\mathrm {e}}^{\frac {4}{x^2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 19, normalized size = 0.95 \begin {gather*} 2 x^{2} e^{4} - x e^{4} e^{\frac {4}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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