Optimal. Leaf size=21 \[ e^{e^{x^2}-\frac {e^{3+x} (-25+x)}{x}} \]
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Rubi [F] time = 3.18, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{\frac {e^{3+x} (25-x)+e^{x^2} x}{x}} \left (2 e^{x^2} x^3+e^{3+x} \left (-25+25 x-x^2\right )\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{e^{x^2}+\frac {e^{3+x} (25-x)}{x}} \left (2 e^{x^2} x^3+e^{3+x} \left (-25+25 x-x^2\right )\right )}{x^2} \, dx\\ &=\int \left (2 e^{e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x^2} x-\frac {e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x} \left (25-25 x+x^2\right )}{x^2}\right ) \, dx\\ &=2 \int e^{e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x^2} x \, dx-\int \frac {e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x} \left (25-25 x+x^2\right )}{x^2} \, dx\\ &=2 \int e^{e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x^2} x \, dx-\int \left (e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x}+\frac {25 e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x}}{x^2}-\frac {25 e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x}}{x}\right ) \, dx\\ &=2 \int e^{e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x^2} x \, dx-25 \int \frac {e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x}}{x^2} \, dx+25 \int \frac {e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x}}{x} \, dx-\int e^{3+e^{x^2}+\frac {e^{3+x} (25-x)}{x}+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.49, size = 21, normalized size = 1.00 \begin {gather*} e^{e^{x^2}-\frac {e^{3+x} (-25+x)}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 21, normalized size = 1.00 \begin {gather*} e^{\left (\frac {x e^{\left (x^{2}\right )} - {\left (x - 25\right )} e^{\left (x + 3\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 21, normalized size = 1.00 \begin {gather*} e^{\left (\frac {25 \, e^{\left (x + 3\right )}}{x} + e^{\left (x^{2}\right )} - e^{\left (x + 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 27, normalized size = 1.29
method | result | size |
risch | \({\mathrm e}^{-\frac {-{\mathrm e}^{x^{2}} x +{\mathrm e}^{3+x} x -25 \,{\mathrm e}^{3+x}}{x}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 21, normalized size = 1.00 \begin {gather*} e^{\left (\frac {25 \, e^{\left (x + 3\right )}}{x} + e^{\left (x^{2}\right )} - e^{\left (x + 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.42, size = 23, normalized size = 1.10 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^3\,{\mathrm {e}}^x}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 19, normalized size = 0.90 \begin {gather*} e^{\frac {x e^{x^{2}} + \left (25 - x\right ) e^{3} e^{x}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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