Optimal. Leaf size=25 \[ e^{e^4-x+3 \left (e^{3/4}+\frac {1}{16 x^2}\right ) x} \]
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Rubi [A] time = 0.34, antiderivative size = 32, normalized size of antiderivative = 1.28, number of steps used = 3, number of rules used = 3, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {6, 12, 6706} \begin {gather*} e^{\frac {48 e^{3/4} x^2-16 x^2+16 e^4 x+3}{16 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {3+16 e^4 x-16 x^2+48 e^{3/4} x^2}{16 x}} \left (-3+\left (-16+48 e^{3/4}\right ) x^2\right )}{16 x^2} \, dx\\ &=\frac {1}{16} \int \frac {e^{\frac {3+16 e^4 x-16 x^2+48 e^{3/4} x^2}{16 x}} \left (-3+\left (-16+48 e^{3/4}\right ) x^2\right )}{x^2} \, dx\\ &=e^{\frac {3+16 e^4 x-16 x^2+48 e^{3/4} x^2}{16 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 24, normalized size = 0.96 \begin {gather*} e^{e^4+\frac {3}{16 x}+\left (-1+3 e^{3/4}\right ) x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 25, normalized size = 1.00 \begin {gather*} e^{\left (\frac {48 \, x^{2} e^{\frac {3}{4}} - 16 \, x^{2} + 16 \, x e^{4} + 3}{16 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 17, normalized size = 0.68 \begin {gather*} e^{\left (3 \, x e^{\frac {3}{4}} - x + \frac {3}{16 \, x} + e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 26, normalized size = 1.04
method | result | size |
gosper | \({\mathrm e}^{\frac {16 x \,{\mathrm e}^{4}+48 x^{2} {\mathrm e}^{\frac {3}{4}}-16 x^{2}+3}{16 x}}\) | \(26\) |
norman | \({\mathrm e}^{\frac {16 x \,{\mathrm e}^{4}+48 x^{2} {\mathrm e}^{\frac {3}{4}}-16 x^{2}+3}{16 x}}\) | \(26\) |
risch | \({\mathrm e}^{\frac {16 x \,{\mathrm e}^{4}+48 x^{2} {\mathrm e}^{\frac {3}{4}}-16 x^{2}+3}{16 x}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.91, size = 37, normalized size = 1.48 \begin {gather*} \frac {{\left (3 \, e^{\left (e^{4} + \frac {3}{4}\right )} - e^{\left (e^{4}\right )}\right )} e^{\left (3 \, x e^{\frac {3}{4}} - x + \frac {3}{16 \, x}\right )}}{3 \, e^{\frac {3}{4}} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.03, size = 20, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^{\frac {3}{16\,x}}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^{3/4}}\,{\mathrm {e}}^{{\mathrm {e}}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 24, normalized size = 0.96 \begin {gather*} e^{\frac {- x^{2} + 3 x^{2} e^{\frac {3}{4}} + x e^{4} + \frac {3}{16}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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