Optimal. Leaf size=23 \[ 2+e^{2 \left (4 e^{2 x}+\frac {1}{4 x}\right )^2} \]
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Rubi [A] time = 0.48, antiderivative size = 29, normalized size of antiderivative = 1.26, number of steps used = 2, number of rules used = 2, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {12, 6706} \begin {gather*} e^{\frac {256 e^{4 x} x^2+32 e^{2 x} x+1}{8 x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {e^{\frac {1+32 e^{2 x} x+256 e^{4 x} x^2}{8 x^2}} \left (-1+512 e^{4 x} x^3+e^{2 x} \left (-16 x+32 x^2\right )\right )}{x^3} \, dx\\ &=e^{\frac {1+32 e^{2 x} x+256 e^{4 x} x^2}{8 x^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.40, size = 21, normalized size = 0.91 \begin {gather*} e^{\frac {\left (1+16 e^{2 x} x\right )^2}{8 x^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 24, normalized size = 1.04 \begin {gather*} e^{\left (\frac {256 \, x^{2} e^{\left (4 \, x\right )} + 32 \, x e^{\left (2 \, x\right )} + 1}{8 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 22, normalized size = 0.96 \begin {gather*} e^{\left (\frac {4 \, e^{\left (2 \, x\right )}}{x} + \frac {1}{8 \, x^{2}} + 32 \, e^{\left (4 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 25, normalized size = 1.09
method | result | size |
risch | \({\mathrm e}^{\frac {256 x^{2} {\mathrm e}^{4 x}+32 x \,{\mathrm e}^{2 x}+1}{8 x^{2}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 22, normalized size = 0.96 \begin {gather*} e^{\left (\frac {4 \, e^{\left (2 \, x\right )}}{x} + \frac {1}{8 \, x^{2}} + 32 \, e^{\left (4 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.06, size = 24, normalized size = 1.04 \begin {gather*} {\mathrm {e}}^{32\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{\frac {1}{8\,x^2}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{2\,x}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 26, normalized size = 1.13 \begin {gather*} e^{\frac {2 \left (16 x^{2} e^{4 x} + 2 x e^{2 x} + \frac {1}{16}\right )}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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