Optimal. Leaf size=18 \[ -1+e^{\left (2 e^{39}+\frac {2}{x}+x\right )^2} \]
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Rubi [A]
time = 0.44, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps
used = 3, number of rules used = 3, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6820, 12, 6838}
\begin {gather*} e^{\frac {\left (x^2+2 e^{39} x+2\right )^2}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^{\frac {\left (2+2 e^{39} x+x^2\right )^2}{x^2}} \left (-4-4 e^{39} x+2 e^{39} x^3+x^4\right )}{x^3} \, dx\\ &=2 \int \frac {e^{\frac {\left (2+2 e^{39} x+x^2\right )^2}{x^2}} \left (-4-4 e^{39} x+2 e^{39} x^3+x^4\right )}{x^3} \, dx\\ &=e^{\frac {\left (2+2 e^{39} x+x^2\right )^2}{x^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 19, normalized size = 1.06 \begin {gather*} e^{\frac {\left (2+2 e^{39} x+x^2\right )^2}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(34\) vs.
\(2(16)=32\).
time = 0.13, size = 35, normalized size = 1.94
method | result | size |
risch | \({\mathrm e}^{\frac {4 \,{\mathrm e}^{39} x^{3}+x^{4}+4 x^{2} {\mathrm e}^{78}+8 \,{\mathrm e}^{39} x +4 x^{2}+4}{x^{2}}}\) | \(35\) |
gosper | \({\mathrm e}^{\frac {4 \,{\mathrm e}^{39} x^{3}+x^{4}+4 x^{2} {\mathrm e}^{78}+8 \,{\mathrm e}^{39} x +4 x^{2}+4}{x^{2}}}\) | \(37\) |
norman | \({\mathrm e}^{\frac {4 x^{2} {\mathrm e}^{78}+\left (4 x^{3}+8 x \right ) {\mathrm e}^{39}+x^{4}+4 x^{2}+4}{x^{2}}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.78, size = 27, normalized size = 1.50 \begin {gather*} e^{\left (x^{2} + 4 \, x e^{39} + \frac {8 \, e^{39}}{x} + \frac {4}{x^{2}} + 4 \, e^{78} + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (16) = 32\).
time = 0.35, size = 33, normalized size = 1.83 \begin {gather*} e^{\left (\frac {x^{4} + 4 \, x^{2} e^{78} + 4 \, x^{2} + 4 \, {\left (x^{3} + 2 \, x\right )} e^{39} + 4}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 34 vs.
\(2 (14) = 28\).
time = 0.09, size = 34, normalized size = 1.89 \begin {gather*} e^{\frac {x^{4} + 4 x^{2} + 4 x^{2} e^{78} + \left (4 x^{3} + 8 x\right ) e^{39} + 4}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 34 vs.
\(2 (16) = 32\).
time = 0.40, size = 34, normalized size = 1.89 \begin {gather*} e^{\left (\frac {x^{4} + 4 \, x^{3} e^{39} + 4 \, x^{2} e^{78} + 4 \, x^{2} + 8 \, x e^{39} + 4}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.79, size = 32, normalized size = 1.78 \begin {gather*} {\mathrm {e}}^{\frac {8\,{\mathrm {e}}^{39}}{x}}\,{\mathrm {e}}^{4\,{\mathrm {e}}^{78}}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^4\,{\mathrm {e}}^{\frac {4}{x^2}}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{39}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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