Optimal. Leaf size=25 \[ -e^{-2-\frac {e^4}{x}+\frac {5 x}{4}}+\frac {x}{3} \]
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Rubi [A] time = 0.20, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12, 14, 6706} \begin {gather*} \frac {x}{3}-e^{\frac {5 x}{4}-\frac {e^4}{x}-2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{12} \int \frac {4 x^2+e^{\frac {-4 e^4-8 x+5 x^2}{4 x}} \left (-12 e^4-15 x^2\right )}{x^2} \, dx\\ &=\frac {1}{12} \int \left (4-\frac {3 e^{-2-\frac {e^4}{x}+\frac {5 x}{4}} \left (4 e^4+5 x^2\right )}{x^2}\right ) \, dx\\ &=\frac {x}{3}-\frac {1}{4} \int \frac {e^{-2-\frac {e^4}{x}+\frac {5 x}{4}} \left (4 e^4+5 x^2\right )}{x^2} \, dx\\ &=-e^{-2-\frac {e^4}{x}+\frac {5 x}{4}}+\frac {x}{3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 25, normalized size = 1.00 \begin {gather*} -e^{-2-\frac {e^4}{x}+\frac {5 x}{4}}+\frac {x}{3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 25, normalized size = 1.00 \begin {gather*} \frac {1}{3} \, x - e^{\left (\frac {5 \, x^{2} - 8 \, x - 4 \, e^{4}}{4 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 30, normalized size = 1.20 \begin {gather*} \frac {1}{3} \, {\left (x e^{4} - 3 \, e^{\left (\frac {5 \, x^{2} + 8 \, x - 4 \, e^{4}}{4 \, x}\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 26, normalized size = 1.04
method | result | size |
risch | \(\frac {x}{3}-{\mathrm e}^{-\frac {-5 x^{2}+4 \,{\mathrm e}^{4}+8 x}{4 x}}\) | \(26\) |
norman | \(\frac {\frac {x^{2}}{3}-x \,{\mathrm e}^{\frac {-4 \,{\mathrm e}^{4}+5 x^{2}-8 x}{4 x}}}{x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.26, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{3} \, x - e^{\left (\frac {5}{4} \, x - \frac {e^{4}}{x} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.95, size = 19, normalized size = 0.76 \begin {gather*} \frac {x}{3}-{\mathrm {e}}^{\frac {5\,x}{4}-\frac {{\mathrm {e}}^4}{x}-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 19, normalized size = 0.76 \begin {gather*} \frac {x}{3} - e^{\frac {\frac {5 x^{2}}{4} - 2 x - e^{4}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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