Optimal. Leaf size=17 \[ \frac {3}{4} e^{x-\frac {65 e^x x}{4}} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(49\) vs. \(2(17)=34\).
time = 0.05, antiderivative size = 49, normalized size of antiderivative = 2.88, number of steps
used = 2, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 2326}
\begin {gather*} \frac {3 e^{\frac {1}{4} \left (4 x-65 e^x x\right )} \left (4 x-65 e^x \left (x^2+x\right )\right )}{4 \left (-65 e^x x-65 e^x+4\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int e^{\frac {1}{4} \left (4 x-65 e^x x\right )} \left (12+12 x+e^x \left (-195 x-195 x^2\right )\right ) \, dx\\ &=\frac {3 e^{\frac {1}{4} \left (4 x-65 e^x x\right )} \left (4 x-65 e^x \left (x+x^2\right )\right )}{4 \left (4-65 e^x-65 e^x x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 17, normalized size = 1.00 \begin {gather*} \frac {3}{4} e^{x-\frac {65 e^x x}{4}} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.44, size = 14, normalized size = 0.82
method | result | size |
risch | \(\frac {3 \,{\mathrm e}^{-\frac {x \left (65 \,{\mathrm e}^{x}-4\right )}{4}} x}{4}\) | \(14\) |
norman | \(\frac {3 \,{\mathrm e}^{-\frac {65 \,{\mathrm e}^{x} x}{4}+x} x}{4}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 11, normalized size = 0.65 \begin {gather*} \frac {3}{4} \, x e^{\left (-\frac {65}{4} \, x e^{x} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 11, normalized size = 0.65 \begin {gather*} \frac {3}{4} \, x e^{\left (-\frac {65}{4} \, x e^{x} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 15, normalized size = 0.88 \begin {gather*} \frac {3 x e^{- \frac {65 x e^{x}}{4} + x}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.14, size = 11, normalized size = 0.65 \begin {gather*} \frac {3\,x\,{\mathrm {e}}^{-\frac {65\,x\,{\mathrm {e}}^x}{4}}\,{\mathrm {e}}^x}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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